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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Universal coding</div> <p><b>Levenshtein coding</b> is a <a href="/wiki/Universal_code_(data_compression)" title="Universal code (data compression)">universal code</a> encoding the non-negative integers developed by <a href="/wiki/Vladimir_Levenshtein" title="Vladimir Levenshtein">Vladimir Levenshtein</a>.<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><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Encoding">Encoding</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Levenshtein_coding&action=edit&section=1" title="Edit section: Encoding"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The code of <a href="/wiki/0_(number)" class="mw-redirect" title="0 (number)">zero</a> is "0"; to code a <a href="/wiki/Positive_number" class="mw-redirect" title="Positive number">positive number</a>: </p> <ol><li>Initialize the step count variable <i>C</i> to 1.</li> <li>Write the <a href="/wiki/Binary_numeral_system" class="mw-redirect" title="Binary numeral system">binary</a> representation of the number without the leading "1" to the beginning of the code.</li> <li>Let <i>M</i> be the number of bits written in step 2.</li> <li>If <i>M</i> is not 0, increment <i>C</i>, repeat from step 2 with M as the new number.</li> <li>Write <i>C</i> "1" bits and a "0" to the beginning of the code.</li></ol> <p>The code begins: </p> <table class="wikitable"> <tbody><tr> <th>Number</th> <th>Encoding</th> <th>Implied probability </th></tr> <tr> <td>0</td> <td><code>0</code></td> <td>1/2 </td></tr> <tr> <td colspan="4"> </td></tr> <tr> <td>1</td> <td><code>10</code></td> <td>1/4 </td></tr> <tr> <td colspan="4"> </td></tr> <tr> <td>2</td> <td><code>110 0</code></td> <td>1/16 </td></tr> <tr> <td>3</td> <td><code>110 1</code></td> <td>1/16 </td></tr> <tr> <td colspan="4"> </td></tr> <tr> <td>4</td> <td><code>1110 0 00</code></td> <td>1/128 </td></tr> <tr> <td>5</td> <td><code>1110 0 01</code></td> <td>1/128 </td></tr> <tr> <td>6</td> <td><code>1110 0 10</code></td> <td>1/128 </td></tr> <tr> <td>7</td> <td><code>1110 0 11</code></td> <td>1/128 </td></tr> <tr> <td colspan="4"> </td></tr> <tr> <td>8</td> <td><code>1110 1 000</code></td> <td>1/256 </td></tr> <tr> <td>9</td> <td><code>1110 1 001</code></td> <td>1/256 </td></tr> <tr> <td>10</td> <td><code>1110 1 010</code></td> <td>1/256 </td></tr> <tr> <td>11</td> <td><code>1110 1 011</code></td> <td>1/256 </td></tr> <tr> <td>12</td> <td><code>1110 1 100</code></td> <td>1/256 </td></tr> <tr> <td>13</td> <td><code>1110 1 101</code></td> <td>1/256 </td></tr> <tr> <td>14</td> <td><code>1110 1 110</code></td> <td>1/256 </td></tr> <tr> <td>15</td> <td><code>1110 1 111</code></td> <td>1/256 </td></tr> <tr> <td colspan="4"> </td></tr> <tr> <td>16</td> <td><code>11110 0 00 0000</code></td> <td>1/4096 </td></tr> <tr> <td>17</td> <td><code>11110 0 00 0001</code></td> <td>1/4096 </td></tr></tbody></table> <p>To decode a Levenshtein-coded integer: </p> <ol><li>Count the number of "1" bits until a "0" is encountered.</li> <li>If the count is zero, the value is zero, otherwise</li> <li>Discard the "1" bits just counted and the first "0" encountered</li> <li>Start with a variable <i>N</i>, set it to a value of 1 and repeat <i>count minus 1</i> times:</li> <li>Read <i>N</i> bits (and remove them from the encoded integer), prepend "1", assign the resulting value to <i>N</i></li></ol> <p>The Levenshtein code of a positive integer is always one bit longer than the <a href="/wiki/Elias_omega_coding" title="Elias omega coding">Elias omega code</a> of that integer. However, there is a Levenshtein code for zero, whereas Elias omega coding would require the numbers to be shifted so that a zero is represented by the code for one instead. </p> <div class="mw-heading mw-heading2"><h2 id="Example_code">Example code</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Levenshtein_coding&action=edit&section=2" title="Edit section: Example code"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Encoding_2">Encoding</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Levenshtein_coding&action=edit&section=3" title="Edit section: Encoding"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr"><pre><span></span><span class="kt">void</span><span class="w"> </span><span class="nf">levenshteinEncode</span><span class="p">(</span><span class="kt">char</span><span class="o">*</span><span class="w"> </span><span class="n">source</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="o">*</span><span class="w"> </span><span class="n">dest</span><span class="p">)</span> <span class="p">{</span> <span class="w"> </span><span class="n">IntReader</span><span class="w"> </span><span class="n">intreader</span><span class="p">(</span><span class="n">source</span><span class="p">);</span> <span class="w"> </span><span class="n">BitWriter</span><span class="w"> </span><span class="n">bitwriter</span><span class="p">(</span><span class="n">dest</span><span class="p">);</span> <span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">intreader</span><span class="p">.</span><span class="n">hasLeft</span><span class="p">())</span> <span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">intreader</span><span class="p">.</span><span class="n">getInt</span><span class="p">();</span> <span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span> <span class="w"> </span><span class="n">bitwriter</span><span class="p">.</span><span class="n">outputBit</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span> <span class="w"> </span><span class="k">else</span> <span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span> <span class="w"> </span><span class="n">BitStack</span><span class="w"> </span><span class="n">bits</span><span class="p">;</span> <span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span> <span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">temp</span><span class="o">>>=</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="c1">// calculate floor(log2(num))</span> <span class="w"> </span><span class="o">++</span><span class="n">m</span><span class="p">;</span> <span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span> <span class="w"> </span><span class="n">bits</span><span class="p">.</span><span class="n">pushBit</span><span class="p">((</span><span class="n">num</span><span class="w"> </span><span class="o">>></span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">&</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span> <span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span> <span class="w"> </span><span class="o">++</span><span class="n">c</span><span class="p">;</span> <span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">);</span> <span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span> <span class="w"> </span><span class="n">bitwriter</span><span class="p">.</span><span class="n">outputBit</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span> <span class="w"> </span><span class="n">bitwriter</span><span class="p">.</span><span class="n">outputBit</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span> <span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">bits</span><span class="p">.</span><span class="n">length</span><span class="p">()</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">)</span> <span class="w"> </span><span class="n">bitwriter</span><span class="p">.</span><span class="n">outputBit</span><span class="p">(</span><span class="n">bits</span><span class="p">.</span><span class="n">popBit</span><span class="p">());</span> <span class="w"> </span><span class="p">}</span> <span class="w"> </span><span class="p">}</span> <span class="p">}</span> </pre></div> <div class="mw-heading mw-heading3"><h3 id="Decoding">Decoding</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Levenshtein_coding&action=edit&section=4" title="Edit section: Decoding"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-highlight mw-highlight-lang-cpp mw-content-ltr" dir="ltr"><pre><span></span><span class="kt">void</span><span class="w"> </span><span class="nf">levenshteinDecode</span><span class="p">(</span><span class="kt">char</span><span class="o">*</span><span class="w"> </span><span class="n">source</span><span class="p">,</span><span class="w"> </span><span class="kt">char</span><span class="o">*</span><span class="w"> </span><span class="n">dest</span><span class="p">)</span> <span class="p">{</span> <span class="w"> </span><span class="n">BitReader</span><span class="w"> </span><span class="n">bitreader</span><span class="p">(</span><span class="n">source</span><span class="p">);</span> <span class="w"> </span><span class="n">IntWriter</span><span class="w"> </span><span class="n">intwriter</span><span class="p">(</span><span class="n">dest</span><span class="p">);</span> <span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">bitreader</span><span class="p">.</span><span class="n">hasLeft</span><span class="p">())</span> <span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span> <span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">bitreader</span><span class="p">.</span><span class="n">inputBit</span><span class="p">())</span><span class="w"> </span><span class="c1">// potentially dangerous with malformed files.</span> <span class="w"> </span><span class="o">++</span><span class="n">n</span><span class="p">;</span> <span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">;</span> <span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span> <span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span> <span class="w"> </span><span class="k">else</span> <span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span> <span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="mi">-1</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span> <span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span> <span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">j</span><span class="p">)</span> <span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="n">bitreader</span><span class="p">.</span><span class="n">inputBit</span><span class="p">();</span> <span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span> <span class="w"> </span><span class="p">}</span> <span class="w"> </span><span class="p">}</span> <span class="w"> </span><span class="n">intwriter</span><span class="p">.</span><span class="n">putInt</span><span class="p">(</span><span class="n">num</span><span class="p">);</span><span class="w"> </span><span class="c1">// write out the value</span> <span class="w"> </span><span class="p">}</span> <span class="w"> </span><span class="n">bitreader</span><span class="p">.</span><span class="n">close</span><span class="p">();</span> <span class="w"> </span><span class="n">intwriter</span><span class="p">.</span><span class="n">close</span><span class="p">();</span> <span class="p">}</span> </pre></div> <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=Levenshtein_coding&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Elias_omega_coding" title="Elias omega coding">Elias omega coding</a></li> <li><a href="/wiki/Iterated_logarithm" title="Iterated logarithm">Iterated logarithm</a></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=Levenshtein_coding&action=edit&section=6" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.compression.ru/download/articles/int/levenstein_1968_on_the_redundancy_and_delay.pdf">"1968 paper by V. I. Levenshtein (in Russian)"</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=1968+paper+by+V.+I.+Levenshtein+%28in+Russian%29&rft_id=http%3A%2F%2Fwww.compression.ru%2Fdownload%2Farticles%2Fint%2Flevenstein_1968_on_the_redundancy_and_delay.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALevenshtein+coding" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavid_Salomon2007" class="citation book cs1">David Salomon (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=81AfzW6vux4C&q=%22Levenstein+coding%22&pg=PA80"><i>Variable-length codes for data compression</i></a>. Springer. p. 80. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-84628-958-3" title="Special:BookSources/978-1-84628-958-3"><bdi>978-1-84628-958-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Variable-length+codes+for+data+compression&rft.pages=80&rft.pub=Springer&rft.date=2007&rft.isbn=978-1-84628-958-3&rft.au=David+Salomon&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D81AfzW6vux4C%26q%3D%2522Levenstein%2Bcoding%2522%26pg%3DPA80&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALevenshtein+coding" 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 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href="/wiki/Template:Compression_methods" title="Template:Compression methods"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Compression_methods" title="Template talk:Compression methods"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Compression_methods" title="Special:EditPage/Template:Compression methods"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Data_compression_methods" style="font-size:114%;margin:0 4em"><a href="/wiki/Data_compression" title="Data compression">Data compression</a> methods</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Lossless_compression" title="Lossless compression">Lossless</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/Entropy_coding" title="Entropy coding">Entropy 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/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 class="mw-selflink selflink">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 href="/wiki/Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski" title="Lempel–Ziv–Storer–Szymanski">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, 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