%!PS-Adobe-2.0 %%Creator: dvips(k) 5.991 Copyright 2011 Radical Eye Software %%Title: arXiv:1309.0316v1 [cs.MM] 2 Sep 2013 %%CreationDate: Fri Jan 4 19:49:08 2019 %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Times-Roman Times-Italic Times-BoldItalic Times-Bold %%+ Symbol NimbusSanL-Regu %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -R2 -P pk -z main.dvi -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2019.01.04:1949 %%BeginProcSet: texc.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /dir 0 def/dyy{/dir 0 def}B/dyt{/dir 1 def}B/dty{/dir 2 def}B/dtt{/dir 3 def}B/p{dir 2 eq{-90 rotate show 90 rotate}{dir 3 eq{-90 rotate show 90 rotate}{show}ifelse}ifelse}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)(LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse} forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{ BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat {BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B /M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M} B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{ 0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc 0 0 % File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 % % @@psencodingfile@{ % author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, % W. Schmidt, P. Lehman", % version = "2.0", % date = "27nov06", % filename = "8r.enc", % email = "tex-fonts@@tug.org", % docstring = "This is the encoding vector for Type1 and TrueType % fonts to be used with TeX. This file is part of the % PSNFSS bundle, version 9" % @} % % The idea is to have all the characters normally included in Type 1 fonts % available for typesetting. This is effectively the characters in Adobe % Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol, % MacRoman, and some extra characters from Lucida. % % Character code assignments were made as follows: % % (1) the Windows ANSI characters are almost all in their Windows ANSI % positions, because some Windows users cannot easily reencode the % fonts, and it makes no difference on other systems. 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b(to)g(distrib)n(ute)f(video)g(contents.)f(NC)j(is)g(ho)n (we)n(v)o(er)c(an)j(ener)o(gy-)1930 4027 y(demanding)22 b(application,)g(especially)i(when)f(the)i(coding)d(operations)1930 4127 y(are)31 b(performed)e(o)o(v)o(er)h(high)h(order)f(\002elds)i (such)f(as)h Ft(GF)12 b Fr(\(2)3706 4097 y Fs(8)3744 4127 y Fr(\))p Fv(,)32 b(hence)1930 4226 y(the)g(need)f(for)g(ener)o (gy-ef)n(\002cient)e(NC)j(schemes.)g(A)g(straightforw)o(ard)1930 4326 y(w)o(ay)19 b(to)f(reduce)g(the)h(NC)g(computational)d(comple)o (xity)h(independently)1930 4426 y(from)27 b(the)g(\002eld)h(size)g(is)h (to)e(reduce)g(the)g(size)i(of)e(the)g(generation,)f(i.e.)1930 4525 y(resorting)j(to)g(messages)h(composed)e(of)i(fe)n(wer)f(symbols.) g(Ho)n(we)n(v)o(er)m(,)1930 4625 y(as)19 b(to)g(smaller)g(messages)f (correspond)e(lo)n(wer)j(ef)n(\002cienc)o(y)e(of)h(the)h(code,)1930 4725 y(generation)30 b(of)i(higher)f(size)i(are)f(usually)g(desirable.) f(Moreo)o(v)o(er)m(,)f(in)1930 4824 y(multimedia)40 b(applications)f 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Fv(])f(and)1930 5322 y(Raptor)26 b([)2211 5323 y SDict begin H.S end 2211 5323 a Black -1 x Fv(7)p Black 2253 5267 a SDict begin H.R end 2253 5267 a 2253 5322 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.raptor) cvn H.B /ANN pdfmark end 2253 5322 a Fv(])g(codes)h(are)g(lo)n(w-comple)o(xity)c(erasure)j (correction)f(codes)1930 5422 y(de\002ned)k(o)o(v)o(er)g Ft(GF)12 b Fr(\(2\))p Fv(.)30 b(The)g(asymptotic)f(performance)e(of)j (rateless)1930 5522 y(codes)39 b(is)h(not)f(f)o(ar)g(from)g(that)g(of)g (coding)f(schemes)h(de\002ned)f(o)o(v)o(er)1930 5621 y(lar)o(ger)28 b(\002elds,)i(b)n(ut)f(their)g(decoding)f(comple)o(xity) f(is)k(much)d(lo)n(wer)h(as)p Black Black eop end end %%Page: 2 2 TeXDict begin HPSdict begin 2 1 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 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Fv(we)h(o)o(v)o(ervie)n(w)f(the)h(e)o (xisting)f(literature)h(on)g(the)g(topic)g(of)g(lo)n(w-)p Black Black 1930 -58 a(comple)o(xity)30 b(NC)i(with)g(a)g(special)f(e)o (ye)g(to)h(mobile)f(applications.)f(In)1930 42 y(Section)2201 42 y SDict begin H.S end 2201 42 a Black Fv(III)p Black 2284 -13 a SDict begin H.R end 2284 -13 a 2284 42 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.3) cvn H.B /ANN pdfmark end 2284 42 a 22 w Fv(we)21 b(o)o(v)o(ervie)n(w)e(NC)j(in)g(lo) n(w-order)d(Galois)i(Fields)h(and)e(we)1930 142 y(analytically)i (describe)h(ho)n(w)f(random)g(recombinations)f(at)i(the)h(nodes)1930 241 y(alter)k(the)g(pack)o(et)g(de)o(gree)e(distrib)n(ution)h(and)g (increase)h(the)g(decoding)1930 341 y(comple)o(xity)-5 b(.)24 b(In)i(Section)2718 342 y SDict begin H.S end 2718 342 a Black -1 x Fv(IV)p Black 2805 285 a SDict begin H.R end 2805 285 a 2805 341 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.4) cvn H.B /ANN pdfmark end 2805 341 a 28 w Fv(we)h(present)f(BC,)h(while)g(in)g(Section)3962 342 y SDict begin H.S end 3962 342 a Black -1 x Fv(V)p Black 4022 285 a SDict begin H.R end 4022 285 a 4022 341 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.5) cvn H.B /ANN pdfmark end 4022 341 a 1930 441 a Fv(we)g(describe)e(their)i (application)e(to)h(P2P)h(video)e(streaming.)h(Finally)-5 b(,)1930 540 y(Section)2200 541 y SDict begin H.S end 2200 541 a Black -1 x Fv(VI)p Black 2288 485 a SDict begin H.R end 2288 485 a 2288 540 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.6) cvn H.B /ANN pdfmark end 2288 540 a 21 w Fv(pro)o(vides)19 b(an)h(e)o(xperimental)e(e)n(v)n(aluation) h(of)h(BC)i(in)f(terms)1930 640 y(of)37 b(computational)e(comple)o (xity)-5 b(,)35 b(encoding)g(ef)n(\002cienc)o(y)h(and)h(video)1930 739 y(quality)-5 b(.)32 b(In)h(Section)2597 740 y SDict begin H.S end 2597 740 a Black -1 x Fv(VII)p Black 2712 684 a SDict begin H.R end 2712 684 a 2712 739 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.7) cvn H.B /ANN pdfmark end 2712 739 a 34 w Fv(we)h(dra)o(w)f(the)g(conclusions)g(and)g (outline)1930 839 y(possible)28 b(future)g(de)n(v)o(elopments)d(of)k (this)g(w)o(ork.)1930 999 y SDict begin H.S end 1930 999 a 1930 999 a SDict begin 12 H.A end 1930 999 a 1930 999 a SDict begin [/View [/XYZ H.V]/Dest (section.2) cvn /DEST pdfmark end 1930 999 a 2618 1084 a Fv(I)t(I)t(.)45 b(R)t Fw(E)t(L)t(A)m(T)t(E)t(D)24 b Fv(W)s Fw(O)t(R)t(K)2013 1234 y Fv(In)51 b(this)h(section,)g(we)f(o)o(v)o(ervie)n(w)f(the)i(e)o (xisting)e(literature)h(on)1930 1333 y(ener)o(gy-ef)n(\002cient)31 b(and)i(lo)n(w-comple)o(xity)f(NC)j(for)e(mobile)g(commu-)1930 1433 y(nications.)h(In)g(its)i(best)f(kno)n(wn)f(form,)f(NC)j(is)f (de\002ned)f(o)o(v)o(er)g(\002nite)1930 1533 y(\002elds)42 b(such)g(as)g Ft(GF)12 b Fr(\(2)2662 1502 y Fs(8)2700 1533 y Fr(\))p Fv(,)42 b(as)h(the)e(size)i(of)e(the)h(\002eld)g (guarantees)1930 1632 y(that)f(the)f(pack)o(ets)g(recei)n(v)o(ed)f(by)h (the)h(nodes)e(are)i(inno)o(v)n(ati)n(v)o(e)d(with)1930 1732 y(high)28 b(probability)-5 b(.)26 b(Due)i(to)h(the)g (computational)d(b)n(urden)h(of)i(directly)1930 1831 y(computing)22 b(multiplications)h(on)h Ft(GF)12 b Fr(\(2)3145 1801 y Fp(q)3182 1831 y Fr(\))p Fv(,)25 b(a)g(common)e(approach)f(is) 1930 1931 y(to)37 b(replace)f(multiplications)f(with)i(additions)f(by)g (means)h(of)f(Look)1930 2031 y(Up)c(T)-7 b(ables)32 b(tables)g (\(LUTs\).)f(In)g([)2968 2032 y SDict begin H.S end 2968 2032 a Black -1 x Fv(10)p Black 3051 1974 a SDict begin H.R end 3051 1974 a 3051 2031 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.toldo2010) cvn H.B /ANN pdfmark end 3051 2031 a Fv(],)g(for)g(e)o(xample,)f(LUTs)i(of)g(the)1930 2130 y(size)44 b(of)g(256)f(bytes)g(were)h(used)f(to)h(solv)o(e)g (multiplications)e(o)o(v)o(er)1930 2230 y Ft(GF)12 b Fr(\(2)2134 2200 y Fs(8)2171 2230 y Fr(\))p Fv(.)46 b(Ho)n(we)n(v)o(er) m(,)d(the)j(latenc)o(y)e(penalty)g(in)i(accessing)f(LUTs)1930 2330 y(stored)30 b(in)h(main)f(memory)f(may)h(throttle)g(the)h(decoder) e(throughput,)1930 2429 y(especially)h(on)g(mobile)f(de)n(vices)h (where)g(the)g(constraints)g(on)g(po)n(wer)1930 2529 y(consumption)f(impose)h(to)i(design)e(processors)g(with)i(small)f (caches.)1930 2628 y(V)-5 b(ingelmann)48 b Fu(et)j(al.)g Fv([)2662 2628 y SDict begin H.S end 2662 2628 a Black Fv(11)p Black 2744 2572 a SDict begin H.R end 2744 2572 a 2744 2628 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.vingelmann2010) cvn H.B /ANN pdfmark end 2744 2628 a Fv(])g(measured)e(the)h (decoder)f(throughput)1930 2728 y(achie)n(v)n(able)36 b(on)h(an)g(iPhone)g(for)g(NC)h(o)o(v)o(er)e Ft(GF)12 b Fr(\(2)3500 2698 y Fs(8)3537 2728 y Fr(\))38 b Fv(and)f Ft(GF)12 b Fr(\(2\))p Fv(.)1930 2828 y(Their)37 b(e)o(xperiments)f(sho) n(wed)h(that)h(the)g(best)h(decoder)d(throughput)1930 2927 y(that)29 b(could)g(be)g(achie)n(v)o(ed)e(o)o(v)o(er)h Ft(GF)12 b Fr(\(2)3107 2897 y Fs(8)3144 2927 y Fr(\))30 b Fv(w)o(as)g(se)n(v)o(eral)f(times)g(lo)n(wer)1930 3027 y(than)34 b(o)o(v)o(er)f Ft(GF)12 b Fr(\(2\))p Fv(.)36 b(Shojania)d Fu(et)i(al.)g Fv([)3150 3027 y SDict begin H.S end 3150 3027 a Black Fv(12)p Black 3233 2970 a SDict begin H.R end 3233 2970 a 3233 3027 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.shojania2009random) cvn H.B /ANN pdfmark end 3233 3027 a Fv(])f(considered)f(NC-based)1930 3127 y(video)38 b(streaming)h(with)g(iPhone)f(de)n(vices)h(and)g(their)g(e)o (xperiments)1930 3226 y(sho)n(wed)d(that)g(the)h(coding)d(operations)h (accounted)g(for)h(more)f(than)1930 3326 y(50\045)26 b(of)g(the)g(processor)f(c)o(ycles.)h(Heide)g(at)g(al.)h([)3379 3327 y SDict begin H.S end 3379 3327 a Black -1 x Fv(13)p Black 3462 3269 a SDict begin H.R end 3462 3269 a 3462 3326 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.heide2008cautious) cvn H.B /ANN pdfmark end 3462 3326 a Fv(])f(also)g(performed)1930 3425 y(video)20 b(streaming)f(e)o(xperiments)g(with)h(high-end)e (mobile)i(phones)f(and)1930 3525 y(went)i(further)e(measuring)g(the)i (impact)f(of)g(NC)i(on)e(the)h(lifetime)f(of)h(the)1930 3625 y(de)n(vice.)j(Their)h(e)o(xperiments)e(demonstrated)h(not)h(only) f(that)h(in)h(some)1930 3724 y(con\002gurations)37 b(the)i(processor)f (could)g(not)h(process)g(the)g(recei)n(v)o(ed)1930 3824 y(pack)o(ets)32 b(f)o(ast)h(enough)d(resulting)h(in)i(a)g(bottleneck)d (with)j(respect)f(to)1930 3924 y(the)21 b(bandwidth)f(a)n(v)n(ailable)g (on)h(the)h(channel,)d(b)n(ut)j(also)f(found)f(out)h(that)1930 4023 y(pack)o(et)35 b(decoding)e(reduced)g(the)i(operational)e(life)j (of)e(the)i(de)n(vices.)1930 4123 y(Angelopoulos)30 b Fu(et)k(al.)f Fv([)2670 4123 y SDict begin H.S end 2670 4123 a Black Fv(14)p Black 2752 4066 a SDict begin H.R end 2752 4066 a 2752 4123 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.Angelopoulos:2011:EHI:2039912.2039928) cvn H.B /ANN pdfmark end 2752 4123 a Fv(])h(sho)n(wed)e(that)h(ener)o(gy)e(ef)n(\002cient)h(NC)i(is)1930 4222 y(feasible)26 b(also)g(on)f(mobile)g(de)n(vices,)g(b)n(ut)h(only)f (at)i(the)e(price)h(of)f(using)1930 4322 y(ad-hoc)h(designed)h(hardw)o (are.)g(Concluding,)e(the)j(e)o(xisting)f(literature)1930 4422 y(sho)n(ws)21 b(that)h(NC)g(o)o(v)o(er)e Ft(GF)12 b Fr(\(2)2812 4392 y Fs(8)2849 4422 y Fr(\))23 b Fv(results)e(in)h(lo)n (w)f(decoder)f(throughput)1930 4521 y(and)34 b(high)g(computational)e (loads)j(on)f(mobile)g(de)n(vices,)g(prompting)1930 4621 y(the)29 b(research)e(for)h(computationally)e(lighter)i(solutions.)2013 4725 y(A)44 b(\002rst)h(step)f(to)n(w)o(ards)f(lo)n(w)h(comple)o(xity)d (NC)k(is)f(to)g(resort)g(to)1930 4824 y(simpler)28 b(coding)f (operations)f(o)o(v)o(er)h Ft(GF)12 b Fr(\(2\))p Fv(,)29 b(also)f(kno)n(wn)f(as)i(binary)1930 4924 y(NC.)f(The)f(main)g(adv)n (antage)f(of)h(binary)f(NC)i(is)g(that)g(multiplications)1930 5023 y(and)h(additions)g(are)h(resolv)o(ed)f(with)h(simple)g(XORs,)g (where)g(a)g(XOR)1930 5123 y(is)f(e)o(x)o(ecuted)e(in)h(one)g (processor)f(clock)h(c)o(ycle)g(a)n(v)n(oiding)f(the)i(latenc)o(y)1930 5223 y(penalties)g(associated)g(with)h(the)f(use)h(of)f(lookup)f (tables.)h(Moreo)o(v)o(er)m(,)1930 5322 y(the)22 b(source)f(can)h(e)o (xploit)f(rateless)i(codes)f(to)g(create)g(encoded)e(pack)o(ets)1930 5422 y(to)35 b(ensure)f(lo)n(w)g(encoding)f(and)h(decoding)f(comple)o (xity)-5 b(.)32 b(Lucani)h(et)1930 5522 y(al.)j([)2075 5523 y SDict begin H.S end 2075 5523 a Black -1 x Fv(15)p Black 2158 5465 a SDict begin H.R end 2158 5465 a 2158 5522 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.lucani2009random) cvn H.B /ANN pdfmark end 2158 5522 a Fv(],)f([)2270 5523 y SDict begin H.S end 2270 5523 a Black -1 x Fv(16)p Black 2353 5465 a SDict begin H.R end 2353 5465 a 2353 5522 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.lucani2010systematic) cvn H.B /ANN pdfmark end 2353 5522 a Fv(])h(in)m(v)o(estigated)d(NC)j (o)o(v)o(er)f Ft(GF)12 b Fr(\(2\))36 b Fv(and)f(sho)n(wed)g(that)1930 5621 y(the)d(performance)c(is)33 b(not)e(f)o(ar)h(from)f(that)g(of)h (NC)g(schemes)g(de\002ned)p Black Black eop end end %%Page: 3 3 TeXDict begin HPSdict begin 3 2 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -270 -415 a SDict begin H.S end -270 -415 a -270 -415 a SDict begin H.R end -270 -415 a -270 -415 a SDict begin [/View [/XYZ H.V]/Dest (page.3) cvn /DEST pdfmark end -270 -415 a Black 3993 -307 a FC(3)p Black -262 -58 a Fv(o)o(v)o(er)41 b(lar)o(ger)h(\002elds)h(such)f(as)h Ft(GF)12 b Fr(\(2)896 -88 y Fs(8)934 -58 y Fr(\))p Fv(,)43 b(albeit)f(using)h(fe)n(wer)f(and)-262 42 y(simpler)26 b(XOR)h(operations.)d(Katti)j Fu(et)f(al.)g Fv([)1028 43 y SDict begin H.S end 1028 43 a Black -1 x Fv(17)p Black 1111 -15 a SDict begin H.R end 1111 -15 a 1111 42 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.katti2008xors) cvn H.B /ANN pdfmark end 1111 42 a Fv(])g(proposed)e(the)i(use)g(of)-262 142 y(binary)32 b(NC)j(for)e(pack)o(et)f(routing)g(in)i(wireless)g (netw)o(orks,)e(sho)n(wing)-262 241 y(the)22 b(sustained)g(throughput)c (together)j(with)h(lo)n(w)g(computational)d(load)-262 341 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a Black -1 x Fv(18)p Black 949 1181 a SDict begin H.R end 949 1181 a 949 1238 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.puducheri) cvn H.B /ANN pdfmark end 949 1238 a Fv(])g(considered)e(NC)j(with)f(L)-8 b(T)-262 1337 y(codes)37 b(and)g(proposed)e(a)j(scheme)f(such)g(that)g(the)h (recombinations)-262 1437 y(at)f(the)g(nodes)e(do)h(not)h(alter)f(the)h (original)e(de)o(gree)g(distrib)n(ution)g(of)-262 1536 y(L)-8 b(T)33 b(codes.)e(Ho)n(we)n(v)o(er)m(,)f(this)i(approach)e (applies)i(only)f(to)h(a)g(netw)o(ork)-262 1636 y(topology)41 b(where)h(one)g(node)g(recombines)e(the)j(pack)o(ets)g(recei)n(v)o(ed) -262 1736 y(from)21 b(tw)o(o)h(sources)f(and)h(relays)f(to)h(a)h (single)e(sink,)h(and)f(hence)g(cannot)-262 1835 y(be)47 b(e)o(xtended)f(to)h(arbitrary)f(netw)o(ork)g(topologies.)g(Thomos)g (and)-262 1935 y(Frossard)34 b([)87 1937 y SDict begin H.S end 87 1937 a Black -2 x Fv(19)p Black 169 1878 a SDict begin H.R end 169 1878 a 169 1935 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.thomos2011degree) cvn H.B /ANN pdfmark end 169 1935 a Fv(])h(e)o(xplored)c(NC)k(with)f(Raptor)g(codes)g(and)f (proposed)-262 2035 y(an)g(optimization)d(frame)n(w)o(ork)g(to)j (control)e(the)h(de)o(gree)f(distrib)n(ution)-262 2134 y(at)26 b(the)g(source)f(as)i(a)f(function)e(of)h(the)h(netw)o(ork)e (topology)-5 b(.)23 b(Ho)n(we)n(v)o(er)m(,)-262 2234 y(the)28 b(requirement)e(that)j(the)f(topology)e(of)i(the)g(netw)o(ork) f(is)i(kno)n(wn)d(at)-262 2333 y(the)k(source)g(mak)o(es)f(this)i (scheme)f(impractical)f(where)g(the)h(netw)o(ork)-262 2433 y(topology)40 b(may)i(be)g(unkno)n(wn)e(at)i(the)g(source,)f(as)i (in)g(mesh)f(P2P)-262 2533 y(communications,)19 b(or)i(changes)g(o)o(v) o(er)f(time,)h(as)h(when)f(roaming)f(users)-262 2632 y(are)29 b(in)m(v)n(olv)o(ed.)-179 2732 y(In)49 b(this)h(w)o(ork,)e(we) h(achie)n(v)o(e)f(controlled-comple)o(xity)c(NC)50 b(by)-262 2832 y(e)o(xploiting)25 b(the)h(concept)f(of)h(\223encoding)e(windo)n (w\224)h(to)h(constrain)f(the)-262 2931 y(encoding)31 b(and)h(recombination)e(process)i(to)g(a)h(subset)g(of)f(the)h(mes-) -262 3031 y(sage)g(symbols.)e(While)i(a)g(thorough)d(description)h(of)h (the)g(encoding)-262 3130 y(windo)n(w)k(concept)g(is)h(pro)o(vided)d (in)j(Section)1149 3131 y SDict begin H.S end 1149 3131 a Black -1 x Fv(IV)p Black 1236 3075 a SDict begin H.R end 1236 3075 a 1236 3130 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.4) cvn H.B /ANN pdfmark end 1236 3130 a Fv(,)g(here)g(we)g(re)n(vie)n(w)-262 3230 y(e)o(xisting)25 b(w)o(orks)f(based)h(on)g(this)g(concept.)f(In)h([)1150 3231 y SDict begin H.S end 1150 3231 a Black -1 x Fv(20)p Black 1232 3173 a SDict begin H.R end 1232 3173 a 1232 3230 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.windowed2006) cvn H.B /ANN pdfmark end 1232 3230 a Fv(])h(a)f(windo)n(w-based)-262 3330 y(rateless)f(coding)d(mechanism)h(is)i(proposed)c(to)j(reduce)f (the)h(decoding)-262 3429 y(comple)o(xity)40 b(in)h(a)h(source-recei)n (v)o(er)c(scenario.)i(Ho)n(we)n(v)o(er)m(,)g(in)h([)1720 3430 y SDict begin H.S end 1720 3430 a Black -1 x Fv(20)p Black 1803 3373 a SDict begin H.R end 1803 3373 a 1803 3429 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.windowed2006) cvn H.B /ANN pdfmark end 1803 3429 a Fv(])-262 3529 y(there)35 b(are)h(no)f(intermediate)g(nodes)g(that)g(recombine)f(pack) o(ets)i(and)-262 3629 y(therefore)k(the)h(problem)e(of)i(preserving)e (the)i(de)o(gree)f(distrib)n(ution)-262 3728 y(\(one)26 b(of)h(the)g(major)f(contrib)n(ution)f(of)h(our)g(paper\))g(is)i(not)e (addressed.)-262 3828 y(Therefore,)35 b(as)k(we)f(detail)f(in)h (Section)979 3829 y SDict begin H.S end 979 3829 a Black -1 x Fv(IV)p Black 1067 3772 a SDict begin H.R end 1067 3772 a 1067 3828 a SDict 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def /DiaF {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill} def /Pent {stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt} def /PentF {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore} def /Circle {stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt} def /CircleF {stroke [] 0 setdash hpt 0 360 arc fill} def /C0 {BL [] 0 setdash 2 copy moveto vpt 90 450 arc} bind def /C1 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath} bind def /C2 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C3 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath} bind def /C4 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath} bind def /C5 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc} bind def /C6 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath} bind def /C7 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath} bind def /C8 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C9 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath} bind def /C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C11 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C12 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C13 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C14 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc} bind def /C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath} bind def /Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath} bind def /Square {dup Rec} bind def /Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def /S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def /S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def /S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def /S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare} bind def /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare} bind def /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & De\ velopment) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec 69d900414434c93d12731064fd536c430f0d1610cd3375452676cd606a5bb242 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284 -309 l 284 -314 284 -321 285 -328 ct 285 -335 285 -342 286 -348 ct 286 -354 286 -360 287 -364 ct 287 -369 288 -372 288 -372 ct 347 -372 l 347 -370 347 -367 346 -362 ct 346 -357 346 -351 346 -344 ct 346 -337 345 -330 345 -321 ct 345 -313 345 -304 345 -295 ct 345 -10 l 345 42 332 81 307 108 ct 281 134 242 147 189 147 ct p 283 -186 m 283 -212 281 -234 275 -253 ct 269 -271 262 -286 253 -298 ct 243 -310 233 -318 221 -324 ct 209 -329 197 -332 185 -332 ct 169 -332 155 -329 144 -324 ct 133 -318 123 -310 116 -298 ct 108 -286 103 -271 99 -252 ct 96 -234 94 -212 94 -186 ct 94 -159 96 -137 99 -118 ct 103 -100 108 -85 115 -74 ct 123 -63 132 -55 143 -50 ct 155 -45 168 -43 184 -43 ct 196 -43 208 -46 220 -51 ct 232 -56 243 -64 252 -76 ct 261 -87 269 -102 275 -120 ct 280 -138 283 -160 283 -186 ct p ef pom pum 9084 3361 t 176 -64 m 176 -1 l 142 -1 l 142 -64 l 9 -64 l 9 -92 l 138 -282 l 176 -282 l 176 -92 l 215 -92 l 215 -64 l 176 -64 l p 142 -241 m 142 -240 141 -239 140 -237 ct 139 -235 138 -233 136 -231 ct 135 -228 134 -226 132 -223 ct 131 -221 130 -219 129 -217 ct 57 -111 l 56 -110 55 -109 54 -107 ct 52 -105 51 -103 50 -102 ct 48 -100 47 -98 46 -96 ct 44 -95 43 -93 43 -92 ct 142 -92 l 142 -241 l p ef pom pum 10690 3064 t 189 147 m 168 147 149 145 132 140 ct 115 136 101 130 90 122 ct 78 113 68 104 61 92 ct 54 81 48 69 45 55 ct 108 46 l 112 63 121 76 135 86 ct 149 95 168 100 191 100 ct 205 100 217 98 229 94 ct 240 90 250 84 258 75 ct 266 66 272 55 277 41 ct 281 28 283 11 283 -9 ct 283 -69 l 283 -69 l 278 -60 272 -51 266 -42 ct 259 -33 251 -26 241 -19 ct 231 -12 220 -7 207 -3 ct 194 1 179 3 163 3 ct 139 3 119 -1 102 -9 ct 85 -17 71 -29 61 -45 ct 50 -60 42 -80 37 -104 ct 32 -127 30 -154 30 -185 ct 30 -215 32 -242 37 -266 ct 42 -290 50 -310 61 -327 ct 72 -343 87 -356 105 -365 ct 122 -374 144 -378 170 -378 ct 196 -378 219 -372 238 -360 ct 258 -348 273 -331 283 -309 ct 284 -309 l 284 -314 284 -321 285 -328 ct 285 -335 285 -342 286 -348 ct 286 -354 286 -360 287 -364 ct 287 -369 288 -372 288 -372 ct 347 -372 l 347 -370 347 -367 346 -362 ct 346 -357 346 -351 346 -344 ct 346 -337 345 -330 345 -321 ct 345 -313 345 -304 345 -295 ct 345 -10 l 345 42 332 81 307 108 ct 281 134 242 147 189 147 ct p 283 -186 m 283 -212 281 -234 275 -253 ct 269 -271 262 -286 253 -298 ct 243 -310 233 -318 221 -324 ct 209 -329 197 -332 185 -332 ct 169 -332 155 -329 144 -324 ct 133 -318 123 -310 116 -298 ct 108 -286 103 -271 99 -252 ct 96 -234 94 -212 94 -186 ct 94 -159 96 -137 99 -118 ct 103 -100 108 -85 115 -74 ct 123 -63 132 -55 143 -50 ct 155 -45 168 -43 184 -43 ct 196 -43 208 -46 220 -51 ct 232 -56 243 -64 252 -76 ct 261 -87 269 -102 275 -120 ct 280 -138 283 -160 283 -186 ct p ef pom pum 11084 3361 t 210 -92 m 210 -77 208 -65 204 -53 ct 200 -41 193 -31 185 -23 ct 177 -14 166 -8 154 -3 ct 141 2 127 4 110 4 ct 96 4 83 2 72 -1 ct 61 -5 52 -9 44 -15 ct 36 -22 30 -29 26 -37 ct 21 -45 18 -54 16 -63 ct 53 -67 l 54 -62 56 -57 59 -52 ct 62 -47 65 -42 70 -38 ct 74 -34 80 -31 87 -29 ct 94 -27 102 -25 111 -25 ct 121 -25 129 -27 137 -30 ct 144 -33 151 -37 156 -42 ct 161 -48 166 -55 169 -63 ct 171 -71 173 -80 173 -91 ct 173 -99 172 -107 169 -115 ct 166 -122 162 -128 157 -133 ct 152 -139 145 -143 138 -146 ct 130 -149 122 -150 112 -150 ct 106 -150 101 -149 95 -148 ct 90 -147 86 -146 81 -144 ct 77 -142 73 -140 70 -138 ct 66 -135 63 -133 60 -130 ct 25 -130 l 34 -282 l 194 -282 l 194 -251 l 67 -251 l 61 -161 l 68 -166 76 -171 85 -174 ct 95 -178 106 -179 119 -179 ct 133 -179 146 -177 157 -173 ct 168 -169 178 -163 186 -155 ct 194 -147 200 -138 204 -127 ct 208 -116 210 -104 210 -92 ct p ef pom pum 12690 3064 t 189 147 m 168 147 149 145 132 140 ct 115 136 101 130 90 122 ct 78 113 68 104 61 92 ct 54 81 48 69 45 55 ct 108 46 l 112 63 121 76 135 86 ct 149 95 168 100 191 100 ct 205 100 217 98 229 94 ct 240 90 250 84 258 75 ct 266 66 272 55 277 41 ct 281 28 283 11 283 -9 ct 283 -69 l 283 -69 l 278 -60 272 -51 266 -42 ct 259 -33 251 -26 241 -19 ct 231 -12 220 -7 207 -3 ct 194 1 179 3 163 3 ct 139 3 119 -1 102 -9 ct 85 -17 71 -29 61 -45 ct 50 -60 42 -80 37 -104 ct 32 -127 30 -154 30 -185 ct 30 -215 32 -242 37 -266 ct 42 -290 50 -310 61 -327 ct 72 -343 87 -356 105 -365 ct 122 -374 144 -378 170 -378 ct 196 -378 219 -372 238 -360 ct 258 -348 273 -331 283 -309 ct 284 -309 l 284 -314 284 -321 285 -328 ct 285 -335 285 -342 286 -348 ct 286 -354 286 -360 287 -364 ct 287 -369 288 -372 288 -372 ct 347 -372 l 347 -370 347 -367 346 -362 ct 346 -357 346 -351 346 -344 ct 346 -337 345 -330 345 -321 ct 345 -313 345 -304 345 -295 ct 345 -10 l 345 42 332 81 307 108 ct 281 134 242 147 189 147 ct p 283 -186 m 283 -212 281 -234 275 -253 ct 269 -271 262 -286 253 -298 ct 243 -310 233 -318 221 -324 ct 209 -329 197 -332 185 -332 ct 169 -332 155 -329 144 -324 ct 133 -318 123 -310 116 -298 ct 108 -286 103 -271 99 -252 ct 96 -234 94 -212 94 -186 ct 94 -159 96 -137 99 -118 ct 103 -100 108 -85 115 -74 ct 123 -63 132 -55 143 -50 ct 155 -45 168 -43 184 -43 ct 196 -43 208 -46 220 -51 ct 232 -56 243 -64 252 -76 ct 261 -87 269 -102 275 -120 ct 280 -138 283 -160 283 -186 ct p ef pom pum 13084 3361 t 210 -92 m 210 -78 208 -65 204 -53 ct 200 -41 194 -31 186 -23 ct 179 -14 169 -8 158 -3 ct 146 2 133 4 119 4 ct 102 4 88 1 76 -5 ct 63 -12 53 -21 45 -32 ct 37 -44 31 -59 27 -76 ct 23 -93 21 -112 21 -134 ct 21 -159 23 -181 28 -200 ct 32 -219 39 -234 48 -247 ct 56 -260 67 -269 79 -276 ct 92 -282 106 -285 121 -285 ct 131 -285 140 -284 148 -282 ct 157 -280 164 -277 171 -273 ct 178 -268 184 -262 189 -255 ct 195 -248 199 -239 202 -228 ct 167 -222 l 164 -234 158 -243 149 -248 ct 141 -253 132 -256 121 -256 ct 111 -256 102 -254 94 -249 ct 86 -244 79 -237 74 -228 ct 68 -219 64 -208 61 -194 ct 58 -180 57 -163 57 -145 ct 63 -157 72 -166 84 -173 ct 96 -179 110 -182 125 -182 ct 138 -182 149 -180 160 -176 ct 170 -172 179 -166 186 -158 ct 194 -150 199 -141 203 -130 ct 207 -118 210 -106 210 -92 ct p 173 -91 m 173 -100 172 -109 169 -117 ct 167 -125 163 -131 159 -137 ct 154 -142 148 -147 141 -150 ct 134 -153 126 -154 116 -154 ct 110 -154 103 -153 96 -151 ct 90 -149 84 -146 78 -142 ct 73 -138 69 -132 65 -125 ct 62 -118 60 -109 60 -99 ct 60 -89 61 -79 64 -70 ct 67 -61 71 -53 76 -47 ct 81 -40 87 -35 94 -31 ct 101 -27 109 -25 117 -25 ct 126 -25 134 -26 141 -29 ct 148 -32 153 -37 158 -42 ct 163 -48 167 -55 169 -63 ct 172 -71 173 -80 173 -91 ct p ef pom gr gs 0 0 m 15999 0 l 15999 3999 l 0 3999 l 0 0 l eoclip newpath gr gr 0 4000 t pom count op_count sub {pop} repeat countdictstack dict_count sub {end} repeat b4_inc_state restore %%PageTrailer %%Trailer %%EOF %%EndDocument @endspecial -262 4887 a(Fig.)d(2.)-19 4887 y SDict begin H.S end -19 4887 a -19 4887 a SDict begin H.R end -19 4887 a -19 4887 a SDict begin [/View [/XYZ H.V]/Dest (figure.2) cvn /DEST pdfmark end -19 4887 a Fw(Encoding)i(v)o(ector)f (for)g(a)f(generation)k(of)c(size)h Fh(N)k Fl(=)19 b(8)j Fw(and)h(three)h(encoding)-262 4962 y(windo)n(ws)h(of)e(size)i Fh(W)k Fl(=)19 b(3)p Fw(.)p Black -179 5223 a Fv(In)34 b(this)g(section)f(we)h(describe)f(the)h(algorithms)e(and)h(the)h (related)-262 5322 y(properties)24 b(that)g(enable)g(BC)j(to)d(preserv) o(e)g(the)h(pack)o(et)f(de)o(gree)f(distri-)-262 5422 y(b)n(ution)31 b(through)e(the)i(recombinations)e(at)i(the)h(netw)o (ork)e(nodes.)g(W)-7 b(e)-262 5522 y(pro)o(v)o(e)17 b(that)j(BC)g(pack) o(et)e(de)o(gree)g(distrib)n(ution)g(is)i(preserv)o(ed)d(by)i(design) -262 5621 y(under)29 b(an)h(arbitrary)f(number)f(of)i(recombinations)e (in)i(the)g(netw)o(ork.)p Black Black 1930 -58 a(This)21 b(property)d(holds)i(for)g(an)h(arbitrary)e(netw)o(ork,)g(although)g (the)i(end-)1930 42 y(to-end)31 b(coding)g(ef)n(\002cienc)o(y)g (depends)g(on)g(the)i(o)o(v)o(erlay)d(topology)g(as)1930 142 y(well.)21 b(The)f(de\002nition)g(of)g(BC)i(co)o(v)o(ers)d(not)h (only)g(the)h(pack)o(et)f(encoding)1930 241 y(process)27 b(at)g(the)g(source)f(node,)g(b)n(ut)h(also)g(the)g(pack)o(et)g (recombination)1930 341 y(and)c(the)g(decoding)e(processes)i(at)g(the)g (netw)o(ork)f(nodes,)h(and)f(is)i(based)1930 441 y(on)k(the)h(concept)e (of)h Fu(encoding)f(window)p Fv(.)2013 539 y(Let)63 b(us)h(consider)d (a)j(generation)d(composed)g(of)i Ft(N)72 b Fv(sym-)1930 639 y(bols)53 b Fr(\()p Ft(x)2201 651 y Fs(0)2239 639 y Ft(;)14 b(:::;)g(x)2429 651 y Fp(N)6 b Fq(\000)p Fs(1)2578 639 y Fr(\))54 b Fv(and)f(a)h(generic)e(encoding)g(v)o(ector)g Ft(g)72 b Fr(=)1930 739 y(\()p Ft(g)2002 751 y Fs(0)2039 739 y Ft(;)14 b(:::;)g(g)2222 751 y Fp(N)6 b Fq(\000)p Fs(1)2370 739 y Fr(\))p Fv(.)38 b(W)-7 b(e)38 b(de\002ne)f(encoding)e (windo)n(w)h(a)i(subset)g(of)f(the)1930 838 y(encoding)d(v)o(ector)h Fr(\()p Ft(g)2586 850 y Fp(f)2629 838 y Ft(;)14 b(:::;)g(g)2812 850 y Fp(l)2837 838 y Fr(\))37 b Fv(where)e Ft(f)45 b Fv(and)35 b Ft(l)j Fv(are,)e(respecti)n(v)o(ely)-5 b(,)1930 938 y(the)38 b Fu(leading)e(edg)o(e)h Fv(and)f(the)i Fu(tr)o(ailing)f(edg)o(e)g Fv(of)g(the)g(windo)n(w)-5 b(.)36 b(The)1930 1037 y(elements)k(of)g(the)h(encoding)d(v)o(ector)h (that)i(do)f(not)g(belong)f(to)i(the)1930 1137 y(encoding)27 b(windo)n(w)i(are)g(equal)g(to)h(zero.W)-7 b(e)29 b(de\002ne)g(the)g (size)i(of)e(the)1930 1237 y(encoding)d(windo)n(w)h(as)i Ft(W)35 b Fr(=)23 b Ft(l)c Fn(\000)e Ft(f)27 b Fr(+)17 b(1)p Fv(;)28 b(for)g(a)g(generation)e(of)i(size)1930 1336 y Ft(N)9 b Fv(,)30 b(there)f(are)h Ft(N)e Fn(\000)19 b Ft(W)31 b Fr(+)19 b(1)30 b Fv(possible)f(encoding)f(windo)n(ws)h(of)g (size)1930 1436 y Ft(W)12 b Fv(.)23 b(W)-7 b(e)24 b(indicate)f(as)g Fn(W)2664 1396 y Fp(f)2657 1460 y(W)2756 1436 y Fv(the)g(encoding)e (windo)n(w)h(that)h(has)g(size)g Ft(W)1930 1536 y Fv(and)32 b(leading)f(edge)h Ft(f)9 b Fv(.)32 b(Figure)2902 1536 y SDict begin H.S end 2902 1536 a Black Fv(2)p Black 2944 1479 a SDict begin H.R end 2944 1479 a 2944 1536 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (figure.2) cvn H.B /ANN pdfmark end 2944 1536 a 33 w Fv(sho)n(ws)g(the)g(encoding)e(v)o (ector)h(for)1930 1635 y(a)e(generation)d(of)i(size)h Ft(N)j Fr(=)23 b(8)28 b Fv(and)g(three)g(of)g(the)h Ft(N)e Fn(\000)17 b Ft(W)31 b Fr(+)17 b(1)23 b(=)g(6)1930 1735 y Fv(possible)d(encoding)e(windo)n(ws)h Fr(\()p Fn(W)2987 1705 y Fs(0)2980 1755 y(3)3025 1735 y Ft(;)14 b(:)g(:)g(:)f(;)h Fn(W)3298 1705 y Fs(5)3291 1755 y(3)3335 1735 y Fr(\))21 b Fv(of)f(size)h Ft(W)35 b Fr(=)23 b(3)p Fv(.)d(Let)1930 1847 y(us)k(no)n(w)f(consider)g(tw)o(o)h(encoding)d(windo)n(ws)i Fn(W)3386 1807 y Fp(f)3425 1782 y Ff(1)3379 1875 y Fp(W)3450 1859 y Ff(1)3512 1847 y Fv(and)g Fn(W)3745 1807 y Fp(f)3784 1782 y Ff(2)3738 1875 y Fp(W)3809 1859 y Ff(2)3870 1847 y Fv(such)1930 1967 y(that)h Ft(f)2129 1937 y Fs(2)2189 1967 y Fn(\025)e Ft(f)2326 1937 y Fs(1)2363 1967 y Fv(:)j(we)f(say)g (that)g Fn(W)2905 1927 y Fp(f)2944 1902 y Ff(1)2898 1995 y Fp(W)2969 1978 y Ff(1)3030 1967 y Fv(and)f Fn(W)3263 1927 y Fp(f)3302 1902 y Ff(2)3256 1995 y Fp(W)3327 1978 y Ff(2)3388 1967 y Fu(o)o(verlap)g Fv(if)h Ft(f)3790 1937 y Fs(2)3850 1967 y Fn(\024)f Ft(l)3965 1937 y Fs(1)4001 1967 y Fv(,)1930 2067 y(i.e.)32 b(if)f Ft(f)2196 2036 y Fs(1)2262 2067 y Fn(\024)d Ft(f)2405 2036 y Fs(2)2470 2067 y Fn(\024)g Ft(l)2590 2036 y Fs(1)2627 2067 y Fv(.)k(F)o(or)f(e)o (xample,)f(in)i(Figure)3504 2067 y SDict begin H.S end 3504 2067 a Black Fv(2)p Black 3546 2010 a SDict begin H.R end 3546 2010 a 3546 2067 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (figure.2) cvn H.B /ANN pdfmark end 3546 2067 a Fv(,)g(windo)n(w)e Fn(W)3985 2036 y Fs(0)3978 2087 y(3)1930 2166 y Fv(o)o(v)o(erlaps)23 b(with)j Fn(W)2497 2136 y Fs(1)2490 2187 y(3)2559 2166 y Fv(and)f Fn(W)2794 2136 y Fs(2)2787 2187 y(3)2831 2166 y Fv(.)g(A)h(k)o(e)o(y)e(dif)n (ference)f(from)h([)3681 2167 y SDict begin H.S end 3681 2167 a Black -1 x Fv(20)p Black 3764 2110 a SDict begin H.R end 3764 2110 a 3764 2166 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.windowed2006) cvn H.B /ANN pdfmark end 3764 2166 a Fv(])h(is)h(that)1930 2266 y(in)38 b(our)g(w)o(ork)f(the)h (encoding)e(windo)n(w)h(is)i(not)f(allo)n(wed)f(to)h(\223wrap)1930 2365 y(around\224)33 b(the)i(encoding)e(v)o(ector)h(boundaries,)e(as)k (the)f(wrap)f(w)o(ould)1930 2465 y(be)25 b(an)g(issue)g(with)g(the)g (recombinations.)d(So,)j(in)g(the)g(design)f(of)h(both)1930 2565 y(the)i(encoding)d(and)i(recombination)e(algorithms)i(of)g(BC,)i (we)f(do)f(not)1930 2664 y(allo)n(w)k(the)g(windo)n(w)f(to)i(wrap)e (around)g(and)g(hence)h(we)g(impose)g(that)1930 2764 y Fr(0)h Fn(\024)f Ft(f)40 b(<)30 b(l)j Fn(\024)d Ft(N)g Fn(\000)22 b Fr(1)p Fv(.)32 b(The)h(reasons)f(behind)f(this)j(and)e (the)h(other)1930 2864 y(dif)n(ferences)h(between)g(the)i(design)f(of)g (BC)i(and)e(other)f(f)o(amilies)i(of)1930 2963 y(codes)g(will)h(be)g (detailed)e(in)i(the)f(rest)h(of)f(this)h(Section.)f(Equipped)1930 3063 y(with)25 b(the)g(concept)f(of)h(encoding)d(windo)n(w)-5 b(,)24 b(we)h(proceed)e(to)j(describe)1930 3162 y(the)j(process)f(to)g (encode)f(pack)o(ets)i(at)g(the)f(source.)1930 3297 y SDict begin H.S end 1930 3297 a 1930 3297 a SDict begin 12 H.A end 1930 3297 a 1930 3297 a SDict begin [/View [/XYZ H.V]/Dest (subsection.4.1) cvn /DEST pdfmark end 1930 3297 a 81 x Fu(A.)41 b(P)-7 b(ac)n(k)o(et)29 b(Encoding)d(at)j(the)f (Sour)m(ce)2013 3503 y Fv(In)33 b(the)h(follo)n(wing,)e(we)i(describe)e (the)i(encoding)e(process)h(at)h(the)1930 3602 y(source)44 b(node)g(for)g(a)h(generation)e(of)h(size)i Ft(N)54 b Fv(and)44 b(an)h(encoding)1930 3702 y(windo)n(w)31 b(of)g(size)i Ft(W)12 b Fv(.)32 b(Ev)o(ery)e(time)i(a)h(ne)n(w)e(pack)o(et)h Ft(P)12 b Fr(\()p Ft(g)s(;)i(y)s Fr(\))32 b Fv(has)g(to)1930 3801 y(be)25 b(encoded,)f(the)h(source)g(dra)o(ws)g(the)h(position)e (of)i(the)f(leading)f(edge)1930 3901 y Ft(f)38 b Fv(of)28 b(the)g(encoding)f(windo)n(w)g(according)g(to)h(the)h(distrib)n(ution:) 2048 4182 y Ft(H)7 b(D)2193 4194 y Fp(N)s(;W)2343 4182 y Fr(\()p Ft(f)i Fr(\))23 b(=)2567 4065 y Fo(\032)2681 4091 y Fp(W)9 b Fs(+1)p 2681 4105 156 4 v 2713 4153 a(2)p Fp(N)2930 4124 y Fv(if)116 b Ft(f)31 b Fr(=)23 b(0)28 b Fv(or)h Ft(f)i Fr(=)23 b Ft(N)k Fn(\000)18 b Ft(W)2742 4208 y Fs(1)p 2730 4222 59 4 v 2730 4269 a Fp(N)2930 4241 y Fv(if)116 b Fr(0)22 b Ft(<)h(f)31 b(<)23 b(N)k Fn(\000)18 b Ft(W)1930 4378 y Fv(As)47 b(in)f(BC)h(the)f(encoding)d (windo)n(w)i(is)i(not)e(allo)n(wed)g(to)h(\223wrap)1930 4478 y(around\224)32 b(as)j(in)f([)2463 4479 y SDict begin H.S end 2463 4479 a Black -1 x Fv(20)p Black 2546 4421 a SDict begin H.R end 2546 4421 a 2546 4478 a SDict begin [/Color [0 1 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (cite.windowed2006) cvn H.B /ANN pdfmark end 2546 4478 a Fv(],)g(not)g(all)h(symbols)e Ft(x)3246 4490 y Fp(i)3309 4478 y Fv(are)h(contained)f(by)h(the)1930 4577 y(same)43 b(number)e(of)h(encoding)f(windo)n(ws.)g(If)i Ft(f)52 b Fv(w)o(as)43 b(dra)o(wn)f(with)1930 4677 y(uniform)23 b(probability)-5 b(,)21 b(some)k(symbols)f(w)o(ould)f(appear)h(in)g (the)h(coded)1930 4776 y(pack)o(ets)45 b(with)g(v)o(ery)f(lo)n(w)h (probability)-5 b(,)42 b(impairing)i(the)h(encoding)1930 4876 y(ef)n(\002cienc)o(y)-5 b(.)23 b(The)j Ft(H)7 b(D)2596 4888 y Fp(N)s(;W)2746 4876 y Fr(\()p Ft(f)i Fr(\))26 b Fv(guarantees)e(that)h(each)g(symbol)g Ft(x)3913 4888 y Fp(i)3967 4876 y Fv(is)1930 4976 y(selected)33 b(for)e(encoding)g (with)h(similar)h(probability)-5 b(,)30 b(which)i(in)g(turn)1930 5075 y(impro)o(v)o(es)27 b(the)h(decoding)f(ef)n(\002cienc)o(y)-5 b(.)1930 5175 y(Then,)33 b(the)h(elements)f(of)h(the)g(encoding)e(v)o (ector)h Ft(g)k Fv(are)d(set)g(to)g(zero)1930 5275 y(outside)e(of)g (the)g(encoding)e(windo)n(w)h(and)h(to)h(one)e(with)i(probability)1940 5342 y Fs(1)p 1940 5356 34 4 v 1940 5403 a(2)2012 5374 y Fv(inside)c(the)f(encoding)e(windo)n(w)-5 b(,)27 b(i.e.)2327 5575 y SDict begin H.S end 2327 5575 a 2327 5575 a SDict begin 12 H.A end 2327 5575 a 2327 5575 a SDict begin [/View [/XYZ H.V]/Dest (equation.4.1) cvn /DEST pdfmark end 2327 5575 a 29 w Fm(P)p Fn(f)p Ft(g)2490 5587 y Fp(i)2539 5575 y Fr(=)22 b(1)p Fn(g)g Fr(=)2820 5458 y Fo(\032)2934 5492 y Fs(1)p 2934 5506 34 4 v 2934 5553 a(2)3060 5525 y Fv(if)116 b Ft(f)32 b Fn(\024)22 b Ft(i)h Fn(\024)f Ft(l)r Fv(,)2930 5624 y Fr(0)88 b Fv(otherwise)o Ft(:)3925 5575 y Fv(\(1\))p Black Black eop end end %%Page: 5 5 TeXDict begin HPSdict begin 5 4 bop 0 0 a SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end 0 0 a -270 -415 a SDict begin H.S end -270 -415 a -270 -415 a SDict begin H.R end -270 -415 a -270 -415 a SDict begin [/View [/XYZ H.V]/Dest (page.5) cvn /DEST pdfmark end -270 -415 a Black 3993 -307 a FC(5)p Black -262 -58 a Fv(Let)29 b Ft(s)h Fv(and)e Ft(t)h Fv(be)g(the)g(positions)f(of)g (the)h(\002rst)h(and)e(the)h(last)g(non-zero)-262 42 y(elements)34 b(of)f Ft(g)k Fv(,)e(i.e.)e Ft(g)479 54 y Fp(s)547 42 y Fr(=)g Ft(g)685 54 y Fp(t)747 42 y Fr(=)f(1)i Fv(and)f Ft(g)1114 54 y Fp(i)1175 42 y Fr(=)f(0)i Fv(for)f(an)o(y)g Ft(i)g(<)g(s)-262 142 y Fv(and)26 b(for)g(an)o(y)g Ft(i)d(>)g(t)p Fv(:)k(we)g(call)g Ft(g)686 154 y Fp(s)748 142 y Fv(and)f Ft(g)935 154 y Fp(t)964 142 y Fv(,)h(respecti)n(v)o(ely)-5 b(,)25 b(the)h Fu(leading)-262 241 y(one)33 b Fv(and)f(the)h Fu(tr)o(ailing)f(one)g Fv(of)h(the)f(encoding)f(v)o(ector)-5 b(.)32 b(Finally)-5 b(,)32 b(the)-262 341 y(source)25 b(combines)g(the)h(original)f(symbols)g(as)i Ft(y)f Fr(=)1292 279 y Fo(P)1380 299 y Fp(N)6 b Fq(\000)p Fs(1)1380 366 y Fp(i)p Fs(=0)1542 341 y Ft(g)1582 353 y Fp(i)1609 341 y Ft(x)1656 353 y Fp(i)1711 341 y Fv(and)-262 441 y(transmits)29 b(the)f(encoded)f(pack)o(et)h Ft(P)12 b Fr(\()p Ft(g)s(;)i(y)s Fr(\))28 b Fv(to)h(the)g(netw)o(ork.)-179 539 y(In)35 b(the)g(follo)n(wing,)e(we)j(say)f(that)g(a)h(pack)o(et)e Ft(P)12 b Fr(\()p Ft(g)s(;)i(y)s Fr(\))36 b Fv(is)g(a)f Fu(Band)-262 639 y(P)-7 b(ac)n(k)o(et)27 b Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))26 b Fv(with)f(leading)f(edge)g Ft(f)34 b Fv(if)26 b Ft(g)1219 651 y Fp(i)1269 639 y Fr(=)d(0)i Fv(for)f Ft(i)32 b(=)-51 b Fn(2)23 b Fr([)p Ft(f)t(;)14 b(l)r Fr(])-262 738 y Fv(and)37 b Fm(P)p Fn(f)p Ft(g)30 750 y Fp(i)95 738 y Fr(=)h(1)p Fn(g)g Fr(=)434 706 y Fs(1)p 434 720 34 4 v 434 767 a(2)515 738 y Fv(for)e Ft(i)j Fn(2)h Fr([)p Ft(f)t(;)14 b(l)r Fr(])p Fv(.)37 b(The)f(de)o(gree)g(distrib)n(ution)-262 838 y(of)31 b(a)h Ft(B)t(P)44 b Fv(follo)n(ws)31 b(the)h(Binomial)f (Distrib)n(ution)f Fn(B)s Fr(\()p Ft(W)n(;)1470 805 y Fs(1)p 1470 819 V 1470 867 a(2)1513 838 y Fr(\))i Fv(and)f(the)-262 939 y(e)o(xpected)26 b(pack)o(et)h(de)o(gree)f(is)i(equal)f(to)946 906 y Fp(W)p 946 920 72 4 v 965 968 a Fs(2)1027 939 y Fv(.)h(It)g(follo)n(ws)f(that)g(pack)o(ets)-262 1039 y(encoded)34 b(according)f(to)j(\()543 1039 y SDict begin H.S end 543 1039 a Black Fv(1)p Black 584 982 a SDict begin H.R end 584 982 a 584 1039 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.4.1) cvn H.B /ANN pdfmark end 584 1039 a Fv(\))g(are)f Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))37 b Fv(and)e(the)h(follo)n(wing)-262 1138 y(property)27 b(holds.)-262 1287 y SDict begin H.S end -262 1287 a -262 1287 a SDict begin 12 H.A end -262 1287 a -262 1287 a SDict begin [/View [/XYZ H.V]/Dest (prop.2) cvn /DEST pdfmark end -262 1287 a Black Fg(Pr)o(oposition)e(2.)p Black 38 w Fu(Let)g Ft(P)471 1257 y Fs(1)508 1287 y Fr(\()p Ft(g)583 1257 y Fs(1)620 1287 y Ft(;)14 b(y)701 1257 y Fs(1)738 1287 y Fr(\))26 b Fu(and)d Ft(P)1010 1257 y Fs(2)1047 1287 y Fr(\()p Ft(g)1122 1257 y Fs(2)1160 1287 y Ft(;)14 b(y)1241 1257 y Fs(2)1277 1287 y Fr(\))26 b Fu(be)f(two)g(pac)n(k)o(ets)-262 1386 y(that)37 b(ar)m(e)o(,)h(r)m (espectively)-5 b(,)37 b Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)880 1356 y Fs(1)918 1386 y Fr(\))38 b Fu(and)e Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)1512 1356 y Fs(2)1550 1386 y Fr(\))p Fu(.)37 b(If)h(the)-262 1499 y(r)m(espective)c(encoding)e(windows)j Fn(W)860 1459 y Fp(f)899 1434 y Ff(1)853 1527 y Fp(W)924 1510 y Ff(1)995 1499 y Fu(and)f Fn(W)1244 1459 y Fp(f)1283 1434 y Ff(2)1237 1527 y Fp(W)1308 1510 y Ff(2)1379 1499 y Fu(o)o(verlap,)f(then)-262 1599 y(pac)n(k)o(et)50 b Ft(P)68 1568 y Fp(r)104 1599 y Fr(\()p Ft(g)179 1568 y Fp(r)216 1599 y Ft(;)14 b(y)297 1568 y Fp(r)333 1599 y Fr(\))63 b(=)g Ft(P)621 1568 y Fs(1)692 1599 y Fn(\010)34 b Ft(P)856 1568 y Fs(2)943 1599 y Fu(is)51 b(a)f Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)1503 1568 y Fp(r)1540 1599 y Fr(\))51 b Fu(whose)-262 1698 y(encoding)27 b(window)h(size)i(is)f Ft(W)687 1668 y Fp(r)747 1698 y Fn(\024)23 b Ft(W)925 1668 y Fs(1)980 1698 y Fr(+)18 b Ft(W)1153 1668 y Fs(2)1190 1698 y Fu(.)-262 1847 y SDict begin H.S end -262 1847 a -262 1847 a SDict begin 12 H.A end -262 1847 a -262 1847 a SDict begin [/View [/XYZ H.V]/Dest (corol.1) cvn /DEST pdfmark end -262 1847 a Black Fg(Cor)o(ollary)i(1.)p Black 35 w Fu(Under)h(the)h(hypothesis)e(of)i(Pr)l(op.)1225 1847 y SDict begin H.S end 1225 1847 a Black Fu(2)p Black 1267 1791 a SDict begin H.R end 1267 1791 a 1267 1847 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (prop.2) cvn H.B /ANN pdfmark end 1267 1847 a Fu(,)g(if)g Ft(W)1468 1816 y Fs(1)1528 1847 y Fr(=)h Ft(W)1706 1816 y Fs(2)1766 1847 y Fr(=)-262 1946 y Ft(W)41 b Fu(and)28 b Ft(f)61 1916 y Fs(1)121 1946 y Fr(=)22 b Ft(f)258 1916 y Fs(2)324 1946 y Fu(then)28 b Ft(W)586 1916 y Fp(r)646 1946 y Fr(=)23 b Ft(W)12 b Fu(.)-262 2095 y Fv(It)22 b(follo)n(ws)e(from)g(the)h (de\002nition)f(of)h(BP)h(that)f(the)g(de)o(gree)e(distrib)n(ution)-262 2194 y(of)g(the)g(recombined)d(pack)o(et)i Ft(P)659 2164 y Fp(r)715 2194 y Fv(follo)n(ws)g(the)h(Binomial)g(Distrib)n(ution)-262 2294 y Fn(B)s Fr(\()p Ft(W)-82 2264 y Fp(r)-46 2294 y Ft(;)1 2261 y Fs(1)p 1 2275 34 4 v 1 2323 a(2)44 2294 y Fr(\))p Fv(.)-262 2439 y SDict begin H.S end -262 2439 a -262 2439 a SDict begin 12 H.A end -262 2439 a -262 2439 a SDict begin [/View [/XYZ H.V]/Dest (subsection.4.2) cvn /DEST pdfmark end -262 2439 a 70 x Fu(B.)41 b(P)-7 b(ac)n(k)o(et)29 b(Decoding)e(at)i(the)f(Network)i(Nodes)-179 2633 y Fv(F)o(or)43 b(the)f(decoding)f(process,)h(we)h(assume)g(that)g(the)f(nodes)g(of) -262 2733 y(the)48 b(netw)o(ork)f(recei)n(v)o(e)h(pack)o(ets)f Ft(P)12 b Fr(\()p Ft(g)s(;)i(y)s Fr(\))49 b Fv(that)f(are)g Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))p Fv(.)-262 2833 y(While)32 b(this)h(assumption)d(is)i(ob)o(viously)e(true)h(for)g (pack)o(ets)h(recei)n(v)o(ed)-262 2932 y(from)k(the)h(source,)e(in)i (the)g(ne)o(xt)f(section)h(we)g(will)g(pro)o(v)o(e)e(that)i(the)-262 3032 y(assumption)29 b(holds)g(also)h(for)g(pack)o(ets)f(recei)n(v)o (ed)g(from)f(the)i(netw)o(ork)-262 3131 y(nodes.)44 b(The)g(recei)n(v)o (ed)f(pack)o(ets)h(are)g(decoded)f(using)h(an)h(ad-hoc)-262 3231 y(modi\002ed)23 b(v)o(ersion)f(of)h(early-decoding)d(Gaussian)k (Elimination,)e(that)-262 3331 y(we)34 b(called)f(\223Sw)o(ap)g (Gaussian)g(Elimination\224)f(\(SGE\).)h(Similarly)g(to)-262 3430 y(the)g(early-decoding)c(GE)k(algorithm,)e(SGE)i(or)o(ganizes)e (the)i(system)-262 3530 y(of)e(recei)n(v)o(ed)e(equations)g(into)i(a)g (triangular)e(matrix)h(that)h(a)n(v)n(oids)g(the)-262 3630 y(triangularization)20 b(process)j(typical)f(of)g(standard)g(GE.)h (SGE)g(solv)o(es)g(a)-262 3729 y(system)f(of)f Ft(N)31 b Fv(linear)21 b(equations)f Ft(GX)29 b Fr(=)23 b Ft(Y)c Fv(,)i(where)g Ft(G)h Fv(is)g(the)g Ft(N)14 b Fn(\002)5 b Ft(N)-262 3829 y Fv(matrix)25 b(that)g(stores)h(linear)f (combinations)e(of)i(the)h(encoding)d(v)o(ectors)-262 3928 y(of)28 b(the)f(recei)n(v)o(ed)f(pack)o(ets.)h(In)h(the)f(follo)n (wing,)f(we)i(use)g(the)f(notation)-262 4028 y Ft(G)-197 4040 y Fp(i)-142 4028 y Fv(to)f(indicate)f(the)h Ft(i)p Fv(-th)f(ro)n(w)h(of)f Ft(G)i Fv(and)e(we)h(use)g(the)g(notation)f Ft(G)1752 4040 y Fp(i;j)-262 4128 y Fv(to)36 b(indicate)g(the)g (element)g(of)f Ft(G)i Fv(at)g(ro)n(w)e Ft(i)p Fv(,)h(column)f Ft(j)5 b Fv(.)37 b(When)e(all)-262 4227 y(the)j(elements)g(of)g Ft(G)385 4239 y Fp(i)451 4227 y Fv(are)g(equal)g(to)g(zero,)f(we)i(say) f(that)g(the)g(ro)n(w)-262 4327 y Ft(i)p Fv(-th)c(is)g(empty)f(and)h (we)g(write)g Ft(G)781 4339 y Fp(i)842 4327 y Fr(=)f Fn(;)p Fv(.)g Ft(Y)53 b Fv(is)35 b(the)f Ft(N)d Fn(\002)22 b Fr(1)34 b Fv(v)o(ector)-262 4427 y(that)27 b(stores)f(the)g (combinations)f(of)h(the)g(payloads)f Ft(y)30 b Fv(of)c(the)g(encoded) -262 4526 y(pack)o(ets)i(recei)n(v)o(ed)f(by)h(the)h(node)e(and)h Ft(X)35 b Fv(is)30 b(the)e Ft(N)f Fn(\002)18 b Fr(1)29 b Fv(v)o(ector)e(that)-262 4626 y(contains)e(the)g(symbols)f Ft(x)517 4638 y Fp(i)571 4626 y Fv(to)h(reco)o(v)o(er)-5 b(.)23 b(F)o(or)i(the)g(sak)o(e)g(of)g(simplicity)-5 b(,)-262 4725 y(we)31 b(describe)e(the)h(operations)e(on)i(the)g Ft(G)h Fv(matrix)e(and)h(the)g(recei)n(v)o(ed)-262 4825 y(encoding)d(v)o(ectors)h Ft(g)k Fv(and)d(we)g(omit)g(the)g(equi)n(v)n (alent)e(operations)g(on)-262 4925 y Ft(y)32 b Fv(and)c Ft(Y)19 b Fv(.)-179 5023 y(The)k(SGE)g(algorithm)e(operates)h(in)h(tw)o (o)g(stages,)g(triangularization)-262 5123 y(and)28 b(diagonalization,) e(as)j(follo)n(ws.)-262 5223 y(The)i(triangularization)d(stage)j(is)h (formalized)d(as)j(Algorithm)1638 5223 y SDict begin H.S end 1638 5223 a Black Fv(1)p Black 1679 5166 a SDict begin H.R end 1679 5166 a 1679 5223 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (algorithm.1) cvn H.B /ANN pdfmark end 1679 5223 a 32 w Fv(and)-262 5322 y(it)24 b(is)h(e)o(x)o(ecuted)c(e)n (v)o(ery)h(time)i(a)f(ne)n(w)h(pack)o(et)e Ft(P)12 b Fr(\()p Ft(g)s(;)i(y)s Fr(\))24 b Fv(is)g(recei)n(v)o(ed.)e(Let)-262 5422 y Ft(g)-222 5434 y Fp(s)-162 5422 y Fv(be)i(the)g(leading)f(one)g (of)h(g,)g(i.e.)g(the)g(\002rst)g(non-zero)e(element)h(of)h Ft(g)s Fv(.)-262 5522 y(If)i Ft(G)-115 5534 y Fp(s)-53 5522 y Fv(is)h(empty)-5 b(,)25 b Ft(g)k Fv(is)d(inserted)g(in)g(the)g Ft(s)p Fv(-th)f(ro)n(w)h(of)f Ft(G)i Fv(\(line)f(5\))g(and)-262 5621 y(the)i(algorithm)d(ends.)i(Otherwise)g Ft(g)j Fv(and)d Ft(G)1071 5633 y Fp(s)1135 5621 y Fv(are)g(sw)o(apped)f(\(line)h(8\))p Black Black 1930 -58 a(to)21 b(refresh)f(the)h(ro)n(ws)g(of)f Ft(G)i Fv(between)e(tw)o(o)h(consecuti)n(v)o(e)e(transmission)1930 42 y(opportunities)24 b(of)i(the)g(node.)f(This)h(sw)o(ap)h(increases)f (the)g(probability)1930 142 y(to)47 b(recombine)d(an)j(inno)o(v)n(ati)n (v)o(e)d(pack)o(et)i(if)g(fe)n(w)h(ro)n(ws)f(of)g Ft(G)i Fv(are)1930 241 y(suitable)31 b(to)g(be)f(recombined)f(as)i(e)o (xplained)e(in)i(Section)3679 242 y SDict begin H.S end 3679 242 a Black -1 x Fv(IV)-8 b(-C)p Black 3841 185 a SDict begin H.R end 3841 185 a 3841 241 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (subsection.4.3) cvn H.B /ANN pdfmark end 3841 241 a Fv(.)31 b(The)1930 341 y(sw)o(ap)g(does)f(not)g (further)f(increase)h(the)h(computational)d(comple)o(xity)1930 441 y(as)35 b(it)f(is)h(performed)c(by)j(sw)o(apping)f(tw)o(o)h (pointers)f(in)h(memory)-5 b(.)31 b(At)1930 540 y(this)39 b(point,)f(if)h Ft(g)i Fv(is)f(identical)e(to)h Ft(G)3080 552 y Fp(s)3116 540 y Fv(,)f Ft(P)51 b Fv(is)40 b(not)e(inno)o(v)n(ati) n(v)o(e)e(and)1930 640 y(the)e(algorithm)f(ends.)g(Otherwise)h(a)h(XOR) f(between)g Ft(g)j Fv(and)c Ft(G)3896 652 y Fp(s)3967 640 y Fv(is)1930 739 y(e)o(x)o(ecuted)25 b(and)i(the)g(algorithm)f (iterates.)h(Figure)3410 740 y SDict begin H.S end 3410 740 a Black -1 x Fv(3)p Black 3452 683 a SDict begin H.R end 3452 683 a 3452 739 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (figure.3) cvn H.B /ANN pdfmark end 3452 739 a 27 w Fv(sho)n(ws)g(matrix)g Ft(G)1930 839 y Fv(after)34 b(5)g(independent)d(pack)o(ets)j(ha)n(v)o(e)f(been)g(recei)n(v)o(ed)f (by)i(the)g(node)1930 939 y(for)28 b(a)h(to)o(y)f(case)h(where)f Ft(N)9 b Fv(=8)28 b(and)g Ft(W)12 b Fv(=5.)1930 1109 y SDict begin H.S end 1930 1109 a 1930 1109 a SDict begin H.R end 1930 1109 a 1930 1109 a SDict begin [/View [/XYZ H.V]/Dest (algorithm.1) cvn /DEST pdfmark end 1930 1109 a 1930 1116 2093 7 v 80 x Fg(Algorithm)30 b(1)f Fv(SGE,)f(T)m(riangularization)p 1930 1227 2093 4 v Black 1930 1244 a SDict begin H.S end 1930 1244 a 1930 1244 a SDict begin 12 H.A end 1930 1244 a 1930 1244 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.1) cvn /DEST pdfmark end 1930 1244 a Black 1978 1306 a Fw(1:)p Black 42 w Fg(r)o(ecei)o(v)o(e)g Ft(P)12 b Fr(\()p Ft(g)s Fr(\))p Fv(.)2568 1306 y SDict begin H.S end 2568 1306 a 2568 1306 a SDict begin 12 H.A end 2568 1306 a 2568 1306 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.2) cvn /DEST pdfmark end 2568 1306 a Black 1978 1406 a Fw(2:)p Black 42 w Fg(while)29 b Fv(true)g Fg(do)1930 1407 y SDict begin H.S end 1930 1407 a 1930 1407 a SDict begin 12 H.A end 1930 1407 a 1930 1407 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.3) cvn /DEST pdfmark end 1930 1407 a Black 1978 1505 a Fw(3:)p Black 125 w Ft(s)23 b Fn( )29 b Fv(position)f(of)g (leading)g(one)g(of)g Ft(g)3315 1505 y SDict begin H.S end 3315 1505 a 3315 1505 a SDict begin 12 H.A end 3315 1505 a 3315 1505 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.4) cvn /DEST pdfmark end 3315 1505 a Black 1978 1605 a Fw(4:)p Black 125 w Fg(if)h Ft(G)2299 1617 y Fp(s)2358 1605 y Fr(=)22 b Fn(;)29 b Fg(then)1930 1617 y SDict begin H.S end 1930 1617 a 1930 1617 a SDict begin 12 H.A end 1930 1617 a 1930 1617 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.5) cvn /DEST pdfmark end 1930 1617 a Black 1978 1704 a Fw(5:)p Black 208 w Ft(G)2302 1716 y Fp(s)2361 1704 y Fn( )23 b Ft(g)2539 1704 y SDict begin H.S end 2539 1704 a 2539 1704 a SDict begin 12 H.A end 2539 1704 a 2539 1704 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.6) cvn /DEST pdfmark end 2539 1704 a Black 1978 1804 a Fw(6:)p Black 208 w Fg(end)1930 1805 y SDict begin H.S end 1930 1805 a 1930 1805 a SDict begin 12 H.A end 1930 1805 a 1930 1805 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.7) cvn /DEST pdfmark end 1930 1805 a Black 1978 1904 a Fw(7:)p Black 125 w Fg(else)1930 1905 y SDict begin H.S end 1930 1905 a 1930 1905 a SDict begin 12 H.A end 1930 1905 a 1930 1905 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.8) cvn /DEST pdfmark end 1930 1905 a Black 1978 2003 a Fw(8:)p Black 208 w Fv(sw)o(ap)29 b Ft(G)2501 2015 y Fp(s)2566 2003 y Fv(and)f Ft(g)2786 2003 y SDict begin H.S end 2786 2003 a 2786 2003 a SDict begin 12 H.A end 2786 2003 a 2786 2003 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.9) cvn /DEST pdfmark end 2786 2003 a Black 1978 2103 a Fw(9:)p Black 208 w Fg(if)h Ft(g)d Fr(=)c Ft(G)2535 2115 y Fp(s)2600 2103 y SDict begin H.S end 2600 2103 a 2600 2103 a SDict begin 12 H.A end 2600 2103 a 2600 2103 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.10) cvn /DEST pdfmark end 2600 2103 a Black 1945 2203 a Fw(10:)p Black 324 w Fg(end)2512 2203 y SDict begin H.S end 2512 2203 a 2512 2203 a SDict begin 12 H.A end 2512 2203 a 2512 2203 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.11) cvn /DEST pdfmark end 2512 2203 a Black 1945 2302 a Fw(11:)p Black 208 w Ft(g)k Fn( )d Ft(g)e Fn(\010)d Ft(G)2618 2314 y Fp(s)1930 2318 y SDict begin H.S end 1930 2318 a 1930 2318 a SDict begin 12 H.A end 1930 2318 a 1930 2318 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.12) cvn /DEST pdfmark end 1930 2318 a Black 1945 2402 a Fw(12:)p Black 125 w Fg(end)29 b(if)1930 2403 y SDict begin H.S end 1930 2403 a 1930 2403 a SDict begin 12 H.A end 1930 2403 a 1930 2403 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.13) cvn /DEST pdfmark end 1930 2403 a Black 1945 2501 a Fw(13:)p Black 42 w Fg(end)g(while)p Black 1930 2539 2093 4 v 2013 2773 a Fv(Under)37 b(the)g(assumption)g(that)g(node)g(recei)n(v)o (es)f(pack)o(ets)i Ft(P)12 b Fr(\()p Ft(g)s(;)i(y)s Fr(\))1930 2872 y Fv(that)52 b(are)f Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))p Fv(,)52 b(the)g(follo)n(wing)e(proposition)f(about)i(the)1930 2972 y(structure)28 b(of)g(matrix)g Ft(G)h Fv(holds:)1930 3141 y SDict begin H.S end 1930 3141 a 1930 3141 a SDict begin 12 H.A end 1930 3141 a 1930 3141 a SDict begin [/View [/XYZ H.V]/Dest (prop.3) cvn /DEST pdfmark end 1930 3141 a Black Fg(Pr)o(oposition)e(3.)p Black 40 w Fu(If)g(the)g(SGE)f(pr)l(ocesses)i(pac)n(k)o(ets)f Ft(P)12 b Fr(\()p Ft(g)s(;)i(y)s Fr(\))27 b Fu(that)g(ar)m(e)1930 3241 y Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))p Fu(,)30 b(then)e Ft(G)h Fu(is)h(an)e(upper)g(triangular)g(band)g(matrix)h (\(i.e)o(.,)1930 3340 y Ft(G)1995 3352 y Fp(i;j)2098 3340 y Fr(=)24 b(0)29 b Fu(if)h Ft(j)g(<)24 b(i)29 b Fu(or)h Ft(j)f(>)24 b(i)19 b Fr(+)g Ft(W)31 b Fn(\000)18 b Fr(1)p Fu(\))29 b(and)g Ft(G)3444 3352 y Fp(i)3501 3340 y Fu(is)i(the)e(encoding)1930 3440 y(vector)g(of)f(pac)n(k)o(et)g Ft(P)12 b Fr(\()p Ft(G)2665 3452 y Fp(i)2694 3440 y Ft(;)i(Y)2779 3452 y Fp(i)2806 3440 y Fr(\))30 b Fu(that)e(is)h(a)g Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))p Fu(.)2096 3559 y(Pr)l(oof:)34 b(The)h(pr)l(oof)f(is)h(b)n(uilt)f(by)h (mathematical)e(induction)f(on)1930 3659 y(the)d(number)e(of)i(r)m (eceived)f(pac)n(k)o(ets)h Ft(k)s Fu(.)1930 3758 y(Basis:)36 b Ft(G)g Fu(is)g(empty)g(when)f(the)g(\002r)o(st)i(pac)n(k)o(et)e Ft(P)12 b Fr(\()p Ft(g)s(;)i(y)s Fr(\))36 b Fu(is)g(r)m(eceived)1930 3858 y(and)25 b Ft(g)j Fu(is)e(inserted)g(in)g Ft(G)2680 3870 y Fp(s)2715 3858 y Fu(,)g(wher)m(e)g Ft(s)g Fu(is)g(the)g (position)e(of)i(the)f(leading)1930 3958 y(one)k(of)h Ft(g)s Fu(.)f Ft(G)2333 3970 y Fp(s)2399 3958 y Fu(is)i(equal)e(to)h Ft(g)i Fu(and)d(since)h Ft(P)42 b Fu(is)31 b(a)e Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))p Fu(,)31 b(the)1930 4057 y(pr)l(oposition)c(is)j(pr)l(o)o(ved.)1930 4157 y(Inductive)19 b(step:)h(Let)h(us)g(assume)f(that)h(the)f(pr)l(oposition)f(holds)h (for)h(the)1930 4257 y(\002r)o(st)27 b Ft(k)j Fu(r)m(eceived)c(pac)n(k) o(ets.)g(The)h Fr(\()p Ft(k)18 b Fr(+)c(1\))p Fu(-th)26 b(P)-7 b(ac)n(k)o(et)26 b Ft(P)12 b Fr(\()p Ft(g)s(;)i(y)s Fr(\))27 b Fu(is)g(then)1930 4356 y(r)m(eceived,)j(and)f(we)j(have)e (two)g(cases)h(to)g(consider)-9 b(.)29 b(if)j Ft(G)3655 4368 y Fp(s)3721 4356 y Fu(is)g(empty)-5 b(,)1930 4456 y(then)39 b Ft(g)j Fu(is)e(inserted)f(in)g Ft(G)2766 4468 y Fp(s)2841 4456 y Fu(and)f(the)h(pr)l(oposition)f(holds)g(for)i (the)1930 4555 y(same)31 b(r)m(eason)g(illustr)o(ated)g(in)g(the)g (Basis)g(step.)h(Otherwise)o(,)f(a)h(swap)1930 4655 y(between)26 b Ft(G)2294 4667 y Fp(s)2357 4655 y Fu(and)f Ft(g)30 b Fu(happens)24 b(and)i(the)g(pr)l(oposition)f(still)j(holds)d(for)1930 4755 y(the)f(same)g(r)m(eason.)f(Then,)g(the)h(algorithm)f(computes)g Ft(g)j Fr(=)d Ft(g)13 b Fn(\010)d Ft(G)3893 4767 y Fp(s)3928 4755 y Fu(:)24 b Ft(g)1930 4854 y Fu(and)k Ft(G)2149 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pom 0.898 c 11174 7057 m 10454 7057 l 10454 6056 l 11893 6056 l 11893 7057 l 11174 7057 l p ef 0.500 c 11174 7057 m 10454 7057 l 10454 6056 l 11893 6056 l 11893 7057 l 11174 7057 l pc pum 10803 6738 t 0.101 c 426 -425 m 272 -218 l 434 0 l 352 0 l 228 -167 l 105 0 l 22 0 l 187 -222 l 36 -425 l 119 -425 l 231 -273 l 344 -425 l 426 -425 l p ef pom pum 11260 7063 t 49 -328 m 223 -328 l 223 -291 l 89 -291 l 89 -211 l 96 -213 102 -215 109 -216 ct 115 -217 121 -217 128 -217 ct 165 -217 194 -207 215 -187 ct 236 -167 247 -140 247 -106 ct 247 -70 236 -43 214 -23 ct 192 -4 161 6 121 6 ct 107 6 93 5 79 2 ct 65 0 50 -3 35 -8 ct 35 -53 l 48 -46 62 -40 76 -37 ct 90 -33 105 -31 120 -31 ct 146 -31 166 -38 180 -51 ct 195 -65 203 -83 203 -106 ct 203 -129 195 -147 180 -160 ct 166 -173 146 -180 120 -180 ct 108 -180 97 -179 85 -176 ct 73 -173 61 -169 49 -164 ct 49 -328 l p ef pom 0.898 c 11174 8057 m 10454 8057 l 10454 7057 l 11893 7057 l 11893 8057 l 11174 8057 l p ef 0.500 c 11174 8057 m 10454 8057 l 10454 7057 l 11893 7057 l 11893 8057 l 11174 8057 l pc pum 10803 7738 t 0.101 c 426 -425 m 272 -218 l 434 0 l 352 0 l 228 -167 l 105 0 l 22 0 l 187 -222 l 36 -425 l 119 -425 l 231 -273 l 344 -425 l 426 -425 l p ef pom pum 11260 8064 t 149 -182 m 129 -182 113 -175 101 -162 ct 90 -148 84 -129 84 -106 ct 84 -82 90 -63 101 -50 ct 113 -36 129 -29 149 -29 ct 168 -29 184 -36 196 -50 ct 208 -63 213 -82 213 -106 ct 213 -129 208 -148 196 -162 ct 184 -175 168 -182 149 -182 ct p 237 -321 m 237 -281 l 226 -286 214 -290 203 -293 ct 192 -296 180 -297 169 -297 ct 140 -297 118 -287 102 -267 ct 87 -248 78 -218 76 -178 ct 84 -190 95 -200 108 -207 ct 121 -214 136 -217 151 -217 ct 184 -217 210 -207 229 -187 ct 248 -167 258 -140 258 -106 ct 258 -72 248 -45 228 -25 ct 208 -4 182 6 149 6 ct 111 6 82 -9 62 -38 ct 41 -67 31 -109 31 -164 ct 31 -216 44 -257 68 -288 ct 93 -319 126 -334 167 -334 ct 179 -334 190 -333 201 -331 ct 213 -329 224 -326 237 -321 ct p ef pom 0.898 c 11169 9057 m 10449 9057 l 10449 8057 l 11889 8057 l 11889 9057 l 11169 9057 l p ef 0.500 c 11169 9057 m 10449 9057 l 10449 8057 l 11889 8057 l 11889 9057 l 11169 9057 l pc pum 10799 8738 t 0.101 c 426 -425 m 272 -218 l 434 0 l 352 0 l 228 -167 l 105 0 l 22 0 l 187 -222 l 36 -425 l 119 -425 l 231 -273 l 344 -425 l 426 -425 l p ef pom pum 11256 9064 t 37 -328 m 248 -328 l 248 -309 l 129 -1 l 82 -1 l 194 -291 l 37 -291 l 37 -328 l p ef pom 0.898 c 11179 2053 m 10458 2053 l 10458 1057 l 11899 1057 l 11899 2053 l 11179 2053 l p ef 0.500 c 11179 2053 m 10458 2053 l 10458 1057 l 11899 1057 l 11899 2053 l 11179 2053 l pc pum 10808 1736 t 0.101 c 426 -425 m 272 -218 l 434 0 l 352 0 l 228 -167 l 105 0 l 22 0 l 187 -222 l 36 -425 l 119 -425 l 231 -273 l 344 -425 l 426 -425 l p ef pom pum 11265 2062 t 143 -299 m 120 -299 103 -288 92 -265 ct 80 -243 74 -209 74 -164 ct 74 -119 80 -85 92 -63 ct 103 -40 120 -29 143 -29 ct 166 -29 183 -40 195 -63 ct 206 -85 212 -119 212 -164 ct 212 -209 206 -243 195 -265 ct 183 -288 166 -299 143 -299 ct p 143 -334 m 180 -334 208 -320 227 -291 ct 247 -262 256 -219 256 -164 ct 256 -109 247 -67 227 -38 ct 208 -9 180 6 143 6 ct 106 6 78 -9 59 -38 ct 39 -67 30 -109 30 -164 ct 30 -219 39 -262 59 -291 ct 78 -320 106 -334 143 -334 ct p ef pom 0.898 c 11179 3051 m 10458 3051 l 10458 2056 l 11899 2056 l 11899 3051 l 11179 3051 l p ef 0.500 c 11179 3051 m 10458 3051 l 10458 2056 l 11899 2056 l 11899 3051 l 11179 3051 l pc pum 10808 2735 t 0.101 c 426 -425 m 272 -218 l 434 0 l 352 0 l 228 -167 l 105 0 l 22 0 l 187 -222 l 36 -425 l 119 -425 l 231 -273 l 344 -425 l 426 -425 l p ef pom pum 11265 3060 t 56 -37 m 128 -37 l 128 -288 l 49 -272 l 49 -312 l 128 -328 l 172 -328 l 172 -37 l 245 -37 l 245 0 l 56 0 l 56 -37 l p ef pom 0.898 c 11179 4061 m 10458 4061 l 10458 3066 l 11899 3066 l 11899 4061 l 11179 4061 l p ef 0.500 c 11179 4061 m 10458 4061 l 10458 3066 l 11899 3066 l 11899 4061 l 11179 4061 l pc pum 10808 3745 t 0.101 c 426 -425 m 272 -218 l 434 0 l 352 0 l 228 -167 l 105 0 l 22 0 l 187 -222 l 36 -425 l 119 -425 l 231 -273 l 344 -425 l 426 -425 l p ef pom pum 11265 4070 t 86 -37 m 241 -37 l 241 0 l 33 0 l 33 -37 l 50 -55 73 -78 102 -108 ct 131 -137 149 -156 157 -164 ct 171 -180 181 -194 186 -205 ct 192 -216 195 -227 195 -238 ct 195 -255 189 -269 177 -280 ct 164 -291 148 -297 129 -297 ct 115 -297 100 -294 85 -289 ct 69 -285 53 -277 35 -267 ct 35 -312 l 53 -319 70 -325 85 -329 ct 101 -332 115 -334 128 -334 ct 162 -334 189 -326 209 -309 ct 229 -292 240 -269 240 -240 ct 240 -227 237 -214 232 -202 ct 227 -190 218 -176 204 -159 ct 201 -155 189 -143 169 -123 ct 150 -102 122 -74 86 -37 ct p ef pom 0.500 c 13674 5048 m 12954 5048 l 12954 4047 l 14393 4047 l 14393 5048 l 13674 5048 l pc 0.898 c 13674 6048 m 12954 6048 l 12954 5048 l 14393 5048 l 14393 6048 l 13674 6048 l p ef 0.500 c 13674 6048 m 12954 6048 l 12954 5048 l 14393 5048 l 14393 6048 l 13674 6048 l pc pum 13303 5729 t 0.101 c 250 40 m 230 90 211 123 192 139 ct 173 154 148 162 117 162 ct 61 162 l 61 104 l 102 104 l 122 104 136 99 147 90 ct 158 81 169 59 182 25 ct 195 -6 l 23 -425 l 97 -425 l 230 -92 l 362 -425 l 436 -425 l 250 40 l p ef pom pum 13760 6055 t 170 -289 m 58 -114 l 170 -114 l 170 -289 l p 158 -328 m 214 -328 l 214 -114 l 261 -114 l 261 -77 l 214 -77 l 214 1 l 170 1 l 170 -77 l 22 -77 l 22 -120 l 158 -328 l p ef pom 0.898 c 13674 7047 m 12954 7047 l 12954 6046 l 14393 6046 l 14393 7047 l 13674 7047 l p ef 0.500 c 13674 7047 m 12954 7047 l 12954 6046 l 14393 6046 l 14393 7047 l 13674 7047 l pc pum 13303 6728 t 0.101 c 250 40 m 230 90 211 123 192 139 ct 173 154 148 162 117 162 ct 61 162 l 61 104 l 102 104 l 122 104 136 99 147 90 ct 158 81 169 59 182 25 ct 195 -6 l 23 -425 l 97 -425 l 230 -92 l 362 -425 l 436 -425 l 250 40 l p ef pom pum 13760 7053 t 49 -328 m 223 -328 l 223 -291 l 89 -291 l 89 -211 l 96 -213 102 -215 109 -216 ct 115 -217 121 -217 128 -217 ct 165 -217 194 -207 215 -187 ct 236 -167 247 -140 247 -106 ct 247 -70 236 -43 214 -23 ct 192 -4 161 6 121 6 ct 107 6 93 5 79 2 ct 65 0 50 -3 35 -8 ct 35 -53 l 48 -46 62 -40 76 -37 ct 90 -33 105 -31 120 -31 ct 146 -31 166 -38 180 -51 ct 195 -65 203 -83 203 -106 ct 203 -129 195 -147 180 -160 ct 166 -173 146 -180 120 -180 ct 108 -180 97 -179 85 -176 ct 73 -173 61 -169 49 -164 ct 49 -328 l p ef pom 0.500 c 13674 8047 m 12954 8047 l 12954 7047 l 14393 7047 l 14393 8047 l 13674 8047 l pc 13669 9047 m 12949 9047 l 12949 8047 l 14389 8047 l 14389 9047 l 13669 9047 l pc 0.898 c 13679 2043 m 12958 2043 l 12958 1047 l 14399 1047 l 14399 2043 l 13679 2043 l p ef 0.500 c 13679 2043 m 12958 2043 l 12958 1047 l 14399 1047 l 14399 2043 l 13679 2043 l pc pum 13308 1726 t 0.101 c 250 40 m 230 90 211 123 192 139 ct 173 154 148 162 117 162 ct 61 162 l 61 104 l 102 104 l 122 104 136 99 147 90 ct 158 81 169 59 182 25 ct 195 -6 l 23 -425 l 97 -425 l 230 -92 l 362 -425 l 436 -425 l 250 40 l p ef pom pum 13765 2052 t 143 -299 m 120 -299 103 -288 92 -265 ct 80 -243 74 -209 74 -164 ct 74 -119 80 -85 92 -63 ct 103 -40 120 -29 143 -29 ct 166 -29 183 -40 195 -63 ct 206 -85 212 -119 212 -164 ct 212 -209 206 -243 195 -265 ct 183 -288 166 -299 143 -299 ct p 143 -334 m 180 -334 208 -320 227 -291 ct 247 -262 256 -219 256 -164 ct 256 -109 247 -67 227 -38 ct 208 -9 180 6 143 6 ct 106 6 78 -9 59 -38 ct 39 -67 30 -109 30 -164 ct 30 -219 39 -262 59 -291 ct 78 -320 106 -334 143 -334 ct p ef pom 0.898 c 13679 3041 m 12958 3041 l 12958 2046 l 14399 2046 l 14399 3041 l 13679 3041 l p ef 0.500 c 13679 3041 m 12958 3041 l 12958 2046 l 14399 2046 l 14399 3041 l 13679 3041 l pc pum 13308 2725 t 0.101 c 250 40 m 230 90 211 123 192 139 ct 173 154 148 162 117 162 ct 61 162 l 61 104 l 102 104 l 122 104 136 99 147 90 ct 158 81 169 59 182 25 ct 195 -6 l 23 -425 l 97 -425 l 230 -92 l 362 -425 l 436 -425 l 250 40 l p ef pom pum 13765 3050 t 56 -37 m 128 -37 l 128 -288 l 49 -272 l 49 -312 l 128 -328 l 172 -328 l 172 -37 l 245 -37 l 245 0 l 56 0 l 56 -37 l p ef pom 0.898 c 13679 4051 m 12958 4051 l 12958 3056 l 14399 3056 l 14399 4051 l 13679 4051 l p ef 0.500 c 13679 4051 m 12958 4051 l 12958 3056 l 14399 3056 l 14399 4051 l 13679 4051 l pc pum 13308 3735 t 0.101 c 250 40 m 230 90 211 123 192 139 ct 173 154 148 162 117 162 ct 61 162 l 61 104 l 102 104 l 122 104 136 99 147 90 ct 158 81 169 59 182 25 ct 195 -6 l 23 -425 l 97 -425 l 230 -92 l 362 -425 l 436 -425 l 250 40 l p ef pom pum 13765 4060 t 86 -37 m 241 -37 l 241 0 l 33 0 l 33 -37 l 50 -55 73 -78 102 -108 ct 131 -137 149 -156 157 -164 ct 171 -180 181 -194 186 -205 ct 192 -216 195 -227 195 -238 ct 195 -255 189 -269 177 -280 ct 164 -291 148 -297 129 -297 ct 115 -297 100 -294 85 -289 ct 69 -285 53 -277 35 -267 ct 35 -312 l 53 -319 70 -325 85 -329 ct 101 -332 115 -334 128 -334 ct 162 -334 189 -326 209 -309 ct 229 -292 240 -269 240 -240 ct 240 -227 237 -214 232 -202 ct 227 -190 218 -176 204 -159 ct 201 -155 189 -143 169 -123 ct 150 -102 122 -74 86 -37 ct p ef pom pum 12062 5386 t 90 -386 m 620 -386 l 620 -316 l 90 -316 l 90 -386 l p 90 -216 m 620 -216 l 620 -146 l 90 -146 l 90 -216 l p ef pom pum 5121 839 t 504 -88 m 504 -254 l 368 -254 l 368 -323 l 587 -323 l 587 -58 l 555 -35 519 -17 480 -6 ct 441 6 400 12 356 12 ct 259 12 184 -16 129 -73 ct 75 -129 48 -208 48 -309 ct 48 -410 75 -489 129 -545 ct 184 -602 259 -630 356 -630 ct 396 -630 434 -625 470 -615 ct 507 -605 540 -590 571 -571 ct 571 -482 l 540 -508 507 -528 472 -541 ct 438 -554 401 -561 363 -561 ct 287 -561 230 -540 193 -498 ct 155 -455 136 -392 136 -309 ct 136 -225 155 -162 193 -120 ct 230 -78 287 -57 363 -57 ct 392 -57 419 -59 442 -64 ct 465 -70 486 -77 504 -88 ct p ef pom pum 10878 839 t 53 -618 m 143 -618 l 297 -388 l 451 -618 l 541 -618 l 342 -321 l 554 0 l 464 0 l 290 -263 l 115 0 l 25 0 l 246 -330 l 53 -618 l p ef pom pum 13410 839 t -2 -619 m 88 -619 l 259 -364 l 429 -619 l 519 -619 l 301 -295 l 301 0 l 217 0 l 217 -295 l -2 -619 l p ef pom pum 234 1696 t 504 -88 m 504 -254 l 368 -254 l 368 -323 l 587 -323 l 587 -58 l 555 -35 519 -17 480 -6 ct 441 6 400 12 356 12 ct 259 12 184 -16 129 -73 ct 75 -129 48 -208 48 -309 ct 48 -410 75 -489 129 -545 ct 184 -602 259 -630 356 -630 ct 396 -630 434 -625 470 -615 ct 507 -605 540 -590 571 -571 ct 571 -482 l 540 -508 507 -528 472 -541 ct 438 -554 401 -561 363 -561 ct 287 -561 230 -540 193 -498 ct 155 -455 136 -392 136 -309 ct 136 -225 155 -162 193 -120 ct 230 -78 287 -57 363 -57 ct 392 -57 419 -59 442 -64 ct 465 -70 486 -77 504 -88 ct p ef pom pum 890 2051 t 156 -326 m 131 -326 112 -314 100 -289 ct 87 -265 81 -228 81 -179 ct 81 -130 87 -93 100 -68 ct 112 -44 131 -31 156 -31 ct 181 -31 200 -44 213 -68 ct 225 -93 231 -130 231 -179 ct 231 -228 225 -265 213 -289 ct 200 -314 181 -326 156 -326 ct p 156 -364 m 196 -364 227 -349 248 -317 ct 269 -285 280 -239 280 -179 ct 280 -118 269 -72 248 -41 ct 227 -9 196 7 156 7 ct 116 7 85 -9 64 -41 ct 43 -72 32 -118 32 -179 ct 32 -239 43 -285 64 -317 ct 85 -349 116 -364 156 -364 ct p ef pom pum 234 2696 t 504 -88 m 504 -254 l 368 -254 l 368 -323 l 587 -323 l 587 -58 l 555 -35 519 -17 480 -6 ct 441 6 400 12 356 12 ct 259 12 184 -16 129 -73 ct 75 -129 48 -208 48 -309 ct 48 -410 75 -489 129 -545 ct 184 -602 259 -630 356 -630 ct 396 -630 434 -625 470 -615 ct 507 -605 540 -590 571 -571 ct 571 -482 l 540 -508 507 -528 472 -541 ct 438 -554 401 -561 363 -561 ct 287 -561 230 -540 193 -498 ct 155 -455 136 -392 136 -309 ct 136 -225 155 -162 193 -120 ct 230 -78 287 -57 363 -57 ct 392 -57 419 -59 442 -64 ct 465 -70 486 -77 504 -88 ct p ef pom pum 890 3051 t 61 -41 m 140 -41 l 140 -314 l 54 -297 l 54 -341 l 140 -358 l 188 -358 l 188 -41 l 267 -41 l 267 0 l 61 0 l 61 -41 l p ef pom pum 234 3696 t 504 -88 m 504 -254 l 368 -254 l 368 -323 l 587 -323 l 587 -58 l 555 -35 519 -17 480 -6 ct 441 6 400 12 356 12 ct 259 12 184 -16 129 -73 ct 75 -129 48 -208 48 -309 ct 48 -410 75 -489 129 -545 ct 184 -602 259 -630 356 -630 ct 396 -630 434 -625 470 -615 ct 507 -605 540 -590 571 -571 ct 571 -482 l 540 -508 507 -528 472 -541 ct 438 -554 401 -561 363 -561 ct 287 -561 230 -540 193 -498 ct 155 -455 136 -392 136 -309 ct 136 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438 -554 401 -561 363 -561 ct 287 -561 230 -540 193 -498 ct 155 -455 136 -392 136 -309 ct 136 -225 155 -162 193 -120 ct 230 -78 287 -57 363 -57 ct 392 -57 419 -59 442 -64 ct 465 -70 486 -77 504 -88 ct p ef pom pum 890 5051 t 199 -193 m 222 -188 241 -178 254 -162 ct 267 -146 273 -127 273 -104 ct 273 -69 261 -41 237 -22 ct 212 -3 178 7 133 7 ct 118 7 103 6 87 3 ct 71 0 54 -5 37 -11 ct 37 -57 l 51 -50 66 -44 82 -40 ct 98 -36 114 -34 132 -34 ct 162 -34 185 -40 201 -52 ct 217 -64 225 -81 225 -104 ct 225 -125 217 -141 203 -153 ct 188 -165 167 -171 141 -171 ct 99 -171 l 99 -211 l 143 -211 l 167 -211 185 -216 198 -225 ct 210 -235 216 -249 216 -267 ct 216 -285 210 -299 197 -309 ct 184 -319 165 -324 141 -324 ct 128 -324 113 -323 98 -320 ct 83 -317 66 -312 48 -306 ct 48 -349 l 67 -355 84 -358 100 -361 ct 116 -363 131 -365 145 -365 ct 182 -365 211 -356 233 -340 ct 254 -323 265 -300 265 -272 ct 265 -252 259 -235 248 -221 ct 236 -208 220 -198 199 -193 ct p ef pom pum 234 5696 t 504 -88 m 504 -254 l 368 -254 l 368 -323 l 587 -323 l 587 -58 l 555 -35 519 -17 480 -6 ct 441 6 400 12 356 12 ct 259 12 184 -16 129 -73 ct 75 -129 48 -208 48 -309 ct 48 -410 75 -489 129 -545 ct 184 -602 259 -630 356 -630 ct 396 -630 434 -625 470 -615 ct 507 -605 540 -590 571 -571 ct 571 -482 l 540 -508 507 -528 472 -541 ct 438 -554 401 -561 363 -561 ct 287 -561 230 -540 193 -498 ct 155 -455 136 -392 136 -309 ct 136 -225 155 -162 193 -120 ct 230 -78 287 -57 363 -57 ct 392 -57 419 -59 442 -64 ct 465 -70 486 -77 504 -88 ct p ef pom pum 890 6051 t 186 -315 m 63 -124 l 186 -124 l 186 -315 l p 173 -358 m 234 -358 l 234 -124 l 285 -124 l 285 -84 l 234 -84 l 234 1 l 186 1 l 186 -84 l 24 -84 l 24 -131 l 173 -358 l p ef pom pum 234 6696 t 504 -88 m 504 -254 l 368 -254 l 368 -323 l 587 -323 l 587 -58 l 555 -35 519 -17 480 -6 ct 441 6 400 12 356 12 ct 259 12 184 -16 129 -73 ct 75 -129 48 -208 48 -309 ct 48 -410 75 -489 129 -545 ct 184 -602 259 -630 356 -630 ct 396 -630 434 -625 470 -615 ct 507 -605 540 -590 571 -571 ct 571 -482 l 540 -508 507 -528 472 -541 ct 438 -554 401 -561 363 -561 ct 287 -561 230 -540 193 -498 ct 155 -455 136 -392 136 -309 ct 136 -225 155 -162 193 -120 ct 230 -78 287 -57 363 -57 ct 392 -57 419 -59 442 -64 ct 465 -70 486 -77 504 -88 ct p ef pom pum 890 7051 t 53 -358 m 243 -358 l 243 -317 l 97 -317 l 97 -230 l 104 -232 111 -234 118 -235 ct 125 -236 133 -237 140 -237 ct 179 -237 211 -226 234 -204 ct 258 -182 269 -152 269 -115 ct 269 -76 257 -46 234 -25 ct 210 -4 176 7 132 7 ct 117 7 102 6 86 3 ct 71 1 55 -3 38 -8 ct 38 -57 l 52 -49 67 -43 82 -40 ct 98 -36 114 -34 131 -34 ct 159 -34 181 -41 197 -56 ct 213 -70 221 -90 221 -115 ct 221 -140 213 -160 197 -174 ct 181 -189 159 -196 131 -196 ct 118 -196 105 -195 92 -192 ct 80 -189 66 -184 53 -178 ct 53 -358 l p ef pom pum 234 7696 t 504 -88 m 504 -254 l 368 -254 l 368 -323 l 587 -323 l 587 -58 l 555 -35 519 -17 480 -6 ct 441 6 400 12 356 12 ct 259 12 184 -16 129 -73 ct 75 -129 48 -208 48 -309 ct 48 -410 75 -489 129 -545 ct 184 -602 259 -630 356 -630 ct 396 -630 434 -625 470 -615 ct 507 -605 540 -590 571 -571 ct 571 -482 l 540 -508 507 -528 472 -541 ct 438 -554 401 -561 363 -561 ct 287 -561 230 -540 193 -498 ct 155 -455 136 -392 136 -309 ct 136 -225 155 -162 193 -120 ct 230 -78 287 -57 363 -57 ct 392 -57 419 -59 442 -64 ct 465 -70 486 -77 504 -88 ct p ef pom pum 890 8051 t 162 -198 m 140 -198 123 -191 110 -176 ct 98 -161 91 -141 91 -115 ct 91 -89 98 -69 110 -54 ct 123 -39 140 -31 162 -31 ct 184 -31 201 -39 214 -54 ct 226 -69 233 -89 233 -115 ct 233 -141 226 -161 214 -176 ct 201 -191 184 -198 162 -198 ct p 258 -350 m 258 -306 l 246 -312 234 -316 221 -319 ct 209 -322 197 -324 185 -324 ct 153 -324 128 -313 111 -291 ct 95 -270 85 -237 82 -193 ct 92 -207 104 -218 118 -225 ct 132 -233 148 -236 165 -236 ct 201 -236 229 -225 250 -204 ct 271 -182 281 -152 281 -115 ct 281 -78 271 -49 249 -26 ct 227 -4 198 7 162 7 ct 121 7 89 -9 67 -41 ct 45 -72 34 -118 34 -179 ct 34 -235 48 -281 75 -314 ct 101 -348 137 -365 183 -365 ct 195 -365 207 -364 219 -361 ct 232 -359 245 -355 258 -350 ct p ef pom pum 234 8796 t 504 -88 m 504 -254 l 368 -254 l 368 -323 l 587 -323 l 587 -58 l 555 -35 519 -17 480 -6 ct 441 6 400 12 356 12 ct 259 12 184 -16 129 -73 ct 75 -129 48 -208 48 -309 ct 48 -410 75 -489 129 -545 ct 184 -602 259 -630 356 -630 ct 396 -630 434 -625 470 -615 ct 507 -605 540 -590 571 -571 ct 571 -482 l 540 -508 507 -528 472 -541 ct 438 -554 401 -561 363 -561 ct 287 -561 230 -540 193 -498 ct 155 -455 136 -392 136 -309 ct 136 -225 155 -162 193 -120 ct 230 -78 287 -57 363 -57 ct 392 -57 419 -59 442 -64 ct 465 -70 486 -77 504 -88 ct p ef pom pum 890 9151 t 40 -358 m 270 -358 l 270 -337 l 140 0 l 90 0 l 212 -317 l 40 -317 l 40 -358 l p ef pom 31 lw 0.000 c 7108 10300 m 7057 10300 l ps 7006 10300 m 6955 10300 l ps 6904 10300 m 6853 10300 l ps 6802 10300 m 6751 10300 l ps 6700 10300 m 6649 10300 l ps 6598 10300 m 6547 10300 l ps 6496 10300 m 6445 10300 l ps 6394 10300 m 6343 10300 l ps 6292 10300 m 6241 10300 l ps 6190 10300 m 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1491 -120 ct 1496 -139 1498 -162 1498 -190 ct 1498 -216 1496 -239 1491 -257 ct 1487 -275 1481 -290 1472 -301 ct 1464 -313 1453 -321 1441 -326 ct 1429 -331 1414 -333 1398 -333 ct 1383 -333 1370 -331 1359 -325 ct 1348 -320 1339 -311 1332 -300 ct 1324 -288 1319 -273 1315 -254 ct 1312 -235 1310 -213 1310 -186 ct p ef 1972 -187 m 1972 -122 1958 -73 1929 -41 ct 1900 -9 1858 7 1804 7 ct 1778 7 1755 3 1734 -5 ct 1714 -13 1696 -24 1682 -41 ct 1668 -57 1657 -77 1650 -101 ct 1642 -125 1639 -154 1639 -187 ct 1639 -316 1694 -380 1806 -380 ct 1835 -380 1860 -376 1881 -368 ct 1902 -360 1919 -348 1933 -332 ct 1946 -315 1956 -295 1962 -271 ct 1969 -247 1972 -219 1972 -187 ct p 1907 -187 m 1907 -216 1905 -240 1900 -258 ct 1896 -277 1889 -292 1880 -304 ct 1872 -315 1861 -323 1849 -327 ct 1837 -332 1823 -334 1807 -334 ct 1791 -334 1777 -332 1764 -327 ct 1751 -322 1740 -314 1731 -303 ct 1722 -291 1716 -276 1711 -257 ct 1706 -239 1704 -215 1704 -187 ct 1704 -158 1706 -134 1711 -115 ct 1716 -96 1723 -81 1732 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countdictstack dict_count sub {end} repeat b4_inc_state restore %%PageTrailer %%Trailer %%EOF %%EndDocument @endspecial -262 986 a Fw(Fig.)33 b(3.)22 986 y SDict begin H.S end 22 986 a 22 986 a SDict begin H.R end 22 986 a 22 986 a SDict begin [/View [/XYZ H.V]/Dest (figure.3) cvn /DEST pdfmark end 22 986 a Fw(Example)g(of)g(matrix)h(G)e (for)g(a)h(generation)j(of)c(N=8)h(symbols)g(and)g(an)-262 1060 y(encoding)24 b(windo)n(w)e(of)f(size)i(W=5.)e(G)g(The)g(matrix)h (is)g(upper)o(-triangular)j(and)d(its)f(rank)-262 1135 y(is)k(equal)g(to)g(the)g(number)g(of)f(linearly)j(independent)h(pack)o (ets)e(recei)n(v)o(ed)i(by)c(the)h(node)-262 1210 y(\(5)k(in)h(the)f(e) o(xample\).)i(Ro)n(ws)e(1)g(and)h(2)f(are)g(suitable)j(for)d (recombination)j(gi)n(v)o(en)f(an)-262 1284 y(encoding)26 b(windo)n(w)f(of)e(leading)j(edge)f Fh(f)728 1261 y Fe(r)782 1284 y Fl(=)20 b(1)p Black -262 1552 a SDict begin H.S end -262 1552 a -262 1552 a SDict begin 12 H.A end -262 1552 a -262 1552 a SDict begin [/View 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1>>/Subtype /Link/Dest (prop.3) cvn H.B /ANN pdfmark end 196 2419 a 38 w Fv(states)38 b(that)f(ro)n(ws)g(of)g Ft(G)h Fv(are)f Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))p Fv(,)38 b(so)g(the)-262 2518 y(linear)26 b(combinations)f(thereof)g(is)i(a)g Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))28 b Fv(gi)n(v)o(en)d(the)h (recom-)-262 2618 y(bination)37 b(process)h(detailed)f(belo)n(w)h (formalized)e(as)j(Algorithm)1768 2618 y SDict begin H.S end 1768 2618 a Black Fv(2)p Black 1810 2561 a SDict begin H.R end 1810 2561 a 1810 2618 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (algorithm.2) cvn H.B /ANN pdfmark end 1810 2618 a Fv(.)-262 2718 y(First,)28 b(the)g(algorithm)e(dra)o(ws)h (the)h(encoding)d(windo)n(w)i(leading)g(edge)-262 2817 y Ft(f)-212 2787 y Fp(r)-140 2817 y Fv(from)33 b(the)i(distrib)n(ution) e Ft(H)7 b(D)754 2829 y Fp(N)s(;W)940 2817 y Fv(and)34 b(computes)f(the)i(relati)n(v)o(e)-262 2917 y(trailing)30 b(edge)f Ft(l)223 2887 y Fp(r)285 2917 y Fr(=)c Ft(f)425 2887 y Fp(r)481 2917 y Fr(+)19 b Ft(W)32 b Fn(\000)19 b Fr(1)p Fv(.)30 b(Let)g Ft(R)c Fr(=)g Fn(f)p Ft(G)1280 2929 y Fp(q)1310 2937 y Ff(0)1346 2917 y Ft(;)14 b(:)g(:)g(:)g(;)g(G) 1596 2929 y Fp(q)1626 2940 y Fd(j)p Fc(R)p Fd(j\000)p Ff(1)1789 2917 y Fn(g)-262 3017 y Fv(be)36 b(the)g(set)h(of)e(ro)n(ws)h (of)g Ft(G)g Fv(for)f(which)h Ft(s)1040 3029 y Fp(q)1070 3037 y Fc(i)1137 3017 y Fn(\025)h Ft(f)1289 2986 y Fp(r)1361 3017 y Fv(and)f Ft(t)1548 3029 y Fp(q)1578 3037 y Fc(i)1645 3017 y Fn(\024)g Ft(l)1773 2986 y Fp(r)1810 3017 y Fv(,)-262 3116 y(where)29 b Ft(s)10 3128 y Fp(q)40 3136 y Fc(i)102 3116 y Fv(and)g Ft(t)282 3128 y Fp(q)312 3136 y Fc(i)373 3116 y Fv(are)h(the)f(position)g(of)h(the)g(leading)e(and)i(trailing) -262 3216 y(one)40 b(of)h Ft(G)75 3228 y Fp(q)105 3236 y Fc(i)136 3216 y Fv(.)g(If)f Ft(R)46 b Fr(=)g Fn(;)p Fv(,)40 b(i.e.)h(there)f(are)g(no)h(suitable)f(ro)n(ws)h(for)-262 3315 y(recombination)22 b(as)k(it)f(may)g(happen)e(when)h(just)h(a)g (fe)n(w)g(pack)o(ets)g(ha)n(v)o(e)-262 3415 y(been)30 b(recei)n(v)o(ed,)f Ft(f)306 3385 y Fp(r)374 3415 y Fv(is)j(dra)o(wn)e (again.)f(The)i(encoding)e(v)o(ector)g Ft(g)1707 3385 y Fp(r)1775 3415 y Fv(is)-262 3515 y(no)n(w)f(calculated)f(as)h(a)h (linear)e(combination)f(of)i(the)g(elements)f(of)h Ft(R)q Fv(,)-262 3614 y(i.e.)j Ft(g)-86 3584 y Fp(r)-22 3614 y Fr(=)70 3552 y Fo(P)157 3573 y Fq(j)p Fp(R)p Fq(j\000)p Fs(1)157 3639 y Fp(i)p Fs(=0)350 3614 y Ft(c)386 3626 y Fp(i)414 3614 y Ft(G)479 3626 y Fp(q)509 3634 y Fc(i)571 3614 y Fv(where)f Ft(c)841 3626 y Fp(i)900 3614 y Fv(is)i(dra)o(wn)d (at)j(random)d(so)i(that)-262 3714 y Fm(P)p Fn(f)p Ft(c)-132 3726 y Fp(i)-67 3714 y Fr(=)39 b(1)p Fn(g)f Fr(=)272 3681 y Fs(1)p 272 3695 34 4 v 272 3743 a(2)316 3714 y Fv(.)f(Similarly)-5 b(,)36 b(the)h(payload)f Ft(y)1220 3684 y Fp(r)1294 3714 y Fv(is)i(calculated)e(as)-262 3828 y Ft(y)-218 3798 y Fp(r)-146 3828 y Fr(=)-46 3766 y Fo(P)42 3786 y Fq(j)p Fp(R)p Fq(j\000)p Fs(1)42 3853 y Fp(i)p Fs(=0)235 3828 y Ft(c)271 3840 y Fp(i)298 3828 y Ft(Y)346 3840 y Fp(q)376 3848 y Fc(i)407 3828 y Fv(.)g(Due)f(to)g (Prop.)952 3828 y SDict begin H.S end 952 3828 a Black Fv(2)p Black 993 3771 a SDict begin H.R end 993 3771 a 993 3828 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (prop.2) cvn H.B /ANN pdfmark end 993 3828 a Fv(,)h(the)f(recombined)e(pack)o(et) -262 3928 y Ft(P)-197 3897 y Fp(r)-118 3928 y Fv(calculated)41 b(by)g(Algorithm)775 3928 y SDict begin H.S end 775 3928 a Black Fv(2)p Black 816 3871 a SDict begin H.R end 816 3871 a 816 3928 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (algorithm.2) cvn H.B /ANN pdfmark end 816 3928 a 43 w Fv(is)h(a)g Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))p Fv(,)43 b(hence)e(the)-262 4027 y(recombination)19 b(process)i(preserv)o(es)f (the)i(pack)o(et)f(de)o(gree)f(distrib)n(ution)-262 4127 y(selected)29 b(at)g(the)f(source.)-262 4226 y(Figure)1 4227 y SDict begin H.S end 1 4227 a Black -1 x Fv(3)p Black 43 4170 a SDict begin H.R end 43 4170 a 43 4226 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (figure.3) cvn H.B /ANN pdfmark end 43 4226 a 46 w Fv(sho)n(ws)46 b(an)g(e)o(xample)e(of)i (the)f(recombination)e(process)-262 4326 y(where)48 b Ft(f)40 4296 y Fp(r)137 4326 y Fr(=)60 b(1)49 b Fv(and)f Ft(l)549 4296 y Fp(r)645 4326 y Fr(=)60 b(5)p Fv(.)49 b(In)f(this)h(e)o(xample,)e(ro)n(ws)i Ft(G)1793 4338 y Fs(1)-262 4426 y Fv(and)44 b Ft(G)-32 4438 y Fs(2)50 4426 y Fv(are)f(suitable)h(for)f(recombination.)e Ft(G)1249 4438 y Fs(1)1331 4426 y Fv(is)k(suitable)f(for)-262 4525 y(recombination)21 b(because)j(its)h(leading)e(and)g(trailing)h(edges)g (are)g(equal)-262 4625 y(to)36 b Ft(f)-111 4595 y Fp(r)-39 4625 y Fv(and)f Ft(l)144 4595 y Fp(r)180 4625 y Fv(,)h(respecti)n(v)o (ely)-5 b(.)33 b(While)j(the)g(trailing)f(edge)f(of)i Ft(G)1702 4637 y Fs(2)1775 4625 y Fv(is)-262 4725 y(greater)e(than)g Ft(l)209 4694 y Fp(r)245 4725 y Fv(,)h(its)h(trailing)e(one)g(is)h (equal)f(to)h Ft(l)1277 4694 y Fp(r)1313 4725 y Fv(,)g(so)g Ft(G)1543 4737 y Fs(2)1615 4725 y Fv(is)h(still)-262 4824 y(suitable)30 b(for)f(recombination.)d(As)31 b(this)f(e)o(xample)e (illustrates,)i(a)g(fe)n(w)-262 4924 y(ro)n(ws)41 b(of)f Ft(G)h Fv(only)f(may)g(be)g(suitable)g(for)g(recombination)e(due)i(to) -262 5023 y(the)j(constraint)f(on)g(the)h Ft(G)g Fv(ro)n(ws,)g (especially)f(during)f(the)i(initial)-262 5123 y(stages)f(of)f(the)g (transmission.)g(Ho)n(we)n(v)o(er)m(,)e(the)i(probability)e(that)j(a) -262 5223 y(pack)o(et)26 b(is)h(is)g(inno)o(v)n(ati)n(v)o(e)d(depends,) h(among)f(others,)i(on)g(the)g(number)-262 5322 y(of)i(independent)e (pack)o(ets)i(already)f(collected)h(by)g(the)g(recei)n(v)o(er)-5 b(.)27 b(The)-262 5422 y(decoding)19 b(process)i(proceeds)e(almost)i (in)g(parallel)f(at)i(all)f(the)g(netw)o(ork)-262 5522 y(nodes,)36 b(i.e.)h(all)h(the)f(nodes)f(ha)n(v)o(e)h(recei)n(v)o(ed)e (a)j(similar)f(number)e(of)-262 5621 y(pack)o(ets)25 b(at)h(a)g(gi)n(v)o(en)e(moment.)g(Therefore,)f(e)n(v)o(en)i(in)g(the)h (case)g(where)p Black Black 1930 -58 a(the)33 b(transmitter)g(has)g(fe) n(w)g(ro)n(ws)g(to)h(recombine,)d(also)i(the)g(recei)n(v)o(er)1930 42 y(has)c(recei)n(v)o(ed)e(fe)n(w)h(ro)n(ws)h(yet,)f(which)g (increases)h(the)f(probability)f(to)1930 142 y(encode)g(an)i(inno)o(v)n (ati)n(v)o(e)d(pack)o(et.)1930 259 y SDict begin H.S end 1930 259 a 1930 259 a SDict begin H.R end 1930 259 a 1930 259 a SDict begin [/View [/XYZ H.V]/Dest (algorithm.2) cvn /DEST pdfmark end 1930 259 a 1930 266 2093 7 v 81 x Fg(Algorithm)k(2)f Fv(P)o(ack)o(et)f(Recombination)p 1930 377 2093 4 v Black 1930 393 a SDict begin H.S end 1930 393 a 1930 393 a SDict begin 12 H.A end 1930 393 a 1930 393 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.14) cvn /DEST pdfmark end 1930 393 a Black 1978 456 a Fw(1:)p Black 42 w Ft(R)c Fr(=)f Fn(;)2316 456 y SDict begin H.S end 2316 456 a 2316 456 a SDict begin 12 H.A end 2316 456 a 2316 456 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.15) cvn /DEST pdfmark end 2316 456 a Black 1978 555 a Fw(2:)p Black 42 w Fg(while)29 b Ft(R)24 b Fr(=)f Fn(;)28 b Fg(do)1930 560 y SDict begin H.S end 1930 560 a 1930 560 a SDict begin 12 H.A end 1930 560 a 1930 560 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.16) cvn /DEST pdfmark end 1930 560 a Black 1978 655 a Fw(3:)p Black 125 w Fv(Dra)o(w)g Ft(f)2416 625 y Fp(r)2482 655 y Fv(as)h Ft(H)7 b(D)2725 667 y Fp(N)s(;W)2875 655 y Fr(\()p Ft(f)2957 625 y Fp(r)2994 655 y Fr(\))3055 655 y SDict begin H.S end 3055 655 a 3055 655 a SDict begin 12 H.A end 3055 655 a 3055 655 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.17) cvn /DEST pdfmark end 3055 655 a Black 1978 755 a Fw(4:)p Black 125 w Ft(R)24 b Fn( )29 b Fv(set)g(of)g(ro)n(ws)f(of)g Ft(G)h Fv(s.t.)g Ft(s)3118 767 y Fp(q)3148 775 y Fc(i)3202 755 y Fn(\025)23 b Ft(f)3340 724 y Fp(r)3405 755 y Fv(and)28 b Ft(t)3584 767 y Fp(q)3614 775 y Fc(i)3668 755 y Fn(\024)23 b Ft(l)3783 724 y Fp(r)1930 778 y SDict begin H.S end 1930 778 a 1930 778 a SDict begin 12 H.A end 1930 778 a 1930 778 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.18) cvn /DEST pdfmark end 1930 778 a Black 1978 854 a Fw(5:)p Black 42 w Fg(end)29 b(while)2418 854 y SDict begin H.S end 2418 854 a 2418 854 a SDict begin 12 H.A end 2418 854 a 2418 854 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.19) cvn /DEST pdfmark end 2418 854 a Black 1978 954 a Fw(6:)p Black 42 w Ft(g)2114 924 y Fp(r)2174 954 y Fr(=)2261 891 y Fo(P)2349 912 y Fq(j)p Fp(R)p Fq(j\000)p Fs(1)2349 979 y Fp(i)p Fs(=0)2542 954 y Ft(c)2578 966 y Fp(i)2605 954 y Ft(G)2670 966 y Fp(q)2700 974 y Fc(i)2731 954 y Fv(;)88 b Ft(y)2886 924 y Fp(r)2945 954 y Fr(=)3033 891 y Fo(P)3120 912 y Fq(j)p Fp(R)p Fq(j\000)p Fs(1)3120 979 y Fp(i)p Fs(=0)3313 954 y Ft(c)3349 966 y Fp(i)3377 954 y Ft(Y)3425 966 y Fp(q)3455 974 y Fc(i)3515 954 y SDict begin H.S end 3515 954 a 3515 954 a SDict begin 12 H.A end 3515 954 a 3515 954 a SDict begin [/View [/XYZ H.V]/Dest (ALC@unique.20) cvn /DEST pdfmark end 3515 954 a Black 1978 1053 a Fw(7:)p Black 42 w Fg(transmit)29 b Ft(P)2470 1023 y Fp(r)2506 1053 y Fr(\()p Ft(g)2581 1023 y Fp(r)2618 1053 y Ft(;)14 b(y)2699 1023 y Fp(r)2735 1053 y Fr(\))p Black 1930 1111 2093 4 v 1930 1342 a SDict begin H.S end 1930 1342 a 1930 1342 a SDict begin 12 H.A end 1930 1342 a 1930 1342 a SDict begin [/View [/XYZ H.V]/Dest (subsection.4.4) cvn /DEST pdfmark end 1930 1342 a 81 x Fu(D.)41 b(Modeling)28 b(the)g(Decoding)f(Comple)n(xity)h(of)h (BC)2013 1549 y Fv(W)-7 b(e)46 b(de\002ne)e(the)h Fu(decoding)e(comple) n(xity)h Fv(\()p Ft(C)3402 1561 y Fp(D)3463 1549 y Fv(\))h(of)f(BC)i (as)g(the)1930 1649 y(computational)41 b(comple)o(xity)f(of)j(the)g (SGE)g(algorithm)e(under)h(the)1930 1749 y(assumption)j(that)i(a)g (netw)o(ork)f(node)f(recei)n(v)o(es)h(pack)o(ets)g(that)h(are)1930 1848 y Ft(B)t(P)12 b Fr(\()p Ft(N)t(;)i(W)e Fr(\))p Fv(.)44 b(In)f(detail,)g(we)h(are)f(interested)g(in)h(calculating)e(the)1930 1948 y(a)n(v)o(erage)c(number)g(of)h(XOR)i(operations)c(between)i(ro)n (ws)h(required)1930 2048 y(to)26 b(reco)o(v)o(er)d(a)j(generation)d(as) j(a)g(function)e(of)h(the)g(generation)e(size)j Ft(N)1930 2147 y Fv(and)31 b(the)g(encoding)f(windo)n(w)g(size)i Ft(W)12 b Fv(.)32 b(The)f(decoding)e(comple)o(xity)1930 2247 y(can)f(be)g(calculated)f(as)i(the)f(sum)g(of)f(the)h(decoding)e (comple)o(xities)h(of)1930 2346 y(the)i(triangularization)c(and)j(the)h (diagonalization)d(stages.)1930 2446 y(The)48 b(decoding)e(comple)o (xity)g(of)i(the)g(triangularization)e(stage)i(is)1930 2551 y(de\002ned)37 b(as)i Ft(C)2386 2508 y Fs(\()p Fp(t)p Fs(\))2380 2575 y Fp(D)2506 2551 y Fv(and)e(increments)g(by)h(one)f (unit)h(e)n(v)o(ery)f(time)h(the)1930 2650 y(XOR)g(at)g(line)f(11)g(of) g(Algorithm)3015 2650 y SDict begin H.S end 3015 2650 a Black Fv(1)p Black 3056 2594 a SDict begin H.R end 3056 2594 a 3056 2650 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (algorithm.1) cvn H.B /ANN pdfmark end 3056 2650 a 38 w Fv(is)h(e)o(x)o(ecuted.)d(W)-7 b(e)39 b(conduct)c(a)1930 2750 y(w)o(orst)28 b(case)f(analysis)h(for)f(the)g(case)h(where)f(the)g (rank)g(of)g Ft(G)h Fv(is)g(equal)1930 2850 y(to)36 b Ft(k)j Fv(after)c(the)h Ft(k)s Fv(-th)f(pack)o(et)g(is)h(recei)n(v)o (ed,)e(i.e.)i(assuming)f(that)g(all)1930 2949 y(the)42 b(pack)o(ets)f(recei)n(v)o(ed)f(by)h(the)g(node)g(are)g(inno)o(v)n(ati) n(v)o(e.)e(Ho)n(we)n(v)o(er)m(,)1930 3049 y(this)d(model)e(turns)h(out) g(to)h(be)f(accurate)g(also)g(for)g(the)h(case)f(where)1930 3149 y Ft(r)r(ank)s Fr(\()p Ft(G)p Fr(\))27 b Ft(<)f(k)s Fv(,)k(as)h(sho)n(wn)f(in)g(Section)3174 3150 y SDict begin H.S end 3174 3150 a Black -1 x Fv(VI)p Black 3261 3093 a SDict begin H.R end 3261 3093 a 3261 3149 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (section.6) cvn H.B /ANN pdfmark end 3261 3149 a Fv(.)h(When)f(the)g Fr(\()p Ft(k)23 b Fr(+)c(1\))p Fv(-th)1930 3248 y(pack)o(et)h Ft(P)12 b Fr(\()p Ft(g)s(;)i(y)s Fr(\))21 b Fv(is)h(recei)n(v)o(ed,)d (the)i(maximum)f(number)f(of)h(ro)n(ws)h(of)g Ft(G)1930 3348 y Fv(with)k(whom)f Ft(P)37 b Fv(can)25 b(collide)f(is)i Ft(k)s Fv(.)f(On)f(the)h(other)f(hand,)g(since)h Ft(g)j Fv(has)1930 3447 y(a)n(v)o(erage)c(de)o(gree)2466 3415 y Fp(W)p 2466 3429 72 4 v 2485 3476 a Fs(2)2547 3447 y Fv(,)h(each)f(ro)n(w)h(will)g(collide)f(with)h(a)g(probability)e(of) 1950 3516 y Fp(W)p 1940 3530 92 4 v 1940 3577 a Fs(2)p Fp(N)2042 3548 y Fv(.)31 b(Therefore,)d(the)j(a)n(v)o(erage)e(number)g (of)h(collisions)h(that)f(happen)1930 3650 y(when)g(the)h Fr(\()p Ft(k)23 b Fr(+)d(1\))p Fv(-th)30 b(pack)o(et)h(is)g(recei)n(v)o (ed)f(is)h(equal)g(to)3713 3617 y Fp(k)p 3702 3631 59 4 v 3702 3679 a(N)3780 3617 y(W)p 3780 3631 72 4 v 3799 3679 a Fs(2)3862 3650 y Fv(.)g(So,)1930 3750 y(the)e(decoding)d(comple) o(xity)g(of)j(the)f(triangularization)e(stage)j(is)2427 4002 y Ft(C)2492 3958 y Fs(\()p Fp(t)p Fs(\))2486 4026 y Fp(D)2597 4002 y Fr(=)2685 3898 y Fp(N)6 b Fq(\000)p Fs(1)2696 3923 y Fo(X)2696 4101 y Fp(k)q Fs(=1)2852 3945 y Ft(k)s(W)p 2852 3982 136 4 v 2861 4059 a Fr(2)p Ft(N)3021 4002 y Fr(=)3119 3945 y Ft(W)12 b Fr(\()p Ft(N)27 b Fn(\000)18 b Fr(2\))p 3119 3982 374 4 v 3284 4059 a(4)3502 4002 y Ft(:)1930 4223 y Fv(The)33 b(decoding)e(comple)o(xity)h(of)h(the)g (diagonalization)e(stage)j(is)g(de-)1930 4327 y(\002ned)27 b(as)g Ft(C)2285 4284 y Fs(\()p Fp(d)p Fs(\))2279 4352 y Fp(D)2404 4327 y Fv(and)f(increments)g(by)g(one)h(unit)f(e)n(v)o(ery) g(time)h(an)g(XOR)1930 4427 y(is)37 b(e)o(x)o(ecuted.)d(The)i(number)f (of)g(required)g(XORs)i(depends)e(on)h(the)1930 4527 y(density)26 b(of)h(the)f Ft(G)i Fv(matrix,)e(that)h(is)g(on)g(the)f (number)f(of)i(elements)f(of)1930 4626 y Ft(G)32 b Fv(that)g(are)f (equal)g(to)h(1)f(e)o(xcept)f(for)h(those)g(on)g(the)h(diagonal.)e Ft(G)i Fv(is)1930 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grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & De\ velopment) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec 69d900414434c93d12731064fd536c430f0d1610cd3375452676cd606a5bb242 c10907a5bd9376f92a21ad5b1848a71c72c2b1f2e98fc6dbfb2e6c7d58f554dd 1e867bfc4b07a94035a628f3e0ae48fd1aae1cd99ea9bd6a0c2a5cfb81777d13 ff195e956f8556495b0e331dfab4b85e7ed17e24a88bdd49ed1e6a99e1ea53bd 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(gnuplot) % /Keywords () /CreationDate (Mon Jan 28 14:41:31 2013) /DOCINFO pdfmark end } ifelse end %%EndProlog %%Page: 1 1 gnudict begin gsave doclip 50 50 translate 0.100 0.100 scale 90 rotate 0 -5040 translate 0 setgray newpath (NimbusSanL-Regu) findfont 320 scalefont setfont BackgroundColor 0 lt 3 1 roll 0 lt exch 0 lt or or not {gsave BackgroundColor C clippath fill grestore} if 1.000 UL LTb 1.000 UL LTa 1760 1344 M 4863 0 V stroke LTb 1760 1344 M 63 0 V 4800 0 R -63 0 V stroke 1568 1344 M [ [(NimbusSanL-Regu) 320.0 0.0 true true 0 ( 0.01)] ] -106.7 MRshow 1.000 UL LTb 1.000 UL LTa 1760 1817 M 4863 0 V stroke LTb 1760 1817 M 63 0 V 4800 0 R -63 0 V stroke 1568 1817 M [ [(NimbusSanL-Regu) 320.0 0.0 true true 0 ( 0.02)] ] -106.7 MRshow 1.000 UL LTb 1.000 UL LTa 1760 2290 M 4863 0 V stroke LTb 1760 2290 M 63 0 V 4800 0 R -63 0 V stroke 1568 2290 M [ [(NimbusSanL-Regu) 320.0 0.0 true true 0 ( 0.03)] ] -106.7 MRshow 1.000 UL LTb 1.000 UL LTa 1760 2763 M 4863 0 V stroke LTb 1760 2763 M 63 0 V 4800 0 R -63 0 V stroke 1568 2763 M [ [(NimbusSanL-Regu) 320.0 0.0 true true 0 ( 0.04)] ] -106.7 MRshow 1.000 UL LTb 1.000 UL LTa 1760 3236 M 4863 0 V stroke LTb 1760 3236 M 63 0 V 4800 0 R -63 0 V stroke 1568 3236 M [ [(NimbusSanL-Regu) 320.0 0.0 true true 0 ( 0.05)] ] -106.7 MRshow 1.000 UL LTb 1.000 UL LTa 1760 3709 M 4863 0 V stroke LTb 1760 3709 M 63 0 V 4800 0 R -63 0 V stroke 1568 3709 M [ [(NimbusSanL-Regu) 320.0 0.0 true true 0 ( 0.06)] ] -106.7 MRshow 1.000 UL LTb 1.000 UL LTa 1760 4182 M 4863 0 V stroke LTb 1760 4182 M 63 0 V 4800 0 R -63 0 V stroke 1568 4182 M [ [(NimbusSanL-Regu) 320.0 0.0 true true 0 ( 0.07)] ] -106.7 MRshow 1.000 UL LTb 1.000 UL LTa 1760 4655 M 4863 0 V stroke LTb 1760 4655 M 63 0 V 4800 0 R -63 0 V stroke 1568 4655 M [ [(NimbusSanL-Regu) 320.0 0.0 true true 0 ( 0.08)] ] -106.7 MRshow 1.000 UL LTb 1.000 UL LTa 1760 1344 M 0 3311 V stroke LTb 1760 1344 M 0 63 V 0 3248 R 0 -63 V stroke 1760 1024 M [ [(NimbusSanL-Regu) 320.0 0.0 true true 0 ( 0.8)] ] 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/ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 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translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & De\ velopment) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec 69d900414434c93d12731064fd536c430f0d1610cd3375452676cd606a5bb242 c10907a5bd9376f92a21ad5b1848a71c72c2b1f2e98fc6dbfb2e6c7d58f554dd 1e867bfc4b07a94035a628f3e0ae48fd1aae1cd99ea9bd6a0c2a5cfb81777d13 ff195e956f8556495b0e331dfab4b85e7ed17e24a88bdd49ed1e6a99e1ea53bd 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2 copy moveto vpt 90 450 arc} bind def /C1 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath} bind def /C2 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C3 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath} bind def /C4 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath} bind def /C5 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc} bind def /C6 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath} bind def /C7 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath} bind def /C8 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C9 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc 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moveto 0 vpt rlineto BL Bsquare} bind def /S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def /S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def /S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare} bind def /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare} bind def /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup 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sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare} bind def /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare} bind def /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & De\ velopment) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec 69d900414434c93d12731064fd536c430f0d1610cd3375452676cd606a5bb242 c10907a5bd9376f92a21ad5b1848a71c72c2b1f2e98fc6dbfb2e6c7d58f554dd 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{gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & De\ velopment) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec 69d900414434c93d12731064fd536c430f0d1610cd3375452676cd606a5bb242 c10907a5bd9376f92a21ad5b1848a71c72c2b1f2e98fc6dbfb2e6c7d58f554dd 1e867bfc4b07a94035a628f3e0ae48fd1aae1cd99ea9bd6a0c2a5cfb81777d13 ff195e956f8556495b0e331dfab4b85e7ed17e24a88bdd49ed1e6a99e1ea53bd 56db08d1b932c6f8710f4f02883a38439bbb0802fab586d7afd17c75c2c867dc 8595e7f5d98f9a3c5a1e366b3823919841929cc44f5fe6d2a0393fdebd1d14ef b6fae1fa9d15b5c57b3b3e241b704a53dd0f8d1edf05b0d574935acd7a667a8e 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exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} 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} bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def 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2 dl2 1 dl1 2 dl2] LC7 DL} def /LT8 {PL [2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 4 dl2] LC8 DL} def /Pnt {stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore} def /Dia {stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt} def /Pls {stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box {stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt} def /Crs {stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke} def /TriU {stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt} def /Star {2 copy Pls Crs} def /BoxF {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill} def /TriUF {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill} def /TriD {stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt} def /TriDF {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill} def /Pent {stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt} def /PentF {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore} def /Circle {stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt} def /CircleF {stroke [] 0 setdash hpt 0 360 arc fill} def /C0 {BL [] 0 setdash 2 copy moveto vpt 90 450 arc} bind def /C1 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath} bind def /C2 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C3 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath} bind def /C4 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath} bind def /C5 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc} bind def /C6 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath} bind def /C7 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath} bind def /C8 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C9 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath} bind def /C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C11 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C12 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C13 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C14 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc} bind def /C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath} bind def /Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath} bind def /Square {dup Rec} bind def /Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def /S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def /S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def /S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def /S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare} bind def /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare} bind def /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & De\ velopment) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec 69d900414434c93d12731064fd536c430f0d1610cd3375452676cd606a5bb242 c10907a5bd9376f92a21ad5b1848a71c72c2b1f2e98fc6dbfb2e6c7d58f554dd 1e867bfc4b07a94035a628f3e0ae48fd1aae1cd99ea9bd6a0c2a5cfb81777d13 ff195e956f8556495b0e331dfab4b85e7ed17e24a88bdd49ed1e6a99e1ea53bd 56db08d1b932c6f8710f4f02883a38439bbb0802fab586d7afd17c75c2c867dc 8595e7f5d98f9a3c5a1e366b3823919841929cc44f5fe6d2a0393fdebd1d14ef b6fae1fa9d15b5c57b3b3e241b704a53dd0f8d1edf05b0d574935acd7a667a8e 8743b27e906be3128e9943b31050d63500866cdaab6903605abffe737e95baa8 cad2c6cd5380ff5961ccbc56980823ae0dc1f87ec51d79b152eaf1610afc7d0a 7275025ea45420cb6462ff426fd3a0f9f6356012188b3b072c9b3ac6e09e111e 66f203b84b28fa74e02f510bf39a9cb0da968a5287382c753a24e4b9b2a1b1b9 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setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & De\ velopment) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec 69d900414434c93d12731064fd536c430f0d1610cd3375452676cd606a5bb242 c10907a5bd9376f92a21ad5b1848a71c72c2b1f2e98fc6dbfb2e6c7d58f554dd 1e867bfc4b07a94035a628f3e0ae48fd1aae1cd99ea9bd6a0c2a5cfb81777d13 ff195e956f8556495b0e331dfab4b85e7ed17e24a88bdd49ed1e6a99e1ea53bd 56db08d1b932c6f8710f4f02883a38439bbb0802fab586d7afd17c75c2c867dc 8595e7f5d98f9a3c5a1e366b3823919841929cc44f5fe6d2a0393fdebd1d14ef 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Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & De\ velopment) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec 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{PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 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setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & De\ velopment) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec 69d900414434c93d12731064fd536c430f0d1610cd3375452676cd606a5bb242 c10907a5bd9376f92a21ad5b1848a71c72c2b1f2e98fc6dbfb2e6c7d58f554dd 1e867bfc4b07a94035a628f3e0ae48fd1aae1cd99ea9bd6a0c2a5cfb81777d13 ff195e956f8556495b0e331dfab4b85e7ed17e24a88bdd49ed1e6a99e1ea53bd 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vpt 2 mul def /hpt2 hpt 2 mul def /Lshow {currentpoint stroke M 0 vshift R Blacktext {gsave 0 setgray show grestore} {show} ifelse} def /Rshow {currentpoint stroke M dup stringwidth pop neg vshift R Blacktext {gsave 0 setgray show grestore} {show} ifelse} def /Cshow {currentpoint stroke M dup stringwidth pop -2 div vshift R Blacktext {gsave 0 setgray show grestore} {show} ifelse} def /UP {dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def} def /DL {Color {setrgbcolor Solid {pop []} if 0 setdash} {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse} def /BL {stroke userlinewidth 2 mul setlinewidth Rounded {1 setlinejoin 1 setlinecap} if} def /AL {stroke userlinewidth 2 div setlinewidth Rounded {1 setlinejoin 1 setlinecap} if} def /UL {dup gnulinewidth mul /userlinewidth exch def dup 1 lt {pop 1} if 10 mul /udl exch def} def /PL {stroke userlinewidth setlinewidth Rounded {1 setlinejoin 1 setlinecap} if} def % Default Line colors /LCw {1 1 1} def /LCb {0 0 0} def /LCa {0 0 0} def /LC0 {1 0 0} def /LC1 {0 1 0} def /LC2 {0 0 1} def /LC3 {1 0 1} def /LC4 {0 1 1} def /LC5 {1 1 0} def /LC6 {0 0 0} def /LC7 {1 0.3 0} def /LC8 {0.5 0.5 0.5} def % Default Line Types /LTw {PL [] 1 setgray} def /LTb {BL [] LCb DL} def /LTa {AL [1 udl mul 2 udl mul] 0 setdash LCa setrgbcolor} def /LT0 {PL [] LC0 DL} def /LT1 {PL [4 dl1 2 dl2] LC1 DL} def /LT2 {PL [2 dl1 3 dl2] LC2 DL} def /LT3 {PL [1 dl1 1.5 dl2] LC3 DL} def /LT4 {PL [6 dl1 2 dl2 1 dl1 2 dl2] LC4 DL} def /LT5 {PL [3 dl1 3 dl2 1 dl1 3 dl2] LC5 DL} def /LT6 {PL [2 dl1 2 dl2 2 dl1 6 dl2] LC6 DL} def /LT7 {PL [1 dl1 2 dl2 6 dl1 2 dl2 1 dl1 2 dl2] LC7 DL} def /LT8 {PL [2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 2 dl2 2 dl1 4 dl2] LC8 DL} def /Pnt {stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore} def /Dia {stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt} def /Pls {stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box {stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt} def /Crs {stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke} def /TriU {stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt} def /Star {2 copy Pls Crs} def /BoxF {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill} def /TriUF {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill} def /TriD {stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt} def /TriDF {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill} def /Pent {stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt} def /PentF {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore} def /Circle {stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt} def /CircleF {stroke [] 0 setdash hpt 0 360 arc fill} def /C0 {BL [] 0 setdash 2 copy moveto vpt 90 450 arc} bind def /C1 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath} bind def /C2 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C3 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath} bind def /C4 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath} bind def /C5 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc} bind def /C6 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath} bind def /C7 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath} bind def /C8 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C9 {BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath} bind def /C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath} bind def /C11 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath} bind def /C12 {BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C13 {BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath} bind def /C14 {BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc} bind def /C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath} bind def /Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath} bind def /Square {dup Rec} bind def /Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def /S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def /S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def /S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def /S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def /S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare} bind def /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare} bind def /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def /DiaE {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke} def /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke} def /TriUE {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke} def /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke} def /PentE {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore} def /CircE {stroke [] 0 setdash hpt 0 360 arc stroke} def /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def /DiaW {stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke} def /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke} def /TriUW {stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke} def /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke} def /PentW {stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore} def /CircW {stroke [] 0 setdash hpt 0 360 arc Opaque stroke} def /BoxFill {gsave Rec 1 setgray fill grestore} def /Density { /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor} def /BoxColFill {gsave Rec PolyFill} def /PolyFill {gsave Density fill grestore grestore} def /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def % % PostScript Level 1 Pattern Fill routine for rectangles % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill {gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 M 0 PFs V} for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi {PFa 4 get mul 0 2 1 roll M PFs 0 V} for } if stroke grestore} def % /languagelevel where {pop languagelevel} {1} ifelse 2 lt {/InterpretLevel1 true def} {/InterpretLevel1 Level1 def} ifelse % % PostScript level 2 pattern fill definitions % /Level2PatternFill { /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8} bind def /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} >> matrix makepattern /Pat1 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke 0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke} >> matrix makepattern /Pat2 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L 8 8 L 8 0 L 0 0 L fill} >> matrix makepattern /Pat3 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L 0 12 M 12 0 L stroke} >> matrix makepattern /Pat4 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L 0 -4 M 12 8 L stroke} >> matrix makepattern /Pat5 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L 0 12 M 8 -4 L 4 12 M 10 0 L stroke} >> matrix makepattern /Pat6 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L 0 -4 M 8 12 L 4 -4 M 10 8 L stroke} >> matrix makepattern /Pat7 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L 12 0 M -4 8 L 12 4 M 0 10 L stroke} >> matrix makepattern /Pat8 exch def << Tile8x8 /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L -4 0 M 12 8 L -4 4 M 8 10 L stroke} >> matrix makepattern /Pat9 exch def /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def } def % % %End of PostScript Level 2 code % /PatternBgnd { TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse } def % % Substitute for Level 2 pattern fill codes with % grayscale if Level 2 support is not selected. % /Level1PatternFill { /Pattern1 {0.250 Density} bind def /Pattern2 {0.500 Density} bind def /Pattern3 {0.750 Density} bind def /Pattern4 {0.125 Density} bind def /Pattern5 {0.375 Density} bind def /Pattern6 {0.625 Density} bind def /Pattern7 {0.875 Density} bind def } def % % Now test for support of Level 2 code % Level1 {Level1PatternFill} {Level2PatternFill} ifelse % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} def /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse } {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def /MLshow { currentpoint stroke M 0 exch R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def /XYsave { [( ) 1 2 true false 3 ()] } bind def /XYrestore { [( ) 1 2 true false 4 ()] } bind def %%BeginProcSet: /usr/share/texmf-texlive/fonts/type1/urw/helvetic/uhvr8a.pfb %!PS-AdobeFont-1.0: NimbusSanL-Regu 1.05a %%Title: NimbusSanL-Regu %%CreationDate: Thu Mar 20 10:08:51 2003 %%Creator: Primoz Peterlin %%DocumentSuppliedResources: font NimbusSanL-Regu % Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development % Generated by PfaEdit 1.0 (http://pfaedit.sf.net/) %%EndComments FontDirectory/NimbusSanL-Regu known{/NimbusSanL-Regu findfont dup/UniqueID known{dup /UniqueID get 5020902 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /NimbusSanL-Regu def /FontBBox [-174 -285 1001 953 ]readonly def /UniqueID 5020902 def /PaintType 0 def /FontInfo 9 dict dup begin /version (1.05a) readonly def /Notice (Copyright \050URW\051++,Copyright 1999 by \050URW\051++ Design & De\ velopment) readonly def /FullName (Nimbus Sans L Regular) readonly def /FamilyName (Nimbus Sans L) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -151 def /UnderlineThickness 50 def end readonly def /Encoding StandardEncoding def currentdict end currentfile eexec 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4948 y Ff(1)1107 5039 y Fc(d)1138 5027 y Ff(2)1170 5039 y Fd(\000)1225 5019 y Fc(d)1256 5007 y Ff(1)1288 5019 y(+)p Fc(d)1362 5007 y Ff(2)1394 5019 y Fd(\000)p Fc(d)1470 5007 y(r)p 1225 5030 V 1350 5061 a Ff(2)1513 5011 y Fr(\))p 712 5068 834 4 v 1065 5133 a(\()1104 5100 y Fc(N)1097 5147 y(d)1128 5135 y Ff(2)1160 5133 y Fr(\))1555 5087 y Ft(:)-262 5279 y Fv(F)o(or)28 b(the)h(la)o(w)g(of)f(total)g(probability)-5 b(,)26 b(we)j(ha)n(v)o(e)f(that)110 5543 y SDict begin H.S end 110 5543 a 110 5543 a SDict begin 12 H.A end 110 5543 a 110 5543 a SDict begin [/View [/XYZ H.V]/Dest (equation.Appendix.A.3) cvn /DEST pdfmark end 110 5543 a Fr(\012)170 5503 y Fp(j)170 5566 y(i)228 5543 y Fr(=)362 5439 y Fp(N)332 5464 y Fo(X)316 5646 y Fp(d)351 5629 y Ff(1)383 5646 y Fs(=0)527 5439 y Fp(N)496 5464 y Fo(X)481 5646 y Fp(d)516 5629 y Ff(2)548 5646 y Fs(=0)646 5543 y Ft(s)685 5555 y Fp(N)748 5543 y Fr(\()p Ft(d)823 5509 y Fs(1)860 5543 y Ft(;)14 b(d)940 5509 y Fs(2)978 5543 y Ft(;)g(i)p Fr(\)\012)1136 5503 y Fp(j)s Fq(\000)p Fs(1)1136 5571 y Fp(d)1171 5555 y Ff(1)1255 5543 y Fr(\012)1315 5503 y Fp(j)s Fq(\000)p Fs(1)1315 5571 y Fp(d)1350 5555 y Ff(2)1435 5543 y Ft(:)276 b Fv(\(3\))p Black Black 1930 -58 a(W)-7 b(e)21 b(indicate)f(as)h Fr(\012)2493 -88 y Fq(1)2584 -58 y Fv(the)g(distrib)n(ution)e(of)h(the) g(de)o(gree)f(of)h(the)g(pack)o(ets)1930 42 y(in)26 b(the)g(netw)o(ork) f(after)h(a)h(number)d(of)i(recombinations)d(that)k(tends)f(to)1930 142 y(in\002nite.)d(If)h Fr(\012)2350 112 y Fs(0)2411 142 y Fv(is)g(not)g(de)o(generate,)d(we)j(ha)n(v)o(e)f(from)f(Equation) 3832 143 y SDict begin H.S end 3832 143 a Black -1 x Fv(3)p Black 3874 85 a SDict begin H.R end 3874 85 a 3874 142 a SDict begin [/Color [1 0 0]/H /I/Border [0 0 1]BorderArrayPatch/BS <</S/S/W 1>>/Subtype /Link/Dest (equation.Appendix.A.3) cvn H.B /ANN pdfmark end 3874 142 a 24 w Fv(that)2767 374 y Fr(\012)2827 340 y Fq(1)2827 395 y Fp(i)2920 374 y Fr(=)3018 245 y Fo(\000)3056 276 y Fp(N)3073 341 y(i)3115 245 y Fo(\001)p 3018 355 135 4 v 3033 431 a Fr(2)3075 407 y Fp(N)3163 374 y Ft(:)1930 564 y Fv(Therefore,)k(the)i(distrib)n (ution)f(of)g(the)h(de)o(gree)f(of)h(the)g(pack)o(ets)g(in)g(the)1930 664 y(netw)o(ork)35 b(follo)n(ws)h(the)h(Binomial)f(Distrib)n(ution)g Fn(B)s Fr(\()p Ft(N)t(;)3651 631 y Fs(1)p 3651 645 34 4 v 3651 692 a(2)3694 664 y Fr(\))i Fv(and)e(the)1930 765 y(a)n(v)o(erage)27 b(de)o(gree)g(of)i(the)f(pack)o(ets)g(in)h(the)f (netw)o(ork)g(tends)g(to)3802 732 y Fp(N)p 3802 746 59 4 v 3815 794 a Fs(2)3870 765 y Fv(.)2742 1016 y SDict begin H.S end 2742 1016 a 2742 1016 a SDict begin 12 H.A end 2742 1016 a 2742 1016 a SDict begin [/View [/XYZ H.V]/Dest (section*.3) cvn /DEST pdfmark end 2742 1016 a 2 w Fv(R)t Fw(E)t(F)t(E)t(R)t(E)t(N)t(C)t(E)t(S)1930 1093 y SDict begin H.S end 1930 1093 a 1930 1093 a SDict begin 9 H.A end 1930 1093 a 1930 1093 a SDict begin [/View [/XYZ H.V]/Dest (cite.fragouli2006network) cvn /DEST pdfmark end 1930 1093 a Black 1963 1167 a Fw([1])p Black 42 w(C.)22 b(Fragouli,)h(J.)e(Le)h(Boudec,)h(and)f(J.)f(W)m(idmer)m(,)i(\223Netw)o (ork)h(coding:)g(an)e(instant)2082 1241 y(primer,)-5 b(\224)30 b Fa(A)n(CM)e(SIGCOMM)i(Computer)g(Communication)h(Re)o(vie)o (w)p Fw(,)f(v)o(ol.)e(36,)2082 1316 y(no.)23 b(1,)h(p.)f(63,)g(2006.) 1930 1333 y SDict begin H.S end 1930 1333 a 1930 1333 a SDict begin 9 H.A end 1930 1333 a 1930 1333 a SDict begin [/View [/XYZ H.V]/Dest (cite.ahlswede2000network) cvn /DEST pdfmark end 1930 1333 a Black 1963 1393 a Fw([2])p Black 42 w(R.)d(Ahlswede,)i(N.)d(Cai,)i(S.)f(Li,)g(and)h(R.)f(Y)-7 b(eung,)21 b(\223Netw)o(ork)i(information)g(\003o)n(w)l(,)-5 b(\224)2082 1468 y Fa(IEEE)29 b(T)l(r)o(ansactions)j(on)f(Information)h (Theory)p Fw(,)f(v)o(ol.)f(46,)g(no.)g(4,)g(pp.)g(1204\226)2082 1543 y(1216,)24 b(2000.)1930 1555 y SDict begin H.S end 1930 1555 a 1930 1555 a SDict begin 9 H.A end 1930 1555 a 1930 1555 a SDict begin [/View [/XYZ H.V]/Dest (cite.wang2007r2) cvn /DEST pdfmark end 1930 1555 a Black 1963 1620 a Fw([3])p Black 42 w(M.)j(W)-5 b(ang)28 b(and)g(B.)g(Li,)f (\223R2)h(Random)h(push)f(with)h(random)f(netw)o(ork)h(coding)2082 1695 y(in)37 b(li)n(v)o(e)h(peer)o(-to-peer)h(streaming,)-5 b(\224)38 b Fa(IEEE)d(J)n(ournal)j(on)f(Selected)i(Ar)n(eas)d(in)2082 1770 y(Communications)p Fw(,)26 b(v)o(ol.)e(25,)f(no.)g(9,)g(pp.)h (1655\2261666,)g(2007.)1930 1786 y SDict begin H.S end 1930 1786 a 1930 1786 a SDict begin 9 H.A end 1930 1786 a 1930 1786 a SDict begin [/View [/XYZ H.V]/Dest (cite.wang2007network) cvn /DEST pdfmark end 1930 1786 a Black 1963 1847 a Fw([4])p Black 42 w(M.)18 b(W)-5 b(ang)18 b(and)h(Li,)e(\223Netw)o (ork)j(coding)g(in)e(li)n(v)o(e)i(peer)o(-to-peer)h(streaming,)-5 b(\224)20 b Fa(IEEE)2082 1922 y(T)l(r)o(ansactions)26 b(on)d(Multimedia)p Fw(,)j(v)o(ol.)e(9,)f(no.)g(8,)g(pp.)h (1554\2261567,)g(2007.)1930 1938 y SDict begin H.S end 1930 1938 a 1930 1938 a SDict begin 9 H.A end 1930 1938 a 1930 1938 a SDict begin [/View [/XYZ H.V]/Dest (cite.Mackay05fountaincodes) cvn /DEST pdfmark end 1930 1938 a Black 1963 1999 a Fw([5])p Black 42 w(D.)15 b(J.)g(C.)g(Mackay)l(,)i(\223F)o(ountain)h (codes,)-5 b(\224)17 b Fa(IEE)e(Communications)p Fw(,)j(v)o(ol.)d(152,) h(no.)f(6,)2082 2074 y(pp.)23 b(1062\2261068,)i(2005.)1930 2090 y SDict begin H.S end 1930 2090 a 1930 2090 a SDict begin 9 H.A end 1930 2090 a 1930 2090 a SDict begin [/View [/XYZ H.V]/Dest (cite.LT) cvn /DEST pdfmark end 1930 2090 a Black 1963 2151 a Fw([6])p Black 42 w(M.)39 b(Luby)l(,)f(\223L)-6 b(T)38 b(codes,)-5 b(\224)41 b(in)e Fa(Pr)m(oceedings)i(of)f(the)g(IEEE)d(Symposium)k(on)2082 2226 y(F)-7 b(oundations)25 b(of)f(Computer)h(Science)h(\(FOCS\))p Fw(,)d(2002,)h(pp.)f(271\226280.)1930 2242 y SDict begin H.S end 1930 2242 a 1930 2242 a SDict begin 9 H.A end 1930 2242 a 1930 2242 a SDict begin [/View [/XYZ H.V]/Dest (cite.raptor) cvn /DEST pdfmark end 1930 2242 a Black 1963 2303 a Fw([7])p Black 42 w(A.)41 b(Shokrollahi,)i(\223Raptor)h (Codes,)-5 b(\224)42 b Fa(IEEE)e(T)l(r)o(ansaction)j(on)f(Information) 2082 2378 y(Theory)p Fw(,)24 b(v)o(ol.)g(52,)f(no.)g(6,)g(pp.)g (2551\2262567,)i(2006.)1930 2394 y SDict begin H.S end 1930 2394 a 1930 2394 a SDict begin 9 H.A end 1930 2394 a 1930 2394 a SDict begin [/View [/XYZ H.V]/Dest (cite.icme2012BC) cvn /DEST pdfmark end 1930 2394 a Black 1963 2455 a Fw([8])p Black 42 w(A.)c(Fiandrotti,)j(V)-9 b(.)22 b(Bioglio,)h(M.)e(Grangetto,)j(E.)d(Magli,)i(and)f(R.)g(Gaeta,)h (\223Band)2082 2530 y(codes:)c(Comple)o(xity)i(adapti)n(v)o(e)g(netw)o (ork)e(coding)g(for)f(p2p)h(video)g(streaming,)-5 b(\224)20 b(in)2082 2604 y Fa(Pr)m(oceedings)28 b(of)f(the)g(IEEE)e (International)k(Confer)n(ence)g(on)d(Multimedia)k(and)2082 2679 y(Expo)24 b(\(ICME\))p Fw(,)f(2012,)h(pp.)f(194\226199.)1930 2696 y SDict begin H.S end 1930 2696 a 1930 2696 a SDict begin 9 H.A end 1930 2696 a 1930 2696 a SDict begin [/View [/XYZ H.V]/Dest (cite.fiandrotti2011complexity) cvn /DEST pdfmark end 1930 2696 a Black 1963 2756 a Fw([9])p Black 42 w(A.)31 b(Fiandrotti,)j(S.)d(Zezza,)h(and)g(E.)f(Magli,)h(\223Comple)o (xity-adapti)n(ve)37 b(random)2082 2831 y(netw)o(ork)d(coding)h(for)d (peer)o(-to-peer)k(video)e(streaming,)-5 b(\224)34 b(in)f Fa(Pr)m(oceedings)i(of)2082 2906 y(the)k(IEEE)e(International)42 b(W)-6 b(orkshop)39 b(on)g(Multimedia)i(Signal)f(Pr)m(ocessing)2082 2980 y(\(MMSP\))p Fw(,)24 b(2011,)f(pp.)h(1\2266.)1930 2997 y SDict begin H.S end 1930 2997 a 1930 2997 a SDict begin 9 H.A end 1930 2997 a 1930 2997 a SDict begin [/View [/XYZ H.V]/Dest (cite.toldo2010) cvn /DEST pdfmark end 1930 2997 a Black 61 x Fw([10])p Black 42 w(M.)17 b(T)-5 b(oldo)18 b(and)g(E.)f(Magli,)h(\223)-5 b(A)18 b(resilient)i(and)e(lo)n (w-delay)i(p2p)e(streaming)i(system)2082 3132 y(based)25 b(on)f(netw)o(ork)i(coding)f(with)g(random)f(multicast)i(trees,)-5 b(\224)26 b(in)e Fa(Pr)m(oceedings)2082 3207 y(of)k(the)g(IEEE)e (International)k(W)-6 b(orkshop)28 b(on)f(Multimedia)j(Signal)f(Pr)m (ocessing)2082 3282 y(\(MMSP\))p Fw(,)24 b(2010,)f(pp.)h(400\226405.) 1930 3299 y SDict begin H.S end 1930 3299 a 1930 3299 a SDict begin 9 H.A end 1930 3299 a 1930 3299 a SDict begin [/View [/XYZ H.V]/Dest (cite.vingelmann2010) cvn /DEST pdfmark end 1930 3299 a Black 60 x Fw([11])p Black 42 w(P)-7 b(.)28 b(V)l(ingelmann,)j(M.)e(V)-9 b(.)29 b(Pedersen,)h(F)-5 b(.)28 b(H.)h(P)-7 b(.)28 b(Fitzek,)i(and)g(J.)f(Heide,)h(\223Mul-)2082 3434 y(timedia)g(distrib)o(ution)g(using)e(netw)o(ork)h(coding)g(on)e (the)h(iphone)h(platform,)-5 b(\224)30 b(in)2082 3509 y Fa(Pr)m(oceedings)c(of)f(the)h(A)n(CM)e(multimedia)j(workshop)f(on)f (Mobile)h(cloud)g(media)2082 3583 y(computing)g(\(MCMC\))p Fw(,)e(2010,)g(pp.)f(3\2266.)1930 3600 y SDict begin H.S end 1930 3600 a 1930 3600 a SDict begin 9 H.A end 1930 3600 a 1930 3600 a SDict begin [/View [/XYZ H.V]/Dest (cite.shojania2009random) cvn /DEST pdfmark end 1930 3600 a Black 61 x Fw([12])p Black 42 w(H.)28 b(Shojania)j(and)e(B.)g(Li,)f (\223Random)i(netw)o(ork)g(coding)g(on)f(the)h(iphone:)g(f)o(act)2082 3735 y(or)37 b(\002ction?\224)h(in)f Fa(Pr)m(oceedings)h(of)f(the)g(A)n (CM)f(International)k(W)-6 b(orkshop)37 b(on)2082 3810 y(Network)30 b(and)e(Oper)o(ating)i(Systems)f(Support)g(for)g(Digital)h (A)o(udio)e(and)g(V)-5 b(ideo)2082 3885 y(\(NOSSD)n(A)e(V\))p Fw(,)23 b(2009,)g(pp.)h(37\22642.)1930 3902 y SDict begin H.S end 1930 3902 a 1930 3902 a SDict begin 9 H.A end 1930 3902 a 1930 3902 a SDict begin [/View [/XYZ H.V]/Dest (cite.heide2008cautious) cvn /DEST pdfmark end 1930 3902 a Black 60 x Fw([13])p Black 42 w(J.)42 b(Heide,)h(M.)f(Pedersen,)h(F)-5 b(.)42 b(Fitzek,)h(and)g(T)-5 b(.)42 b(Larsen,)g(\223Cautious)j(vie)n (w)2082 4037 y(on)36 b(netw)o(ork)i(coding-from)g(theory)f(to)f (practice,)-5 b(\224)39 b Fa(KICS-IEEE)d(J)n(ournal)i(of)2082 4111 y(Communications)20 b(and)d(Networks)h(\(JCN\))p Fw(,)f(v)o(ol.)f(10,)h(no.)f(4,)g(pp.)g(403\226411,)i(2008.)1930 4128 y SDict begin H.S end 1930 4128 a 1930 4128 a SDict begin 9 H.A end 1930 4128 a 1930 4128 a SDict begin [/View [/XYZ H.V]/Dest (cite.Angelopoulos:2011:EHI:2039912.2039928) cvn /DEST pdfmark end 1930 4128 a Black 61 x Fw([14])p Black 42 w(G.)23 b(Angelopoulos,)j (M.)d(M)t(\264)-26 b(edard,)25 b(and)g(A.)e(P)-7 b(.)23 b(Chandrakasan,)j(\223Ener)o(gy-a)o(w)o(are)2082 4263 y(hardw)o(are)19 b(implementation)g(of)e(netw)o(ork)h(coding,)-5 b(\224)18 b(in)e Fa(Pr)m(oceedings)i(of)f(the)g(IFIP)2082 4338 y(TC)h(6th)h(international)j(confer)n(ence)f(on)d(Networking)p Fw(.)51 b(Springer)o(-V)-7 b(erlag,)21 b(2011,)2082 4413 y(pp.)i(137\226144.)1930 4430 y SDict begin H.S end 1930 4430 a 1930 4430 a SDict begin 9 H.A end 1930 4430 a 1930 4430 a SDict begin [/View [/XYZ H.V]/Dest (cite.lucani2009random) cvn /DEST pdfmark end 1930 4430 a Black 60 x Fw([15])p Black 42 w(D.)31 b(Lucani,)h(M.)f(M)t(\264)-26 b(edard,)33 b(and)f(M.)f(Stojano)o(vic,)j(\223Random)f(linear)g(netw)o(ork)2082 4565 y(coding)e(for)e(time-di)n(vision)j(duple)o(xing:)g(\002eld)d (size)h(considerations,)-5 b(\224)33 b(in)c Fa(Pr)m(o-)2082 4640 y(ceedings)i(of)e(the)h(IEEE)d(Global)k(Communications)g(Confer)n (ence)o(,)g(Exhibition)2082 4714 y(and)24 b(Industry)h(F)-7 b(orum)23 b(\(GLOBECOM\))p Fw(,)f(2009,)i(pp.)f(1\2266.)1930 4731 y SDict begin H.S end 1930 4731 a 1930 4731 a SDict begin 9 H.A end 1930 4731 a 1930 4731 a SDict begin [/View [/XYZ H.V]/Dest (cite.lucani2010systematic) cvn /DEST pdfmark end 1930 4731 a Black 61 x Fw([16])p Black 42 w(D.)d(Lucani,)i(M.)e(M)t (\264)-26 b(edard,)22 b(and)g(M.)e(Stojano)o(vic,)j(\223Systematic)h (netw)o(ork)e(coding)2082 4866 y(for)j(time-di)n(vision)j(duple)o (xing,)-5 b(\224)28 b(in)d Fa(Pr)m(oceedings)i(of)e(the)g(IEEE)f (International)2082 4941 y(Symposium)h(on)f(Information)h(Theory)g (\(ISIT\))p Fw(,)e(2010,)h(pp.)f(2403\2262407.)1930 4958 y SDict begin H.S end 1930 4958 a 1930 4958 a SDict begin 9 H.A end 1930 4958 a 1930 4958 a SDict begin [/View 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