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class="mw-page-title-main">Lempel–Ziv–Storer–Szymanski</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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href="https://de.wikipedia.org/wiki/Lempel-Ziv-Storer-Szymanski-Algorithmus" title="Lempel-Ziv-Storer-Szymanski-Algorithmus – German" lang="de" hreflang="de" data-title="Lempel-Ziv-Storer-Szymanski-Algorithmus" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/LZSS" title="LZSS – Spanish" lang="es" hreflang="es" data-title="LZSS" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/LZSS" title="LZSS – French" lang="fr" hreflang="fr" data-title="LZSS" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski" title="Lempel–Ziv–Storer–Szymanski – Japanese" lang="ja" hreflang="ja" data-title="Lempel–Ziv–Storer–Szymanski" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/LZSS" title="LZSS – Polish" lang="pl" hreflang="pl" data-title="LZSS" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/LZSS" title="LZSS – Russian" lang="ru" hreflang="ru" data-title="LZSS" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a 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href="/wiki/Lossless_data_compression" class="mw-redirect" title="Lossless data compression">lossless data compression</a> <a href="/wiki/Algorithm" title="Algorithm">algorithm</a>, a derivative of <a href="/wiki/LZ77" class="mw-redirect" title="LZ77">LZ77</a>, that was created in 1982 by <a href="/w/index.php?title=James_A._Storer&action=edit&redlink=1" class="new" title="James A. Storer (page does not exist)">James A. Storer</a> and <a href="/w/index.php?title=Thomas_Szymanski&action=edit&redlink=1" class="new" title="Thomas Szymanski (page does not exist)">Thomas Szymanski</a>. LZSS was described in article "Data compression via textual substitution" published in <i>Journal of the ACM</i> (1982, pp. 928–951).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>LZSS is a <a href="/wiki/Dictionary_coding" class="mw-redirect" title="Dictionary coding">dictionary coding</a> technique. It attempts to replace a string of symbols with a reference to a dictionary location of the same string. </p><p>The main difference between LZ77 and LZSS is that in LZ77 the dictionary reference could actually be longer than the string it was replacing. In LZSS, such references are omitted if the length is less than the "break even" point. Furthermore, LZSS uses one-bit flags to indicate whether the next chunk of data is a literal (byte) or a reference to an offset/length pair. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski&action=edit&section=1" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Here is the beginning of Dr. Seuss's <i><a href="/wiki/Green_Eggs_and_Ham" title="Green Eggs and Ham">Green Eggs and Ham</a></i>, with character numbers at the beginning of lines for convenience. Green Eggs and Ham is a good example to illustrate LZSS compression because the book itself only contains 50 unique words, despite having a word count of 170.<sup id="cite_ref-floss_2-0" class="reference"><a href="#cite_note-floss-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Thus, words are repeated, however not in succession. </p> <pre> 0: I am Sam 9: 10: Sam I am 19: 20: That Sam-I-am! 35: That Sam-I-am! 50: I do not like 64: that Sam-I-am! 79: 80: Do you like green eggs and ham? 112: 113: I do not like them, Sam-I-am. 143: I do not like green eggs and ham. </pre> <p>This text takes 177 bytes in uncompressed form. Assuming a break even point of 2 bytes (and thus 2 byte pointer/offset pairs), and one byte newlines, this text compressed with LZSS becomes 95 bytes long: </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski_Example.png" class="mw-file-description"><img alt="A color coded example to help illustrate the recycling of repeated information to minimize storage." src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski_Example.png/170px-Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski_Example.png" decoding="async" width="170" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski_Example.png/255px-Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski_Example.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski_Example.png/340px-Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski_Example.png 2x" data-file-width="662" data-file-height="196" /></a><figcaption>A color coded example of LZSS compression in action.</figcaption></figure> <pre> 0: I am Sam 9: 10: (5,3) (0,4) 16: 17: That(4,4)-I-am!(19,15) 32: I do not like 46: t(21,14) 50: Do you(58,5) green eggs and ham? 79: (49,14) them,(24,9).(112,15)(92,18). </pre> <p>Note: this does not include the 11 bytes of flags indicating whether the next chunk of text is a pointer or a literal. Adding it, the text becomes 106 bytes long, which is still shorter than the original 177 bytes. </p> <div class="mw-heading mw-heading2"><h2 id="Implementations">Implementations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski&action=edit&section=2" title="Edit section: Implementations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many popular archivers like <a href="/wiki/ARJ" title="ARJ">ARJ</a>, <a href="/wiki/RAR_(file_format)" title="RAR (file format)">RAR</a>, <a href="/wiki/Zoo_(file_format)" title="Zoo (file format)">ZOO</a>, <a href="/wiki/LHarc" class="mw-redirect" title="LHarc">LHarc</a> use LZSS rather than LZ77 as the primary compression algorithm; the encoding of literal characters and of length-distance pairs varies, with the most common option being <a href="/wiki/Huffman_coding" title="Huffman coding">Huffman coding</a>. Most implementations stem from a <a href="/wiki/Public_domain" title="Public domain">public domain</a> 1989 code by <a href="/wiki/Haruhiko_Okumura" title="Haruhiko Okumura">Haruhiko Okumura</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Version 4 of the <a href="/wiki/Allegro_library" class="mw-redirect" title="Allegro library">Allegro library</a> can encode and decode an LZSS format,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> but the feature was cut from version 5. The <a href="/wiki/Game_Boy_Advance" title="Game Boy Advance">Game Boy Advance</a> BIOS can decode a slightly modified LZSS format.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Apple's <a href="/wiki/MacOS" title="MacOS">macOS</a> uses LZSS as one of the compression methods for kernel code.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Lempel%E2%80%93Ziv%E2%80%93Welch" title="Lempel–Ziv–Welch">Lempel–Ziv–Welch</a> (LZW)</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFStorerSzymanski1982" class="citation journal cs1">Storer, James A.; Szymanski, Thomas G. (October 1982). <a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F322344.322346">"Data Compression via Textual Substitution"</a>. <i><a href="/wiki/Journal_of_the_ACM" title="Journal of the ACM">Journal of the ACM</a></i>. <b>29</b> (4): 928–951. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F322344.322346">10.1145/322344.322346</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+ACM&rft.atitle=Data+Compression+via+Textual+Substitution&rft.volume=29&rft.issue=4&rft.pages=928-951&rft.date=1982-10&rft_id=info%3Adoi%2F10.1145%2F322344.322346&rft.aulast=Storer&rft.aufirst=James+A.&rft.au=Szymanski%2C+Thomas+G.&rft_id=https%3A%2F%2Fdoi.org%2F10.1145%252F322344.322346&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski" class="Z3988"></span></span> </li> <li id="cite_note-floss-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-floss_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.cnn.com/2009/LIVING/wayoflife/01/23/mf.seuss.stories.behind/index.html">"10 stories behind Dr. Seuss stories"</a>. <a href="/wiki/CNN" title="CNN">CNN</a>. January 23, 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-01-26</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=10+stories+behind+Dr.+Seuss+stories&rft.pub=CNN&rft.date=2009-01-23&rft_id=http%3A%2F%2Fwww.cnn.com%2F2009%2FLIVING%2Fwayoflife%2F01%2F23%2Fmf.seuss.stories.behind%2Findex.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Simtel.net mirror. <a rel="nofollow" class="external text" href="https://web.archive.org/web/19990203141013/http://oak.oakland.edu/pub/simtelnet/msdos/arcutils/lz_comp2.zip">Haruhiko Okumura implementation of 1989.</a> Archived on February 3, 1999.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Haruhiko Okumura. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160110174426/https://oku.edu.mie-u.ac.jp/~okumura/compression/history.html">History of Data Compression in Japan.</a> Archived on January 10, 2016.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a href="/wiki/Shawn_Hargreaves" class="mw-redirect" title="Shawn Hargreaves">Hargreaves, Shawn</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://pl.wikipedia.org/wiki/Shawn_Hargreaves" class="extiw" title="pl:Shawn Hargreaves">pl</a>]</span>, et al. <a rel="nofollow" class="external text" href="https://github.com/liballeg/allegro5/blob/4.4/src/lzss.c">Allegro source code: lzss.c</a>. Accessed on July 13, 2016.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKorth" class="citation web cs1">Korth, Martin. <a rel="nofollow" class="external text" href="https://problemkaputt.de/gbatek-lz-decompression-functions.htm">"GBATEK LZ Decompression Functions"</a>. <i>problemkaputt.de</i><span class="reference-accessdate">. Retrieved <span class="nowrap">7 June</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=problemkaputt.de&rft.atitle=GBATEK+LZ+Decompression+Functions&rft.aulast=Korth&rft.aufirst=Martin&rft_id=https%3A%2F%2Fproblemkaputt.de%2Fgbatek-lz-decompression-functions.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://github.com/opensource-apple/kext_tools/blob/bc71a85/compression.c">"kext_tools/compression.c"</a>. <i>GitHub</i>. Apple Open Source<span class="reference-accessdate">. Retrieved <span class="nowrap">28 December</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=GitHub&rft.atitle=kext_tools%2Fcompression.c&rft_id=https%3A%2F%2Fgithub.com%2Fopensource-apple%2Fkext_tools%2Fblob%2Fbc71a85%2Fcompression.c&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski" class="Z3988"></span></span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl 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href="/wiki/Adaptive_coding" title="Adaptive coding">Adaptive coding</a></li> <li><a href="/wiki/Arithmetic_coding" title="Arithmetic coding">Arithmetic</a></li> <li><a href="/wiki/Asymmetric_numeral_systems" title="Asymmetric numeral systems">Asymmetric numeral systems</a></li> <li><a href="/wiki/Golomb_coding" title="Golomb coding">Golomb</a></li> <li><a href="/wiki/Huffman_coding" title="Huffman coding">Huffman</a> <ul><li><a href="/wiki/Adaptive_Huffman_coding" title="Adaptive Huffman coding">Adaptive</a></li> <li><a href="/wiki/Canonical_Huffman_code" title="Canonical Huffman code">Canonical</a></li> <li><a href="/wiki/Modified_Huffman_coding" title="Modified Huffman coding">Modified</a></li></ul></li> <li><a href="/wiki/Range_coding" title="Range coding">Range</a></li> <li><a href="/wiki/Shannon_coding" title="Shannon coding">Shannon</a></li> <li><a href="/wiki/Shannon%E2%80%93Fano_coding" title="Shannon–Fano coding">Shannon–Fano</a></li> <li><a href="/wiki/Shannon%E2%80%93Fano%E2%80%93Elias_coding" title="Shannon–Fano–Elias coding">Shannon–Fano–Elias</a></li> <li><a href="/wiki/Tunstall_coding" title="Tunstall coding">Tunstall</a></li> <li><a href="/wiki/Unary_coding" title="Unary coding">Unary</a></li> <li><a href="/wiki/Universal_code_(data_compression)" title="Universal code (data compression)">Universal</a> <ul><li><a href="/wiki/Exponential-Golomb_coding" title="Exponential-Golomb coding">Exp-Golomb</a></li> <li><a href="/wiki/Fibonacci_coding" title="Fibonacci coding">Fibonacci</a></li> <li><a href="/wiki/Elias_gamma_coding" title="Elias gamma coding">Gamma</a></li> <li><a href="/wiki/Levenshtein_coding" title="Levenshtein coding">Levenshtein</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;"><a href="/wiki/Dictionary_coder" title="Dictionary coder">Dictionary type</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Byte_pair_encoding" title="Byte pair encoding">Byte pair encoding</a></li> <li><a href="/wiki/LZ77_and_LZ78" title="LZ77 and LZ78">Lempel–Ziv</a> <ul><li><a href="/wiki/842_(compression_algorithm)" title="842 (compression algorithm)">842</a></li> <li><a href="/wiki/LZ4_(compression_algorithm)" title="LZ4 (compression algorithm)">LZ4</a></li> <li><a href="/wiki/LZJB" class="mw-redirect" title="LZJB">LZJB</a></li> <li><a href="/wiki/Lempel%E2%80%93Ziv%E2%80%93Oberhumer" title="Lempel–Ziv–Oberhumer">LZO</a></li> <li><a href="/wiki/LZRW" title="LZRW">LZRW</a></li> <li><a class="mw-selflink selflink">LZSS</a></li> <li><a href="/wiki/Lempel%E2%80%93Ziv%E2%80%93Welch" title="Lempel–Ziv–Welch">LZW</a></li> <li><a href="/wiki/LZWL" title="LZWL">LZWL</a></li> <li><a href="/wiki/Snappy_(compression)" title="Snappy (compression)">Snappy</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;">Other types</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Burrows%E2%80%93Wheeler_transform" title="Burrows–Wheeler transform">BWT</a></li> <li><a href="/wiki/Context_tree_weighting" title="Context tree weighting">CTW</a></li> <li><a href="/wiki/Context_mixing" title="Context mixing">CM</a></li> <li><a href="/wiki/Delta_encoding" title="Delta encoding">Delta</a> <ul><li><a href="/wiki/Incremental_encoding" title="Incremental encoding">Incremental</a></li></ul></li> <li><a href="/wiki/Dynamic_Markov_compression" title="Dynamic Markov compression">DMC</a></li> <li><a href="/wiki/Differential_pulse-code_modulation" title="Differential pulse-code modulation">DPCM</a></li> <li><a href="/wiki/Grammar-based_code" title="Grammar-based code">Grammar</a> <ul><li><a href="/wiki/Re-Pair" title="Re-Pair">Re-Pair</a></li> <li><a href="/wiki/Sequitur_algorithm" title="Sequitur algorithm">Sequitur</a></li></ul></li> <li><a href="/wiki/Discrete_cosine_transform" title="Discrete cosine transform">LDCT</a></li> <li><a href="/wiki/Move-to-front_transform" title="Move-to-front transform">MTF</a></li> <li><a href="/wiki/PAQ" title="PAQ">PAQ</a></li> <li><a href="/wiki/Prediction_by_partial_matching" title="Prediction by partial matching">PPM</a></li> <li><a href="/wiki/Run-length_encoding" title="Run-length encoding">RLE</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;">Hybrid</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li>LZ77 + Huffman <ul><li><a href="/wiki/Deflate" title="Deflate">Deflate</a></li> <li><a href="/wiki/LZX" title="LZX">LZX</a></li> <li><a href="/wiki/Lempel%E2%80%93Ziv%E2%80%93Stac" title="Lempel–Ziv–Stac">LZS</a></li></ul></li> <li>LZ77 + ANS <ul><li><a href="/wiki/LZFSE" title="LZFSE">LZFSE</a></li></ul></li> <li>LZ77 + Huffman + ANS <ul><li><a href="/wiki/Zstd" title="Zstd">Zstandard</a></li></ul></li> <li>LZ77 + Huffman + context <ul><li><a href="/wiki/Brotli" title="Brotli">Brotli</a></li></ul></li> <li>LZSS + Huffman <ul><li><a href="/wiki/LHA_(file_format)" title="LHA (file format)">LHA/LZH</a></li></ul></li> <li>LZ77 + Range <ul><li><a href="/wiki/Lempel%E2%80%93Ziv%E2%80%93Markov_chain_algorithm" title="Lempel–Ziv–Markov chain algorithm">LZMA</a></li> <li>LZHAM</li></ul></li> <li>RLE + BWT + MTF + Huffman <ul><li><a href="/wiki/Bzip2" title="Bzip2">bzip2</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Lossy_compression" title="Lossy compression">Lossy</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;"><a href="/wiki/Transform_coding" title="Transform coding">Transform type</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discrete_cosine_transform" title="Discrete cosine transform">Discrete cosine transform</a> <ul><li><a href="/wiki/Discrete_cosine_transform" title="Discrete cosine transform">DCT</a></li> <li><a href="/wiki/Modified_discrete_cosine_transform" title="Modified discrete cosine transform">MDCT</a></li></ul></li> <li><a href="/wiki/Discrete_sine_transform" title="Discrete sine transform">DST</a></li> <li><a href="/wiki/Fast_Fourier_transform" title="Fast Fourier transform">FFT</a></li> <li><a href="/wiki/Wavelet_transform" title="Wavelet transform">Wavelet</a> <ul><li><a href="/wiki/Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li> <li><a href="/wiki/Discrete_wavelet_transform" title="Discrete wavelet transform">DWT</a></li> <li><a href="/wiki/Set_partitioning_in_hierarchical_trees" title="Set partitioning in hierarchical trees">SPIHT</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;">Predictive type</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Differential_pulse-code_modulation" title="Differential pulse-code modulation">DPCM</a> <ul><li><a href="/wiki/Adaptive_differential_pulse-code_modulation" title="Adaptive differential pulse-code modulation">ADPCM</a></li></ul></li> <li><a href="/wiki/Linear_predictive_coding" title="Linear predictive coding">LPC</a> <ul><li><a href="/wiki/Algebraic_code-excited_linear_prediction" title="Algebraic code-excited linear prediction">ACELP</a></li> <li><a href="/wiki/Code-excited_linear_prediction" title="Code-excited linear prediction">CELP</a></li> <li><a href="/wiki/Log_area_ratio" title="Log area ratio">LAR</a></li> <li><a href="/wiki/Line_spectral_pairs" title="Line spectral pairs">LSP</a></li> <li><a href="/wiki/Warped_linear_predictive_coding" title="Warped linear predictive coding">WLPC</a></li></ul></li> <li>Motion <ul><li><a href="/wiki/Motion_compensation" title="Motion compensation">Compensation</a></li> <li><a href="/wiki/Motion_estimation" title="Motion estimation">Estimation</a></li> <li><a href="/wiki/Motion_vector" class="mw-redirect" title="Motion vector">Vector</a></li></ul></li> <li><a href="/wiki/Psychoacoustics" title="Psychoacoustics">Psychoacoustic</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Data_compression#Audio" title="Data compression">Audio</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bit_rate" title="Bit rate">Bit rate</a> <ul><li><a href="/wiki/Average_bitrate" title="Average bitrate">ABR</a></li> <li><a href="/wiki/Constant_bitrate" title="Constant bitrate">CBR</a></li> <li><a href="/wiki/Variable_bitrate" title="Variable bitrate">VBR</a></li></ul></li> <li><a href="/wiki/Companding" title="Companding">Companding</a></li> <li><a href="/wiki/Convolution" title="Convolution">Convolution</a></li> <li><a href="/wiki/Dynamic_range" title="Dynamic range">Dynamic range</a></li> <li><a href="/wiki/Latency_(audio)" title="Latency (audio)">Latency</a></li> <li><a href="/wiki/Nyquist%E2%80%93Shannon_sampling_theorem" title="Nyquist–Shannon sampling theorem">Nyquist–Shannon theorem</a></li> <li><a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">Sampling</a></li> <li><a href="/wiki/Silence_compression" title="Silence compression">Silence compression</a></li> <li><a href="/wiki/Sound_quality" title="Sound quality">Sound quality</a></li> <li><a href="/wiki/Speech_coding" title="Speech coding">Speech coding</a></li> <li><a href="/wiki/Sub-band_coding" title="Sub-band coding">Sub-band coding</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;"><a href="/wiki/Audio_codec" title="Audio codec">Codec</a> parts</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/A-law_algorithm" title="A-law algorithm">A-law</a></li> <li><a href="/wiki/%CE%9C-law_algorithm" title="Μ-law algorithm">μ-law</a></li> <li><a href="/wiki/Differential_pulse-code_modulation" title="Differential pulse-code modulation">DPCM</a> <ul><li><a href="/wiki/Adaptive_differential_pulse-code_modulation" title="Adaptive differential pulse-code modulation">ADPCM</a></li> <li><a href="/wiki/Delta_modulation" title="Delta modulation">DM</a></li></ul></li> <li><a href="/wiki/Fourier_transform" title="Fourier transform">FT</a> <ul><li><a href="/wiki/Fast_Fourier_transform" title="Fast Fourier transform">FFT</a></li></ul></li> <li><a href="/wiki/Linear_predictive_coding" title="Linear predictive coding">LPC</a> <ul><li><a href="/wiki/Algebraic_code-excited_linear_prediction" title="Algebraic code-excited linear prediction">ACELP</a></li> <li><a href="/wiki/Code-excited_linear_prediction" title="Code-excited linear prediction">CELP</a></li> <li><a href="/wiki/Log_area_ratio" title="Log area ratio">LAR</a></li> <li><a href="/wiki/Line_spectral_pairs" title="Line spectral pairs">LSP</a></li> <li><a href="/wiki/Warped_linear_predictive_coding" title="Warped linear predictive coding">WLPC</a></li></ul></li> <li><a href="/wiki/Modified_discrete_cosine_transform" title="Modified discrete cosine transform">MDCT</a></li> <li><a href="/wiki/Psychoacoustics" title="Psychoacoustics">Psychoacoustic model</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Image_compression" title="Image compression">Image</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chroma_subsampling" title="Chroma subsampling">Chroma subsampling</a></li> <li><a href="/wiki/Coding_tree_unit" title="Coding tree unit">Coding tree unit</a></li> <li><a href="/wiki/Color_space" title="Color space">Color space</a></li> <li><a href="/wiki/Compression_artifact" title="Compression artifact">Compression artifact</a></li> <li><a href="/wiki/Image_resolution" title="Image resolution">Image resolution</a></li> <li><a href="/wiki/Macroblock" title="Macroblock">Macroblock</a></li> <li><a href="/wiki/Pixel" title="Pixel">Pixel</a></li> <li><a href="/wiki/Peak_signal-to-noise_ratio" title="Peak signal-to-noise ratio">PSNR</a></li> <li><a href="/wiki/Quantization_(image_processing)" title="Quantization (image processing)">Quantization</a></li> <li><a href="/wiki/Standard_test_image" title="Standard test image">Standard test image</a></li> <li><a href="/wiki/Texture_compression" title="Texture compression">Texture compression</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;">Methods</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chain_code" title="Chain code">Chain code</a></li> <li><a href="/wiki/Discrete_cosine_transform" title="Discrete cosine transform">DCT</a></li> <li><a href="/wiki/Deflate" title="Deflate">Deflate</a></li> <li><a href="/wiki/Fractal_compression" title="Fractal compression">Fractal</a></li> <li><a href="/wiki/Karhunen%E2%80%93Lo%C3%A8ve_theorem" class="mw-redirect" title="Karhunen–Loève theorem">KLT</a></li> <li><a href="/wiki/Pyramid_(image_processing)" title="Pyramid (image processing)">LP</a></li> <li><a href="/wiki/Run-length_encoding" title="Run-length encoding">RLE</a></li> <li><a href="/wiki/Wavelet_transform" title="Wavelet transform">Wavelet</a> <ul><li><a href="/wiki/Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li> <li><a href="/wiki/Discrete_wavelet_transform" title="Discrete wavelet transform">DWT</a></li> <li><a href="/wiki/Embedded_zerotrees_of_wavelet_transforms" title="Embedded zerotrees of wavelet transforms">EZW</a></li> <li><a href="/wiki/Set_partitioning_in_hierarchical_trees" title="Set partitioning in hierarchical trees">SPIHT</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Data_compression#Video" title="Data compression">Video</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bit_rate" title="Bit rate">Bit rate</a> <ul><li><a href="/wiki/Average_bitrate" title="Average bitrate">ABR</a></li> <li><a href="/wiki/Constant_bitrate" title="Constant bitrate">CBR</a></li> <li><a href="/wiki/Variable_bitrate" title="Variable bitrate">VBR</a></li></ul></li> <li><a href="/wiki/Display_resolution" title="Display resolution">Display resolution</a></li> <li><a href="/wiki/Film_frame" title="Film frame">Frame</a></li> <li><a href="/wiki/Frame_rate" title="Frame rate">Frame rate</a></li> <li><a href="/wiki/Video_compression_picture_types" title="Video compression picture types">Frame types</a></li> <li><a href="/wiki/Interlaced_video" title="Interlaced video">Interlace</a></li> <li><a href="/wiki/Video#Characteristics_of_video_streams" title="Video">Video characteristics</a></li> <li><a href="/wiki/Video_quality" title="Video quality">Video quality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:7.0em;font-weight:normal;"><a href="/wiki/Video_codec" title="Video codec">Codec</a> parts</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Discrete_cosine_transform" title="Discrete cosine transform">DCT</a></li> <li><a href="/wiki/Differential_pulse-code_modulation" title="Differential pulse-code modulation">DPCM</a></li> <li><a href="/wiki/Deblocking_filter" title="Deblocking filter">Deblocking filter</a></li> <li><a href="/wiki/Lapped_transform" title="Lapped transform">Lapped transform</a></li> <li>Motion <ul><li><a href="/wiki/Motion_compensation" title="Motion compensation">Compensation</a></li> <li><a href="/wiki/Motion_estimation" title="Motion estimation">Estimation</a></li> <li><a href="/wiki/Motion_vector" class="mw-redirect" title="Motion vector">Vector</a></li></ul></li> <li><a href="/wiki/Wavelet_transform" title="Wavelet transform">Wavelet</a> <ul><li><a href="/wiki/Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li> <li><a href="/wiki/Discrete_wavelet_transform" title="Discrete wavelet transform">DWT</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Information_theory" title="Information theory">Theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Compressed_data_structure" title="Compressed data structure">Compressed data structures</a> <ul><li><a href="/wiki/Compressed_suffix_array" title="Compressed suffix array">Compressed suffix array</a></li> <li><a href="/wiki/FM-index" title="FM-index">FM-index</a></li></ul></li> <li><a href="/wiki/Entropy_(information_theory)" title="Entropy (information theory)">Entropy</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a> <ul><li><a href="/wiki/Timeline_of_information_theory" title="Timeline of information theory">Timeline</a></li></ul></li> <li><a href="/wiki/Kolmogorov_complexity" title="Kolmogorov complexity">Kolmogorov complexity</a></li> <li><a href="/wiki/Prefix_code" title="Prefix code">Prefix code</a></li> <li><a href="/wiki/Quantization_(signal_processing)" title="Quantization (signal processing)">Quantization</a></li> <li><a href="/wiki/Rate%E2%80%93distortion_theory" title="Rate–distortion theory">Rate–distortion</a></li> <li><a href="/wiki/Redundancy_(information_theory)" title="Redundancy (information theory)">Redundancy</a></li> <li><a href="/wiki/Data_compression_symmetry" title="Data compression symmetry">Symmetry</a></li> <li><a href="/wiki/Smallest_grammar_problem" title="Smallest grammar problem">Smallest grammar problem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Community</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hutter_Prize" title="Hutter Prize">Hutter Prize</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mark_Adler" title="Mark Adler">Mark Adler</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Template"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/16px-Symbol_template_class_pink.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/23px-Symbol_template_class_pink.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Symbol_template_class_pink.svg/31px-Symbol_template_class_pink.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Template:Compression_formats" title="Template:Compression formats">Compression formats</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Template"><img alt="" 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