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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Modified Huffman coding</span></span>
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<p><b>Modified Huffman coding</b> is used in <a href="Fax" title="Fax">fax</a> machines to encode black-on-white images (<a href="Bitmap" title="Bitmap">bitmaps</a>). It combines the variable-length codes of <a href="Huffman_coding" title="Huffman coding">Huffman coding</a> with the coding of repetitive data in <a href="Run-length_encoding" title="Run-length encoding">run-length encoding</a>.
</p><p>The basic Huffman coding provides a way to compress files with much repeating data, like a file containing text, where the alphabet letters are the repeating objects. However, a single scan line contains only two kinds of elements – white pixels and black pixels – which can be represented directly as 0 and 1. This "alphabet" of only two <a href="Symbols" class="mw-redirect" title="Symbols">symbols</a> is too small to apply the <a href="Huffman_coding" title="Huffman coding">Huffman coding</a> directly. But if we first use run-length encoding, we can have more objects to encode. Here is an example taken from the article on <a href="Run-length_encoding" title="Run-length encoding">run-length encoding</a>:
</p><p>A hypothetical scan line, with B representing a black pixel and W representing white, might read as follows:
</p>
<pre>WWWWWWWWWWWWBWWWWWWWWWWWWBBBWWWWWWWWWWWWWWWWWWWWWWWWBWWWWWWWWWWWWWW
</pre>
<p>With a run-length encoding (RLE) data compression algorithm applied to the above hypothetical scan line, it can be rendered as follows:
</p>
<pre>12W1B12W3B24W1B14W
</pre>
<p>Here we see that we have several different numbers in addition to the two items "white" and "black." These numbers provide plenty of additional items to use, so the Huffman coding can be directly applied to the sequence above to reduce the size even more.
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<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Fax#Compression" title="Fax">Fax compression</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>
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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20020628195336/http://www.netnam.vn/unescocourse/computervision/104.htm">"Modified Huffman coding from UNESCO"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.netnam.vn/unescocourse/computervision/104.htm">the original</a> on 2002-06-28.</cite></li></ul>
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</style><div id="Data_compression_methods241" style="font-size:114%;margin:0 4em"><a href="Data_compression" title="Data compression">Data compression</a> methods</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Lossless_compression" title="Lossless compression">Lossless</a><br>type</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:1%"><a href="Entropy_coding" title="Entropy coding">Entropy</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="Adaptive_coding" title="Adaptive coding">Adaptive coding</a></li>
<li><a href="Arithmetic_coding" title="Arithmetic coding">Arithmetic</a></li>
<li><a href="Asymmetric_numeral_systems" title="Asymmetric numeral systems">Asymmetric numeral systems</a></li>
<li><a href="Golomb_coding" title="Golomb coding">Golomb</a></li>
<li><a href="Huffman_coding" title="Huffman coding">Huffman</a>
<ul><li><a href="Adaptive_Huffman_coding" title="Adaptive Huffman coding">Adaptive</a></li>
<li><a href="Canonical_Huffman_code" title="Canonical Huffman code">Canonical</a></li>
</ul></li>
<li><a href="Range_coding" title="Range coding">Range</a></li>
<li><a href="Shannon_coding" title="Shannon coding">Shannon</a></li>
<li><a href="Shannon%E2%80%93Fano_coding" title="Shannon–Fano coding">Shannon–Fano</a></li>
<li><a href="Shannon%E2%80%93Fano%E2%80%93Elias_coding" title="Shannon–Fano–Elias coding">Shannon–Fano–Elias</a></li>
<li><a href="Tunstall_coding" title="Tunstall coding">Tunstall</a></li>
<li><a href="Unary_coding" title="Unary coding">Unary</a></li>
<li><a href="Universal_code_(data_compression)" title="Universal code (data compression)">Universal</a>
<ul><li><a href="Exponential-Golomb_coding" title="Exponential-Golomb coding">Exp-Golomb</a></li>
<li><a href="Fibonacci_coding" title="Fibonacci coding">Fibonacci</a></li>
<li><a href="Elias_gamma_coding" title="Elias gamma coding">Gamma</a></li>
<li><a href="Levenshtein_coding" title="Levenshtein coding">Levenshtein</a></li></ul></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Dictionary_coder" title="Dictionary coder">Dictionary</a></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="Byte-pair_encoding" title="Byte-pair encoding">Byte-pair encoding</a></li>
<li><a href="LZ77_and_LZ78" title="LZ77 and LZ78">Lempel–Ziv</a>
<ul><li><a href="842_(compression_algorithm)" title="842 (compression algorithm)">842</a></li>
<li><a href="LZ4_(compression_algorithm)" title="LZ4 (compression algorithm)">LZ4</a></li>
<li><a href="LZJB" class="mw-redirect" title="LZJB">LZJB</a></li>
<li><a href="Lempel%E2%80%93Ziv%E2%80%93Oberhumer" title="Lempel–Ziv–Oberhumer">LZO</a></li>
<li><a href="LZRW" title="LZRW">LZRW</a></li>
<li><a href="Lempel%E2%80%93Ziv%E2%80%93Storer%E2%80%93Szymanski" title="Lempel–Ziv–Storer–Szymanski">LZSS</a></li>
<li><a href="Lempel%E2%80%93Ziv%E2%80%93Welch" title="Lempel–Ziv–Welch">LZW</a></li>
<li><a href="LZWL" title="LZWL">LZWL</a></li>
<li><a href="Snappy_(compression)" title="Snappy (compression)">Snappy</a></li></ul></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</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="Burrows%E2%80%93Wheeler_transform" title="Burrows–Wheeler transform">BWT</a></li>
<li><a href="Context_tree_weighting" title="Context tree weighting">CTW</a></li>
<li><a href="Context_mixing" title="Context mixing">CM</a></li>
<li><a href="Delta_encoding" title="Delta encoding">Delta</a>
<ul><li><a href="Incremental_encoding" title="Incremental encoding">Incremental</a></li></ul></li>
<li><a href="Dynamic_Markov_compression" title="Dynamic Markov compression">DMC</a></li>
<li><a href="Differential_pulse-code_modulation" title="Differential pulse-code modulation">DPCM</a></li>
<li><a href="Grammar-based_code" title="Grammar-based code">Grammar</a>
<ul><li><a href="Re-Pair" title="Re-Pair">Re-Pair</a></li>
<li><a href="Sequitur_algorithm" title="Sequitur algorithm">Sequitur</a></li></ul></li>
<li><a href="Discrete_cosine_transform" title="Discrete cosine transform">LDCT</a></li>
<li><a href="Move-to-front_transform" title="Move-to-front transform">MTF</a></li>
<li><a href="PAQ" title="PAQ">PAQ</a></li>
<li><a href="Prediction_by_partial_matching" title="Prediction by partial matching">PPM</a></li>
<li><a href="Run-length_encoding" title="Run-length encoding">RLE</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Hybrid</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li>LZ77 + Huffman
<ul><li><a href="Deflate" title="Deflate">Deflate</a></li>
<li><a href="LZX" title="LZX">LZX</a></li>
<li><a href="Lempel%E2%80%93Ziv%E2%80%93Stac" title="Lempel–Ziv–Stac">LZS</a></li></ul></li>
<li>LZ77 + ANS
<ul><li><a href="LZFSE" title="LZFSE">LZFSE</a></li></ul></li>
<li>LZ77 + Huffman + ANS
<ul><li><a href="Zstd" title="Zstd">Zstandard</a></li></ul></li>
<li>LZ77 + Huffman + context
<ul><li><a href="Brotli" title="Brotli">Brotli</a></li></ul></li>
<li>LZSS + Huffman
<ul><li><a href="LHA_(file_format)" title="LHA (file format)">LHA/LZH</a></li></ul></li>
<li>LZ77 + Range
<ul><li><a href="LZMA" title="LZMA">LZMA</a></li>
<li>LZHAM</li></ul></li>
<li>RLE + BWT + MTF + Huffman
<ul><li><a href="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="Lossy_compression" title="Lossy compression">Lossy</a><br>type</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:1%"><a href="Transform_coding" title="Transform coding">Transform</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="Discrete_cosine_transform" title="Discrete cosine transform">Discrete cosine transform</a>
<ul><li><a href="Discrete_cosine_transform" title="Discrete cosine transform">DCT</a></li>
<li><a href="Modified_discrete_cosine_transform" title="Modified discrete cosine transform">MDCT</a></li></ul></li>
<li><a href="Discrete_sine_transform" title="Discrete sine transform">DST</a></li>
<li><a href="Fast_Fourier_transform" title="Fast Fourier transform">FFT</a></li>
<li><a href="Wavelet_transform" title="Wavelet transform">Wavelet</a>
<ul><li><a href="Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li>
<li><a href="Discrete_wavelet_transform" title="Discrete wavelet transform">DWT</a></li>
<li><a href="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:1%">Predictive</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="Differential_pulse-code_modulation" title="Differential pulse-code modulation">DPCM</a>
<ul><li><a href="Adaptive_differential_pulse-code_modulation" title="Adaptive differential pulse-code modulation">ADPCM</a></li></ul></li>
<li><a href="Linear_predictive_coding" title="Linear predictive coding">LPC</a>
<ul><li><a href="Algebraic_code-excited_linear_prediction" title="Algebraic code-excited linear prediction">ACELP</a></li>
<li><a href="Code-excited_linear_prediction" title="Code-excited linear prediction">CELP</a></li>
<li><a href="Log_area_ratio" title="Log area ratio">LAR</a></li>
<li><a href="Line_spectral_pairs" title="Line spectral pairs">LSP</a></li>
<li><a href="Warped_linear_predictive_coding" title="Warped linear predictive coding">WLPC</a></li></ul></li>
<li>Motion
<ul><li><a href="Motion_compensation" title="Motion compensation">Compensation</a></li>
<li><a href="Motion_estimation" title="Motion estimation">Estimation</a></li>
<li><a href="Motion_vector" class="mw-redirect" title="Motion vector">Vector</a></li></ul></li>
<li><a href="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="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:1%">Concepts</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="Bit_rate" title="Bit rate">Bit rate</a>
<ul><li><a href="Average_bitrate" title="Average bitrate">ABR</a></li>
<li><a href="Constant_bitrate" title="Constant bitrate">CBR</a></li>
<li><a href="Variable_bitrate" title="Variable bitrate">VBR</a></li></ul></li>
<li><a href="Companding" title="Companding">Companding</a></li>
<li><a href="Convolution" title="Convolution">Convolution</a></li>
<li><a href="Dynamic_range" title="Dynamic range">Dynamic range</a></li>
<li><a href="Latency_(audio)" title="Latency (audio)">Latency</a></li>
<li><a href="Nyquist%E2%80%93Shannon_sampling_theorem" title="Nyquist–Shannon sampling theorem">Nyquist–Shannon theorem</a></li>
<li><a href="Sampling_(signal_processing)" title="Sampling (signal processing)">Sampling</a></li>
<li><a href="Silence_compression" title="Silence compression">Silence compression</a></li>
<li><a href="Sound_quality" title="Sound quality">Sound quality</a></li>
<li><a href="Speech_coding" title="Speech coding">Speech coding</a></li>
<li><a href="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:1%"><a href="Audio_codec" title="Audio codec">Codec</a><br>parts</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="A-law_algorithm" title="A-law algorithm">A-law</a></li>
<li><a href="%CE%9C-law_algorithm" title="Μ-law algorithm">μ-law</a></li>
<li><a href="Differential_pulse-code_modulation" title="Differential pulse-code modulation">DPCM</a>
<ul><li><a href="Adaptive_differential_pulse-code_modulation" title="Adaptive differential pulse-code modulation">ADPCM</a></li>
<li><a href="Delta_modulation" title="Delta modulation">DM</a></li></ul></li>
<li><a href="Fourier_transform" title="Fourier transform">FT</a>
<ul><li><a href="Fast_Fourier_transform" title="Fast Fourier transform">FFT</a></li></ul></li>
<li><a href="Linear_predictive_coding" title="Linear predictive coding">LPC</a>
<ul><li><a href="Algebraic_code-excited_linear_prediction" title="Algebraic code-excited linear prediction">ACELP</a></li>
<li><a href="Code-excited_linear_prediction" title="Code-excited linear prediction">CELP</a></li>
<li><a href="Log_area_ratio" title="Log area ratio">LAR</a></li>
<li><a href="Line_spectral_pairs" title="Line spectral pairs">LSP</a></li>
<li><a href="Warped_linear_predictive_coding" title="Warped linear predictive coding">WLPC</a></li></ul></li>
<li><a href="Modified_discrete_cosine_transform" title="Modified discrete cosine transform">MDCT</a></li>
<li><a href="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="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:1%">Concepts</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="Chroma_subsampling" title="Chroma subsampling">Chroma subsampling</a></li>
<li><a href="Coding_tree_unit" title="Coding tree unit">Coding tree unit</a></li>
<li><a href="Color_space" title="Color space">Color space</a></li>
<li><a href="Compression_artifact" title="Compression artifact">Compression artifact</a></li>
<li><a href="Image_resolution" title="Image resolution">Image resolution</a></li>
<li><a href="Macroblock" title="Macroblock">Macroblock</a></li>
<li><a href="Pixel" title="Pixel">Pixel</a></li>
<li><a href="Peak_signal-to-noise_ratio" title="Peak signal-to-noise ratio">PSNR</a></li>
<li><a href="Quantization_(image_processing)" title="Quantization (image processing)">Quantization</a></li>
<li><a href="Standard_test_image" title="Standard test image">Standard test image</a></li>
<li><a href="Texture_compression" title="Texture compression">Texture compression</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Methods</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="Chain_code" title="Chain code">Chain code</a></li>
<li><a href="Discrete_cosine_transform" title="Discrete cosine transform">DCT</a></li>
<li><a href="Deflate" title="Deflate">Deflate</a></li>
<li><a href="Fractal_compression" title="Fractal compression">Fractal</a></li>
<li><a href="Karhunen%E2%80%93Lo%C3%A8ve_theorem" class="mw-redirect" title="Karhunen–Loève theorem">KLT</a></li>
<li><a href="Pyramid_(image_processing)" title="Pyramid (image processing)">LP</a></li>
<li><a href="Run-length_encoding" title="Run-length encoding">RLE</a></li>
<li><a href="Wavelet_transform" title="Wavelet transform">Wavelet</a>
<ul><li><a href="Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li>
<li><a href="Discrete_wavelet_transform" title="Discrete wavelet transform">DWT</a></li>
<li><a href="Embedded_zerotrees_of_wavelet_transforms" title="Embedded zerotrees of wavelet transforms">EZW</a></li>
<li><a href="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="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:1%">Concepts</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="Bit_rate" title="Bit rate">Bit rate</a>
<ul><li><a href="Average_bitrate" title="Average bitrate">ABR</a></li>
<li><a href="Constant_bitrate" title="Constant bitrate">CBR</a></li>
<li><a href="Variable_bitrate" title="Variable bitrate">VBR</a></li></ul></li>
<li><a href="Display_resolution" title="Display resolution">Display resolution</a></li>
<li><a href="Film_frame" title="Film frame">Frame</a></li>
<li><a href="Frame_rate" title="Frame rate">Frame rate</a></li>
<li><a href="Video_compression_picture_types" title="Video compression picture types">Frame types</a></li>
<li><a href="Interlaced_video" title="Interlaced video">Interlace</a></li>
<li><a href="Video#Characteristics_of_video_streams" title="Video">Video characteristics</a></li>
<li><a href="Video_quality" title="Video quality">Video quality</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Video_codec" title="Video codec">Codec</a><br>parts</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="Discrete_cosine_transform" title="Discrete cosine transform">DCT</a></li>
<li><a href="Differential_pulse-code_modulation" title="Differential pulse-code modulation">DPCM</a></li>
<li><a href="Deblocking_filter" title="Deblocking filter">Deblocking filter</a></li>
<li><a href="Lapped_transform" title="Lapped transform">Lapped transform</a></li>
<li>Motion
<ul><li><a href="Motion_compensation" title="Motion compensation">Compensation</a></li>
<li><a href="Motion_estimation" title="Motion estimation">Estimation</a></li>
<li><a href="Motion_vector" class="mw-redirect" title="Motion vector">Vector</a></li></ul></li>
<li><a href="Wavelet_transform" title="Wavelet transform">Wavelet</a>
<ul><li><a href="Daubechies_wavelet" title="Daubechies wavelet">Daubechies</a></li>
<li><a href="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="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="Compressed_data_structure" title="Compressed data structure">Compressed data structures</a>
<ul><li><a href="Compressed_suffix_array" title="Compressed suffix array">Compressed suffix array</a></li>
<li><a href="FM-index" title="FM-index">FM-index</a></li></ul></li>
<li><a href="Entropy_(information_theory)" title="Entropy (information theory)">Entropy</a></li>
<li><a href="Information_theory" title="Information theory">Information theory</a>
<ul><li><a href="Timeline_of_information_theory" title="Timeline of information theory">Timeline</a></li></ul></li>
<li><a href="Kolmogorov_complexity" title="Kolmogorov complexity">Kolmogorov complexity</a></li>
<li><a href="Prefix_code" title="Prefix code">Prefix code</a></li>
<li><a href="Quantization_(signal_processing)" title="Quantization (signal processing)">Quantization</a></li>
<li><a href="Rate%E2%80%93distortion_theory" title="Rate–distortion theory">Rate–distortion</a></li>
<li><a href="Redundancy_(information_theory)" title="Redundancy (information theory)">Redundancy</a></li>
<li><a href="Data_compression_symmetry" title="Data compression symmetry">Symmetry</a></li>
<li><a href="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="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="Mark_Adler" title="Mark Adler">Mark Adler</a></li>
<li><a href="Phil_Katz" title="Phil Katz">Phil Katz</a></li></ul>
</div></td></tr></tbody></table></div>
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