Data compression

<h2 id="lossless">Lossless</h2>
Main article: <a href="/facts/Lossless_compression/LS702KsN">Lossless compression</a>
<a href="/facts/Lossless_data_compression/LS702KsN">Lossless data compression</a> <a href="/facts/Algorithm/fnl5NmRt">algorithms</a> usually exploit <a href="/facts/Redundancy_(information_theory)/HnbfBLE0">statistical redundancy</a> to represent data without losing any <a href="/facts/Self-information/EkUdL669">information</a>, so that the process is reversible. Lossless compression is possible because most real-world data exhibits statistical redundancy. For example, an image may have areas of color that do not change over several pixels; instead of coding "red pixel, red pixel, ..." the data may be encoded as "279 red pixels". This is a basic example of <a href="/facts/Run-length_encoding/3k6x9afM">run-length encoding</a>; there are many schemes to reduce file size by eliminating redundancy.
The <a href="/facts/Lempel%E2%80%93Ziv/HGH09JM9">Lempel–Ziv</a> (LZ) compression methods are among the most popular algorithms for lossless storage.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> <a href="/facts/DEFLATE/XnBt1GKV">DEFLATE</a> is a variation on LZ optimized for decompression speed and compression ratio,<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> but compression can be slow. In the mid-1980s, following work by <a href="/facts/Terry_Welch/N3yr3mud">Terry Welch</a>, the <a href="/facts/Lempel%E2%80%93Ziv%E2%80%93Welch/hJfgYm9j">Lempel–Ziv–Welch</a> (LZW) algorithm rapidly became the method of choice for most general-purpose compression systems. LZW is used in <a href="/facts/GIF/HfIBWrIC">GIF</a> images, programs such as <a href="/facts/PKZIP/kTgEHX8w">PKZIP</a>, and hardware devices such as modems.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> LZ methods use a table-based compression model where table entries are substituted for repeated strings of data. For most LZ methods, this table is generated dynamically from earlier data in the input. The table itself is often <a href="/facts/Huffman_coding/dBgMBz48">Huffman encoded</a>. <a href="/facts/Grammar-based_codes/z308LVJV">Grammar-based codes</a> like this can compress highly repetitive input extremely effectively, for instance, a biological <a href="/facts/Data_collection/rEGBdDzj">data collection</a> of the same or closely related species, a huge versioned document collection, internet archival, etc. The basic task of grammar-based codes is constructing a context-free grammar deriving a single string. Other practical grammar compression algorithms include <a href="/facts/Sequitur_algorithm/8KougpNI">Sequitur</a> and <a href="/facts/Re-Pair/gz3cKCEN">Re-Pair</a>.
The strongest modern lossless compressors use <a href="/facts/Randomized_algorithm/Fngl1zgk">probabilistic</a> models, such as <a href="/facts/Prediction_by_partial_matching/cc621LIE">prediction by partial matching</a>. The <a href="/facts/Burrows%E2%80%93Wheeler_transform/yxIc9E94">Burrows–Wheeler transform</a> can also be viewed as an indirect form of statistical modelling.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> In a further refinement of the direct use of <a href="/facts/Probabilistic_model/jKkT5ftm">probabilistic modelling</a>, statistical estimates can be coupled to an algorithm called <a href="/facts/Arithmetic_coding/WU0H4oNu">arithmetic coding</a>. Arithmetic coding is a more modern coding technique that uses the mathematical calculations of a <a href="/facts/Finite-state_machine/GMusWd0a">finite-state machine</a> to produce a string of encoded bits from a series of input data symbols. It can achieve superior compression compared to other techniques such as the better-known Huffman algorithm. It uses an internal memory state to avoid the need to perform a one-to-one mapping of individual input symbols to distinct representations that use an integer number of bits, and it clears out the internal memory only after encoding the entire string of data symbols. Arithmetic coding applies especially well to adaptive data compression tasks where the statistics vary and are context-dependent, as it can be easily coupled with an adaptive model of the <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> of the input data. An early example of the use of arithmetic coding was in an optional (but not widely used) feature of the <a href="/facts/JPEG/HQ8QS3uB">JPEG</a> image coding standard.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> It has since been applied in various other designs including <a href="/facts/H.263/KSxo04Gy">H.263</a>, <a href="/facts/H.264/MPEG-4_AVC/soCzKcmJ">H.264/MPEG-4 AVC</a> and <a href="/facts/HEVC/6gp7DC1a">HEVC</a> for video coding.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a>
Archive software typically has the ability to adjust the "dictionary size", where a larger size demands more <a href="/facts/Random-access_memory/DuD4bxh6">random-access memory</a> during compression and decompression, but compresses stronger, especially on repeating patterns in files' content.<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a><a class="footnote-ref" id="fnref:13" href="#fn:13">13</a>

<h2 id="lossy">Lossy</h2>
Main article: <a href="/facts/Lossy_compression/jHW7DDv3">Lossy compression</a>

In the late 1980s, digital images became more common, and standards for lossless <a href="/facts/Image_compression/q9bfesUr">image compression</a> emerged. In the early 1990s, lossy compression methods began to be widely used.<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a> In these schemes, some loss of information is accepted as dropping nonessential detail can save storage space. There is a corresponding <a href="/facts/Trade-off/xY3nXnJN">trade-off</a> between preserving information and reducing size. Lossy data compression schemes are designed by research on how people perceive the data in question. For example, the human eye is more sensitive to subtle variations in <a href="/facts/Luminance/yAqK94ny">luminance</a> than it is to the variations in color. JPEG image compression works in part by rounding off nonessential bits of information.<a class="footnote-ref" id="fnref:15" href="#fn:15">15</a> A number of popular compression formats exploit these perceptual differences, including <a href="/facts/Psychoacoustics/1GRCBbfQ">psychoacoustics</a> for sound, and <a href="/facts/Psychovisual/wy2YpcIq">psychovisuals</a> for images and video.
Most forms of lossy compression are based on <a href="/facts/Transform_coding/JGJISRFW">transform coding</a>, especially the <a href="/facts/Discrete_cosine_transform/gPpDhPwP">discrete cosine transform</a> (DCT). It was first proposed in 1972 by <a href="/facts/N._Ahmed/LImldyWe">Nasir Ahmed</a>, who then developed a working algorithm with T. Natarajan and <a href="/facts/K._R._Rao/DwrVrQ6u">K. R. Rao</a> in 1973, before introducing it in January 1974.<a class="footnote-ref" id="fnref:16" href="#fn:16">16</a><a class="footnote-ref" id="fnref:17" href="#fn:17">17</a> DCT is the most widely used lossy compression method, and is used in multimedia formats for images (such as JPEG and <a href="/facts/HEIF/knA4bTT6">HEIF</a>),<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a> <a href="/facts/Video_compression/gMFuY4FT">video</a> (such as <a href="/facts/MPEG/ygmT7JBB">MPEG</a>, <a href="/facts/H.264/AVC/soCzKcmJ">AVC</a> and HEVC) and audio (such as <a href="/facts/MP3/yrBpxUSD">MP3</a>, <a href="/facts/Advanced_Audio_Coding/VAG9NpI4">AAC</a> and <a href="/facts/Vorbis/rqJDTF0T">Vorbis</a>).
Lossy image compression is used in <a href="/facts/Digital_camera/LSGTserm">digital cameras</a>, to increase storage capacities. Similarly, <a href="/facts/DVD/7fJsHJrN">DVDs</a>, <a href="/facts/Blu-ray/zyPalhfG">Blu-ray</a> and <a href="/facts/Streaming_video/4rPhSq0Y">streaming video</a> use lossy <a href="/facts/Video_coding_format/Dmzykxmn">video coding formats</a>. Lossy compression is extensively used in video.
In lossy audio compression, methods of psychoacoustics are used to remove non-audible (or less audible) components of the <a href="/facts/Audio_signal/rFSTI9IF">audio signal</a>. Compression of human speech is often performed with even more specialized techniques; <a href="/facts/Speech_coding/xs5gvMXq">speech coding</a> is distinguished as a separate discipline from general-purpose audio compression. Speech coding is used in <a href="/facts/Internet_telephony/5QGBbXYg">internet telephony</a>, for example, audio compression is used for CD ripping and is decoded by the audio players.<a class="footnote-ref" id="fnref:19" href="#fn:19">19</a>
Lossy compression can cause <a href="/facts/Generation_loss/KbuLJnrA">generation loss</a>.

<h2 id="theory">Theory</h2>
The theoretical basis for compression is provided by <a href="/facts/Information_theory/qNLH3U5P">information theory</a> and, more specifically, <a href="/facts/Shannon%27s_source_coding_theorem/MHSHNrcI">Shannon's source coding theorem</a>; domain-specific theories include <a href="/facts/Algorithmic_information_theory/Tltn3I0Y">algorithmic information theory</a> for lossless compression and <a href="/facts/Rate%E2%80%93distortion_theory/a5P5krWF">rate–distortion theory</a> for lossy compression. These areas of study were essentially created by <a href="/facts/Claude_Shannon/EremsCws">Claude Shannon</a>, who published fundamental papers on the topic in the late 1940s and early 1950s. Other topics associated with compression include <a href="/facts/Coding_theory/SBqStoGL">coding theory</a> and <a href="/facts/Statistical_inference/sJLjubxm">statistical inference</a>.<a class="footnote-ref" id="fnref:20" href="#fn:20">20</a>

<h3>Machine learning</h3>
There is a close connection between <a href="/facts/Machine_learning/e0w0XJTu">machine learning</a> and compression. A system that predicts the <a href="/facts/Posterior_probabilities/fojsMD0D">posterior probabilities</a> of a sequence given its entire history can be used for optimal data compression (by using <a href="/facts/Arithmetic_coding/WU0H4oNu">arithmetic coding</a> on the output distribution). Conversely, an optimal compressor can be used for prediction (by finding the symbol that compresses best, given the previous history). This equivalence has been used as a justification for using data compression as a benchmark for "general intelligence".<a class="footnote-ref" id="fnref:21" href="#fn:21">21</a><a class="footnote-ref" id="fnref:22" href="#fn:22">22</a><a class="footnote-ref" id="fnref:23" href="#fn:23">23</a>
An alternative view can show compression algorithms implicitly map strings into implicit <a href="/facts/Feature_space_vector/nzAhYxfu">feature space vectors</a>, and compression-based similarity measures compute similarity within these feature spaces. For each compressor C(.) we define an associated vector space ℵ, such that C(.) maps an input string x, corresponding to the vector norm ||~x||. An exhaustive examination of the feature spaces underlying all compression algorithms is precluded by space; instead, feature vectors chooses to examine three representative lossless compression methods, LZW, LZ77, and PPM.<a class="footnote-ref" id="fnref:24" href="#fn:24">24</a>
According to <a href="/facts/AIXI/lVfxaghv">AIXI</a> theory, a connection more directly explained in <a href="/facts/Hutter_Prize/6M1AvbXt">Hutter Prize</a>, the best possible compression of x is the smallest possible software that generates x. For example, in that model, a zip file's compressed size includes both the zip file and the unzipping software, since you can not unzip it without both, but there may be an even smaller combined form.
Examples of AI-powered audio/video compression software include <a href="/facts/NVIDIA_Maxine/8QfCgqbu">NVIDIA Maxine</a>, AIVC.<a class="footnote-ref" id="fnref:25" href="#fn:25">25</a> Examples of software that can perform AI-powered image compression include <a href="/facts/OpenCV/V1tXAxyz">OpenCV</a>, <a href="/facts/TensorFlow/kDwfBeNd">TensorFlow</a>, <a href="/facts/MATLAB/qPjLISCk">MATLAB</a>'s Image Processing Toolbox (IPT) and High-Fidelity Generative Image Compression.<a class="footnote-ref" id="fnref:26" href="#fn:26">26</a>
In <a href="/facts/Unsupervised_machine_learning/8a6f61MC">unsupervised machine learning</a>, <a href="/facts/K-means_clustering/vxIcqHwN">k-means clustering</a> can be utilized to compress data by grouping similar data points into clusters. This technique simplifies handling extensive datasets that lack predefined labels and finds widespread use in fields such as <a href="/facts/Image_compression/q9bfesUr">image compression</a>.<a class="footnote-ref" id="fnref:27" href="#fn:27">27</a>
Data compression aims to reduce the size of data files, enhancing storage efficiency and speeding up data transmission. K-means clustering, an unsupervised machine learning algorithm, is employed to partition a dataset into a specified number of clusters, k, each represented by the <a href="/facts/Centroid/H6dDbg0h">centroid</a> of its points. This process condenses extensive datasets into a more compact set of representative points. Particularly beneficial in <a href="/facts/Image_processing/zenalNCf">image</a> and <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>, k-means clustering aids in data reduction by replacing groups of data points with their centroids, thereby preserving the core information of the original data while significantly decreasing the required storage space.<a class="footnote-ref" id="fnref:28" href="#fn:28">28</a>
<a href="/facts/Large_language_model/WnogWVJY">Large language models</a> (LLMs) are also efficient lossless data compressors on some data sets, as demonstrated by <a href="/facts/DeepMind/n5ehBwCx">DeepMind</a>'s research with the Chinchilla 70B model. Developed by DeepMind, Chinchilla 70B effectively compressed data, outperforming conventional methods such as <a href="/facts/Portable_Network_Graphics/mwgK6xw5">Portable Network Graphics</a> (PNG) for images and <a href="/facts/Free_Lossless_Audio_Codec/TbqpHlWy">Free Lossless Audio Codec</a> (FLAC) for audio. It achieved compression of image and audio data to 43.4% and 16.4% of their original sizes, respectively. There is, however, some reason to be concerned that the data set used for testing overlaps the LLM training data set, making it possible that the Chinchilla 70B model is only an efficient compression tool on data it has already been trained on.<a class="footnote-ref" id="fnref:29" href="#fn:29">29</a><a class="footnote-ref" id="fnref:30" href="#fn:30">30</a>

<h3>Data differencing</h3>

Data compression can be viewed as a special case of <a href="/facts/Data_differencing/b6RXlK2z">data differencing</a>.<a class="footnote-ref" id="fnref:31" href="#fn:31">31</a><a class="footnote-ref" id="fnref:32" href="#fn:32">32</a> Data differencing consists of producing a difference given a source and a target, with patching reproducing the target given a source and a difference. Since there is no separate source and target in data compression, one can consider data compression as data differencing with empty source data, the compressed file corresponding to a difference from nothing. This is the same as considering absolute <a href="/facts/Entropy_(information_theory)/NLg4NLvt">entropy</a> (corresponding to data compression) as a special case of <a href="/facts/Relative_entropy/nh7SjlPE">relative entropy</a> (corresponding to data differencing) with no initial data.
The term differential compression is used to emphasize the data differencing connection.

<h2 id="uses">Uses</h2>
<h3>Image</h3>
Main article: <a href="/facts/Image_compression/q9bfesUr">Image compression</a>
<a href="/facts/Entropy_coding/44I0n8F8">Entropy coding</a> originated in the 1940s with the introduction of <a href="/facts/Shannon%E2%80%93Fano_coding/6QNppyt9">Shannon–Fano coding</a>,<a class="footnote-ref" id="fnref:33" href="#fn:33">33</a> the basis for <a href="/facts/Huffman_coding/dBgMBz48">Huffman coding</a> which was developed in 1950.<a class="footnote-ref" id="fnref:34" href="#fn:34">34</a> <a href="/facts/Transform_coding/JGJISRFW">Transform coding</a> dates back to the late 1960s, with the introduction of <a href="/facts/Fast_Fourier_transform/caT7UUCh">fast Fourier transform</a> (FFT) coding in 1968 and the <a href="/facts/Hadamard_transform/JFD5uojA">Hadamard transform</a> in 1969.<a class="footnote-ref" id="fnref:35" href="#fn:35">35</a>
An important image compression technique is the <a href="/facts/Discrete_cosine_transform/gPpDhPwP">discrete cosine transform</a> (DCT), a technique developed in the early 1970s.<a class="footnote-ref" id="fnref:36" href="#fn:36">36</a> DCT is the basis for JPEG, a <a href="/facts/Lossy_compression/jHW7DDv3">lossy compression</a> format which was introduced by the <a href="/facts/Joint_Photographic_Experts_Group/KQK08bjR">Joint Photographic Experts Group</a> (JPEG) in 1992.<a class="footnote-ref" id="fnref:37" href="#fn:37">37</a> JPEG greatly reduces the amount of data required to represent an image at the cost of a relatively small reduction in image quality and has become the most widely used <a href="/facts/Image_file_format/tLGQogv3">image file format</a>.<a class="footnote-ref" id="fnref:38" href="#fn:38">38</a><a class="footnote-ref" id="fnref:39" href="#fn:39">39</a> Its highly efficient DCT-based compression algorithm was largely responsible for the wide proliferation of <a href="/facts/Digital_image/3TNT47Mv">digital images</a> and <a href="/facts/Digital_photo/a2UfweJh">digital photos</a>.<a class="footnote-ref" id="fnref:40" href="#fn:40">40</a>
<a href="/facts/Lempel%E2%80%93Ziv%E2%80%93Welch/hJfgYm9j">Lempel–Ziv–Welch</a> (LZW) is a <a href="/facts/Lossless_compression/LS702KsN">lossless compression</a> algorithm developed in 1984. It is used in the <a href="/facts/GIF/HfIBWrIC">GIF</a> format, introduced in 1987.<a class="footnote-ref" id="fnref:41" href="#fn:41">41</a> <a href="/facts/DEFLATE/XnBt1GKV">DEFLATE</a>, a lossless compression algorithm specified in 1996, is used in the <a href="/facts/Portable_Network_Graphics/mwgK6xw5">Portable Network Graphics</a> (PNG) format.<a class="footnote-ref" id="fnref:42" href="#fn:42">42</a>
<a href="/facts/Wavelet_compression/4vk3W5be">Wavelet compression</a>, the use of <a href="/facts/Wavelet/3XcX4uIP">wavelets</a> in image compression, began after the development of DCT coding.<a class="footnote-ref" id="fnref:43" href="#fn:43">43</a> The <a href="/facts/JPEG_2000/GAzXdHI2">JPEG 2000</a> standard was introduced in 2000.<a class="footnote-ref" id="fnref:44" href="#fn:44">44</a> In contrast to the DCT algorithm used by the original JPEG format, JPEG 2000 instead uses <a href="/facts/Discrete_wavelet_transform/19DVnk4n">discrete wavelet transform</a> (DWT) algorithms.<a class="footnote-ref" id="fnref:45" href="#fn:45">45</a><a class="footnote-ref" id="fnref:46" href="#fn:46">46</a><a class="footnote-ref" id="fnref:47" href="#fn:47">47</a> JPEG 2000 technology, which includes the <a href="/facts/Motion_JPEG_2000/6YfSeDAG">Motion JPEG 2000</a> extension, was selected as the <a href="/facts/Video_coding_standard/Dmzykxmn">video coding standard</a> for <a href="/facts/Digital_cinema/fc312V6y">digital cinema</a> in 2004.<a class="footnote-ref" id="fnref:48" href="#fn:48">48</a>

<h3>Audio</h3>
See also: <a href="/facts/Audio_coding_format/qHAhppfD">Audio coding format</a> and <a href="/facts/Audio_codec/DkXoa6YP">Audio codec</a>
Audio data compression, not to be confused with <a href="/facts/Dynamic_range_compression/oVSzPxFY">dynamic range compression</a>, has the potential to reduce the transmission <a href="/facts/Bandwidth_(computing)/lY6Tb4gX">bandwidth</a> and storage requirements of audio data. <a href="/facts/List_of_codecs/e5nTCc5X">Audio compression formats compression algorithms</a> are implemented in <a href="/facts/Software/RP79lVSW">software</a> as audio <a href="/facts/Codec/C7b7Am8t">codecs</a>. In both lossy and lossless compression, <a href="/facts/Redundancy_(information_theory)/HnbfBLE0">information redundancy</a> is reduced, using methods such as <a href="/facts/Coding_theory/SBqStoGL">coding</a>, <a href="/facts/Quantization_(signal_processing)/fddS3BE2">quantization</a>, DCT and <a href="/facts/Linear_prediction/u8gzoURe">linear prediction</a> to reduce the amount of information used to represent the uncompressed data.
Lossy audio compression algorithms provide higher compression and are used in numerous audio applications including <a href="/facts/Vorbis/rqJDTF0T">Vorbis</a> and <a href="/facts/MP3/yrBpxUSD">MP3</a>. These algorithms almost all rely on <a href="/facts/Psychoacoustics/1GRCBbfQ">psychoacoustics</a> to eliminate or reduce fidelity of less audible sounds, thereby reducing the space required to store or transmit them.<a class="footnote-ref" id="fnref:49" href="#fn:49">49</a><a class="footnote-ref" id="fnref:50" href="#fn:50">50</a>
The acceptable trade-off between loss of audio quality and transmission or storage size depends upon the application. For example, one 640 MB <a href="/facts/Compact_disc/g51GRloc">compact disc</a> (CD) holds approximately one hour of uncompressed <a href="/facts/High_fidelity/K6kaTHSw">high fidelity</a> music, less than 2 hours of music compressed losslessly, or 7 hours of music compressed in the <a href="/facts/MP3/yrBpxUSD">MP3</a> format at a medium <a href="/facts/Bit_rate/ppUNMmVd">bit rate</a>. A digital sound recorder can typically store around 200 hours of clearly intelligible speech in 640 MB.<a class="footnote-ref" id="fnref:51" href="#fn:51">51</a>
Lossless audio compression produces a representation of digital data that can be decoded to an exact digital duplicate of the original. Compression ratios are around 50–60% of the original size,<a class="footnote-ref" id="fnref:52" href="#fn:52">52</a> which is similar to those for generic lossless data compression. Lossless codecs use <a href="/facts/Curve_fitting/zrLKw6Xj">curve fitting</a> or linear prediction as a basis for estimating the signal. Parameters describing the estimation and the difference between the estimation and the actual signal are coded separately.<a class="footnote-ref" id="fnref:53" href="#fn:53">53</a>
A number of lossless audio compression formats exist. See <a href="/facts/List_of_codecs/e5nTCc5X">list of lossless codecs</a> for a listing. Some formats are associated with a distinct system, such as <a href="/facts/Direct_Stream_Transfer/f4a7Gu0V">Direct Stream Transfer</a>, used in <a href="/facts/Super_Audio_CD/f4a7Gu0V">Super Audio CD</a> and <a href="/facts/Meridian_Lossless_Packing/uUXCuWSE">Meridian Lossless Packing</a>, used in <a href="/facts/DVD-Audio/X5I65Vxd">DVD-Audio</a>, <a href="/facts/Dolby_TrueHD/ySxj3zIY">Dolby TrueHD</a>, <a href="/facts/Blu-ray/zyPalhfG">Blu-ray</a> and <a href="/facts/HD_DVD/ULvpqYxb">HD DVD</a>.
Some <a href="/facts/Audio_file_format/hLgkfATf">audio file formats</a> feature a combination of a lossy format and a lossless correction; this allows stripping the correction to easily obtain a lossy file. Such formats include <a href="/facts/MPEG-4_SLS/0hcHB4NH">MPEG-4 SLS</a> (Scalable to Lossless), <a href="/facts/WavPack/MN8nT9Gj">WavPack</a>, and <a href="/facts/OptimFROG_DualStream/NHF2DoKS">OptimFROG DualStream</a>.
When audio files are to be processed, either by further compression or for <a href="/facts/Audio_editing/vbbu6a3M">editing</a>, it is desirable to work from an unchanged original (uncompressed or losslessly compressed). Processing of a lossily compressed file for some purpose usually produces a final result inferior to the creation of the same compressed file from an uncompressed original. In addition to sound editing or mixing, lossless audio compression is often used for archival storage, or as master copies.

<h4>Lossy audio compression</h4>

Lossy audio compression is used in a wide range of applications. In addition to standalone audio-only applications of file playback in MP3 players or computers, digitally compressed audio streams are used in most video DVDs, digital television, streaming media on the <a href="/facts/Internet/Xw1rVvJU">Internet</a>, satellite and cable radio, and increasingly in terrestrial radio broadcasts. Lossy compression typically achieves far greater compression than lossless compression, by discarding less-critical data based on <a href="/facts/Psychoacoustic/1GRCBbfQ">psychoacoustic</a> optimizations.<a class="footnote-ref" id="fnref:54" href="#fn:54">54</a>
Psychoacoustics recognizes that not all data in an audio stream can be perceived by the human <a href="/facts/Auditory_system/fJYTKjje">auditory system</a>. Most lossy compression reduces redundancy by first identifying perceptually irrelevant sounds, that is, sounds that are very hard to hear. Typical examples include high frequencies or sounds that occur at the same time as louder sounds. Those irrelevant sounds are coded with decreased accuracy or not at all.
Due to the nature of lossy algorithms, <a href="/facts/Audio_quality/YMdRK86Y">audio quality</a> suffers a <a href="/facts/Digital_generation_loss/KbuLJnrA">digital generation loss</a> when a file is decompressed and recompressed. This makes lossy compression unsuitable for storing the intermediate results in professional audio engineering applications, such as sound editing and multitrack recording. However, lossy formats such as <a href="/facts/MP3/yrBpxUSD">MP3</a> are very popular with end-users as the file size is reduced to 5-20% of the original size and a megabyte can store about a minute's worth of music at adequate quality.
Several proprietary lossy compression algorithms have been developed that provide higher quality audio performance by using a combination of lossless and lossy algorithms with adaptive bit rates and lower compression ratios. Examples include <a href="/facts/AptX/cSevMczh">aptX</a>, <a href="/facts/LDAC_(codec)/IMFHz8ux">LDAC</a>, <a href="/facts/LHDC_(codec)/2osrkypU">LHDC</a>, <a href="/facts/Master_Quality_Authenticated/alxKG7Se">MQA</a> and SCL6.

<h5>Coding methods</h5>
To determine what information in an audio signal is perceptually irrelevant, most lossy compression algorithms use transforms such as the <a href="/facts/Modified_discrete_cosine_transform/jCaDMSNY">modified discrete cosine transform</a> (MDCT) to convert <a href="/facts/Time_domain/1w6mP2MU">time domain</a> sampled waveforms into a transform domain, typically the <a href="/facts/Frequency_domain/pyTVrUSq">frequency domain</a>. Once transformed, component frequencies can be prioritized according to how audible they are. Audibility of spectral components is assessed using the <a href="/facts/Absolute_threshold_of_hearing/Fn3TzQ3p">absolute threshold of hearing</a> and the principles of <a href="/facts/Simultaneous_masking/aMTJrGMc">simultaneous masking</a>—the phenomenon wherein a signal is masked by another signal separated by frequency—and, in some cases, <a href="/facts/Temporal_masking/aMTJrGMc">temporal masking</a>—where a signal is masked by another signal separated by time. <a href="/facts/Equal-loudness_contour/TamhqmSc">Equal-loudness contours</a> may also be used to weigh the perceptual importance of components. Models of the human ear-brain combination incorporating such effects are often called <a href="/facts/Psychoacoustic_model/1GRCBbfQ">psychoacoustic models</a>.<a class="footnote-ref" id="fnref:55" href="#fn:55">55</a>
Other types of lossy compressors, such as the <a href="/facts/Linear_predictive_coding/2Bl1xdSN">linear predictive coding</a> (LPC) used with speech, are source-based coders. LPC uses a model of the human vocal tract to analyze speech sounds and infer the parameters used by the model to produce them moment to moment. These changing parameters are transmitted or stored and used to drive another model in the decoder which reproduces the sound.
Lossy formats are often used for the distribution of streaming audio or interactive communication (such as in cell phone networks). In such applications, the data must be decompressed as the data flows, rather than after the entire data stream has been transmitted. Not all audio codecs can be used for streaming applications.<a class="footnote-ref" id="fnref:56" href="#fn:56">56</a>
<a href="/facts/Latency_(engineering)/6Bjhn30H">Latency</a> is introduced by the methods used to encode and decode the data. Some codecs will analyze a longer segment, called a frame, of the data to optimize efficiency, and then code it in a manner that requires a larger segment of data at one time to decode. The inherent latency of the coding algorithm can be critical; for example, when there is a two-way transmission of data, such as with a telephone conversation, significant delays may seriously degrade the perceived quality.
In contrast to the speed of compression, which is proportional to the number of operations required by the algorithm, here latency refers to the number of samples that must be analyzed before a block of audio is processed. In the minimum case, latency is zero samples (e.g., if the coder/decoder simply reduces the number of bits used to quantize the signal). Time domain algorithms such as LPC also often have low latencies, hence their popularity in speech coding for telephony. In algorithms such as MP3, however, a large number of samples have to be analyzed to implement a psychoacoustic model in the frequency domain, and latency is on the order of 23 ms.

<h5>Speech encoding</h5>
<a href="/facts/Speech_encoding/xs5gvMXq">Speech encoding</a> is an important category of audio data compression. The perceptual models used to estimate what aspects of speech a human ear can hear are generally somewhat different from those used for music. The range of frequencies needed to convey the sounds of a human voice is normally far narrower than that needed for music, and the sound is normally less complex. As a result, speech can be encoded at high quality using a relatively low bit rate.
This is accomplished, in general, by some combination of two approaches:

<ul><li>Only encoding sounds that could be made by a single human voice.</li>
<li>Throwing away more of the data in the signal—keeping just enough to reconstruct an "intelligible" voice rather than the full frequency range of human <a href="/facts/Hearing/EPYrVkSx">hearing</a>.</li></ul>
The earliest algorithms used in speech encoding (and audio data compression in general) were the <a href="/facts/A-law_algorithm/PI9UC1nc">A-law algorithm</a> and the <a href="/facts/%CE%9C-law_algorithm/Ve8vJ6mb">μ-law algorithm</a>.

<h4>History</h4>

Early audio research was conducted at <a href="/facts/Bell_Labs/fKP5Gk0H">Bell Labs</a>. There, in 1950, <a href="/facts/C._Chapin_Cutler/HzbKmD9T">C. Chapin Cutler</a> filed the patent on <a href="/facts/Differential_pulse-code_modulation/v8H09k06">differential pulse-code modulation</a> (DPCM).<a class="footnote-ref" id="fnref:57" href="#fn:57">57</a> In 1973, <a href="/facts/Adaptive_DPCM/Q6cFrNUb">Adaptive DPCM</a> (ADPCM) was introduced by P. Cummiskey, <a href="/facts/Nikil_Jayant/WqT1a12L">Nikil S. Jayant</a> and <a href="/facts/James_L._Flanagan/SX7EGc37">James L. Flanagan</a>.<a class="footnote-ref" id="fnref:58" href="#fn:58">58</a><a class="footnote-ref" id="fnref:59" href="#fn:59">59</a>
<a href="/facts/Perceptual_coding/1GRCBbfQ">Perceptual coding</a> was first used for <a href="/facts/Speech_coding/xs5gvMXq">speech coding</a> compression, with <a href="/facts/Linear_predictive_coding/2Bl1xdSN">linear predictive coding</a> (LPC).<a class="footnote-ref" id="fnref:60" href="#fn:60">60</a> Initial concepts for LPC date back to the work of <a href="/facts/Fumitada_Itakura/RnbyhGNI">Fumitada Itakura</a> (<a href="/facts/Nagoya_University/0MABJXSj">Nagoya University</a>) and Shuzo Saito (<a href="/facts/Nippon_Telegraph_and_Telephone/a3gI457X">Nippon Telegraph and Telephone</a>) in 1966.<a class="footnote-ref" id="fnref:61" href="#fn:61">61</a> During the 1970s, <a href="/facts/Bishnu_S._Atal/bI2098fu">Bishnu S. Atal</a> and <a href="/facts/Manfred_R._Schroeder/0AQPXT8L">Manfred R. Schroeder</a> at <a href="/facts/Bell_Labs/fKP5Gk0H">Bell Labs</a> developed a form of LPC called <a href="/facts/Adaptive_predictive_coding/7uAwy6mJ">adaptive predictive coding</a> (APC), a perceptual coding algorithm that exploited the masking properties of the human ear, followed in the early 1980s with the <a href="/facts/Code-excited_linear_prediction/Shkm4bjo">code-excited linear prediction</a> (CELP) algorithm which achieved a significant <a href="/facts/Data_compression_ratio/eDEWGzTv">compression ratio</a> for its time.<a class="footnote-ref" id="fnref:62" href="#fn:62">62</a> Perceptual coding is used by modern audio compression formats such as <a href="/facts/MP3/yrBpxUSD">MP3</a><a class="footnote-ref" id="fnref:63" href="#fn:63">63</a> and <a href="/facts/Advanced_Audio_Codec/VAG9NpI4">AAC</a>.
<a href="/facts/Discrete_cosine_transform/gPpDhPwP">Discrete cosine transform</a> (DCT), developed by <a href="/facts/N._Ahmed/LImldyWe">Nasir Ahmed</a>, T. Natarajan and <a href="/facts/K._R._Rao/DwrVrQ6u">K. R. Rao</a> in 1974,<a class="footnote-ref" id="fnref:64" href="#fn:64">64</a> provided the basis for the <a href="/facts/Modified_discrete_cosine_transform/jCaDMSNY">modified discrete cosine transform</a> (MDCT) used by modern audio compression formats such as MP3,<a class="footnote-ref" id="fnref:65" href="#fn:65">65</a> <a href="/facts/Dolby_Digital/58JfURnU">Dolby Digital</a>,<a class="footnote-ref" id="fnref:66" href="#fn:66">66</a><a class="footnote-ref" id="fnref:67" href="#fn:67">67</a> and AAC.<a class="footnote-ref" id="fnref:68" href="#fn:68">68</a> MDCT was proposed by J. P. Princen, A. W. Johnson and A. B. Bradley in 1987,<a class="footnote-ref" id="fnref:69" href="#fn:69">69</a> following earlier work by Princen and Bradley in 1986.<a class="footnote-ref" id="fnref:70" href="#fn:70">70</a>
The world's first commercial <a href="/facts/Broadcast_automation/dRRN2o0f">broadcast automation</a> audio compression system was developed by Oscar Bonello, an engineering professor at the <a href="/facts/University_of_Buenos_Aires/Jr5Hg023">University of Buenos Aires</a>.
<a class="footnote-ref" id="fnref:71" href="#fn:71">71</a>
In 1983, using the psychoacoustic principle of the masking of critical bands first published in 1967,<a class="footnote-ref" id="fnref:72" href="#fn:72">72</a> he started developing a practical application based on the recently developed <a href="/facts/IBM_PC/yhcJGMPL">IBM PC</a> computer, and the broadcast automation system was launched in 1987 under the name <a href="/facts/Audicom/Y9GEatQp">Audicom</a>.
<a class="footnote-ref" id="fnref:73" href="#fn:73">73</a>
35 years later, almost all the radio stations in the world were using this technology manufactured by a number of companies because the inventor refused to patent his work, preferring to publish it and leave it in the public domain.
<a class="footnote-ref" id="fnref:74" href="#fn:74">74</a>
A literature compendium for a large variety of audio coding systems was published in the IEEE's Journal on Selected Areas in Communications (JSAC), in February 1988. While there were some papers from before that time, this collection documented an entire variety of finished, working audio coders, nearly all of them using perceptual techniques and some kind of frequency analysis and back-end noiseless coding.<a class="footnote-ref" id="fnref:75" href="#fn:75">75</a>

<h3>Video</h3>
See also: <a href="/facts/Video_coding_format/Dmzykxmn">Video coding format</a> and <a href="/facts/Video_codec/psfSuqg7">Video codec</a>
<a href="/facts/Uncompressed_video/Me7fBF9w">Uncompressed video</a> requires a very high <a href="/facts/Uncompressed_video/Me7fBF9w">data rate</a>. Although <a href="/facts/List_of_codecs/e5nTCc5X">lossless video compression</a> codecs perform at a compression factor of 5 to 12, a typical <a href="/facts/H.264/soCzKcmJ">H.264</a> lossy compression video has a compression factor between 20 and 200.<a class="footnote-ref" id="fnref:76" href="#fn:76">76</a>
The two key video compression techniques used in <a href="/facts/Video_coding_standards/Dmzykxmn">video coding standards</a> are the DCT and <a href="/facts/Motion_compensation/6BM2Ylxn">motion compensation</a> (MC). Most video coding standards, such as the <a href="/facts/H.26x/Bzyj7FEY">H.26x</a> and <a href="/facts/MPEG/ygmT7JBB">MPEG</a> formats, typically use motion-compensated DCT video coding (block motion compensation).<a class="footnote-ref" id="fnref:77" href="#fn:77">77</a><a class="footnote-ref" id="fnref:78" href="#fn:78">78</a>
Most video codecs are used alongside audio compression techniques to store the separate but complementary data streams as one combined package using so-called <a href="/facts/Container_format/mSfwwdSA">container formats</a>.<a class="footnote-ref" id="fnref:79" href="#fn:79">79</a>

<h4>Encoding theory</h4>
Video data may be represented as a series of still image frames. Such data usually contains abundant amounts of spatial and temporal <a href="/facts/Redundancy_(information_theory)/HnbfBLE0">redundancy</a>. Video compression algorithms attempt to reduce redundancy and store information more compactly.
Most <a href="/facts/Video_compression_formats/Dmzykxmn">video compression formats</a> and <a href="/facts/Video_codec/psfSuqg7">codecs</a> exploit both spatial and temporal redundancy (e.g. through difference coding with <a href="/facts/Motion_compensation/6BM2Ylxn">motion compensation</a>). Similarities can be encoded by only storing differences between e.g. temporally adjacent frames (inter-frame coding) or spatially adjacent pixels (intra-frame coding). <a href="/facts/Inter-frame/NgBrpVDl">Inter-frame</a> compression (a temporal <a href="/facts/Delta_encoding/2NQlyAUc">delta encoding</a>) (re)uses data from one or more earlier or later frames in a sequence to describe the current frame. <a href="/facts/Intra-frame_coding/wk2Sl9EU">Intra-frame coding</a>, on the other hand, uses only data from within the current frame, effectively being still-image compression.<a class="footnote-ref" id="fnref:80" href="#fn:80">80</a>
The <a href="/facts/Video_coding_format/Dmzykxmn">intra-frame video coding formats</a> used in camcorders and video editing employ simpler compression that uses only intra-frame prediction. This simplifies video editing software, as it prevents a situation in which a compressed frame refers to data that the editor has deleted.
Usually, video compression additionally employs <a href="/facts/Lossy_compression/jHW7DDv3">lossy compression</a> techniques like <a href="/facts/Quantization_(image_processing)/hXzWCrmY">quantization</a> that reduce aspects of the source data that are (more or less) irrelevant to the human visual perception by exploiting perceptual features of human vision. For example, small differences in color are more difficult to perceive than are changes in brightness. Compression algorithms can average a color across these similar areas in a manner similar to those used in JPEG image compression.<a class="footnote-ref" id="fnref:81" href="#fn:81">81</a> As in all lossy compression, there is a <a href="/facts/Trade-off/xY3nXnJN">trade-off</a> between <a href="/facts/Video_quality/9XmPrYUy">video quality</a> and <a href="/facts/Bit_rate/ppUNMmVd">bit rate</a>, cost of processing the compression and decompression, and system requirements. Highly compressed video may present visible or distracting <a href="/facts/Compression_artifact/7DhxoVAv">artifacts</a>.
Other methods other than the prevalent DCT-based transform formats, such as <a href="/facts/Fractal_compression/d2qUg7sc">fractal compression</a>, <a href="/facts/Matching_pursuit/CehQ67U0">matching pursuit</a> and the use of a <a href="/facts/Discrete_wavelet_transform/19DVnk4n">discrete wavelet transform</a> (DWT), have been the subject of some research, but are typically not used in practical products. <a href="/facts/Wavelet_compression/4vk3W5be">Wavelet compression</a> is used in still-image coders and video coders without motion compensation. Interest in fractal compression seems to be waning, due to recent theoretical analysis showing a comparative lack of effectiveness of such methods.<a class="footnote-ref" id="fnref:82" href="#fn:82">82</a>

<h5>Inter-frame coding</h5>
Main article: <a href="/facts/Inter_frame/NgBrpVDl">Inter frame</a>
Further information: <a href="/facts/Motion_compensation/6BM2Ylxn">Motion compensation</a>
In inter-frame coding, individual frames of a video sequence are compared from one frame to the next, and the <a href="/facts/Video_codec/psfSuqg7">video compression codec</a> records the <a href="/facts/Residual_frame/Wk1xL1cE">differences</a> to the reference frame. If the frame contains areas where nothing has moved, the system can simply issue a short command that copies that part of the previous frame into the next one. If sections of the frame move in a simple manner, the compressor can emit a (slightly longer) command that tells the decompressor to shift, rotate, lighten, or darken the copy. This longer command still remains much shorter than data generated by intra-frame compression. Usually, the encoder will also transmit a residue signal which describes the remaining more subtle differences to the reference imagery. Using entropy coding, these residue signals have a more compact representation than the full signal. In areas of video with more motion, the compression must encode more data to keep up with the larger number of pixels that are changing. Commonly during explosions, flames, flocks of animals, and in some panning shots, the high-frequency detail leads to quality decreases or to increases in the <a href="/facts/Variable_bitrate/RrRLn4dl">variable bitrate</a>.

<h4>Hybrid block-based transform formats</h4>

Many commonly used video compression methods (e.g., those in standards approved by the <a href="/facts/ITU-T/9nJwkPYx">ITU-T</a> or <a href="/facts/ISO/IacYR7Yg">ISO</a>) share the same basic architecture that dates back to <a href="/facts/H.261/2XzQrNgo">H.261</a> which was standardized in 1988 by the ITU-T. They mostly rely on the DCT, applied to rectangular blocks of neighboring pixels, and temporal prediction using <a href="/facts/Motion_vector/3PmP9Nfh">motion vectors</a>, as well as nowadays also an in-loop filtering step.
In the prediction stage, various <a href="/facts/Data_deduplication/sHuJ8zya">deduplication</a> and difference-coding techniques are applied that help decorrelate data and describe new data based on already transmitted data.
Then rectangular blocks of remaining <a href="/facts/Pixel/UzwBvXBV">pixel</a> data are transformed to the frequency domain. In the main lossy processing stage, frequency domain data gets quantized in order to reduce information that is irrelevant to human visual perception.
In the last stage statistical redundancy gets largely eliminated by an <a href="/facts/Entropy_coder/44I0n8F8">entropy coder</a> which often applies some form of arithmetic coding.
In an additional in-loop filtering stage various filters can be applied to the reconstructed image signal. By computing these filters also inside the encoding loop they can help compression because they can be applied to reference material before it gets used in the prediction process and they can be guided using the original signal. The most popular example are <a href="/facts/Deblocking_filter/vYmrEGh9">deblocking filters</a> that blur out blocking artifacts from quantization discontinuities at transform block boundaries.

<h4>History</h4>
Main article: <a href="/facts/Video_coding_format/Dmzykxmn">Video coding format § History</a>
In 1967, A.H. Robinson and C. Cherry proposed a <a href="/facts/Run-length_encoding/3k6x9afM">run-length encoding</a> bandwidth compression scheme for the transmission of analog television signals.<a class="footnote-ref" id="fnref:83" href="#fn:83">83</a> The DCT, which is fundamental to modern video compression,<a class="footnote-ref" id="fnref:84" href="#fn:84">84</a> was introduced by <a href="/facts/N._Ahmed/LImldyWe">Nasir Ahmed</a>, T. Natarajan and <a href="/facts/K._R._Rao/DwrVrQ6u">K. R. Rao</a> in 1974.<a class="footnote-ref" id="fnref:85" href="#fn:85">85</a><a class="footnote-ref" id="fnref:86" href="#fn:86">86</a>
<a href="/facts/H.261/2XzQrNgo">H.261</a>, which debuted in 1988, commercially introduced the prevalent basic architecture of video compression technology.<a class="footnote-ref" id="fnref:87" href="#fn:87">87</a> It was the first <a href="/facts/Video_coding_format/Dmzykxmn">video coding format</a> based on DCT compression.<a class="footnote-ref" id="fnref:88" href="#fn:88">88</a> H.261 was developed by a number of companies, including <a href="/facts/Hitachi/KeK38e82">Hitachi</a>, <a href="/facts/PictureTel/gmEhMF1E">PictureTel</a>, <a href="/facts/Nippon_Telegraph_and_Telephone/a3gI457X">NTT</a>, <a href="/facts/BT_plc/RV9sGpcD">BT</a> and <a href="/facts/Toshiba/QHRaw8Tr">Toshiba</a>.<a class="footnote-ref" id="fnref:89" href="#fn:89">89</a>
The most popular <a href="/facts/Video_coding_standard/Dmzykxmn">video coding standards</a> used for codecs have been the <a href="/facts/MPEG/ygmT7JBB">MPEG</a> standards. <a href="/facts/MPEG-1/ewnQQLPD">MPEG-1</a> was developed by the <a href="/facts/Motion_Picture_Experts_Group/ygmT7JBB">Motion Picture Experts Group</a> (MPEG) in 1991, and it was designed to compress <a href="/facts/VHS/aN1lffdC">VHS</a>-quality video. It was succeeded in 1994 by <a href="/facts/MPEG-2/SpuH5FJu">MPEG-2</a>/<a href="/facts/H.262/uKxBALVh">H.262</a>,<a class="footnote-ref" id="fnref:90" href="#fn:90">90</a> which was developed by a number of companies, primarily <a href="/facts/Sony/7x4tCtBd">Sony</a>, <a href="/facts/Technicolor_SA/gw0LfI7V">Thomson</a> and <a href="/facts/Mitsubishi_Electric/aRfAQNS8">Mitsubishi Electric</a>.<a class="footnote-ref" id="fnref:91" href="#fn:91">91</a> MPEG-2 became the standard video format for <a href="/facts/DVD/7fJsHJrN">DVD</a> and <a href="/facts/SD_digital_television/dvqEXg2A">SD digital television</a>.<a class="footnote-ref" id="fnref:92" href="#fn:92">92</a> In 1999, it was followed by <a href="/facts/MPEG-4_Visual/qrahXdyN">MPEG-4</a>/<a href="/facts/H.263/KSxo04Gy">H.263</a>.<a class="footnote-ref" id="fnref:93" href="#fn:93">93</a> It was also developed by a number of companies, primarily Mitsubishi Electric, <a href="/facts/Hitachi/KeK38e82">Hitachi</a> and <a href="/facts/Panasonic/TqkBQmgj">Panasonic</a>.<a class="footnote-ref" id="fnref:94" href="#fn:94">94</a>
<a href="/facts/H.264/MPEG-4_AVC/soCzKcmJ">H.264/MPEG-4 AVC</a> was developed in 2003 by a number of organizations, primarily Panasonic, <a href="/facts/Godo_kaisha/MGA9QHD6">Godo Kaisha IP Bridge</a> and <a href="/facts/LG_Electronics/9aeXYv1t">LG Electronics</a>.<a class="footnote-ref" id="fnref:95" href="#fn:95">95</a> AVC commercially introduced the modern <a href="/facts/Context-adaptive_binary_arithmetic_coding/nTRVHwH1">context-adaptive binary arithmetic coding</a> (CABAC) and <a href="/facts/Context-adaptive_variable-length_coding/f6auheYI">context-adaptive variable-length coding</a> (CAVLC) algorithms. AVC is the main video encoding standard for <a href="/facts/Blu-ray_Disc/zyPalhfG">Blu-ray Discs</a>, and is widely used by video sharing websites and streaming internet services such as <a href="/facts/YouTube/db276jst">YouTube</a>, <a href="/facts/Netflix/TKtlFVY9">Netflix</a>, <a href="/facts/Vimeo/3f9cQCEt">Vimeo</a>, and <a href="/facts/ITunes_Store/c3XFlT3q">iTunes Store</a>, web software such as <a href="/facts/Adobe_Flash_Player/IvnaoU7v">Adobe Flash Player</a> and <a href="/facts/Microsoft_Silverlight/SYKe8yL1">Microsoft Silverlight</a>, and various <a href="/facts/HDTV/AuE6FRFI">HDTV</a> broadcasts over terrestrial and satellite television.

<h3>Genetics</h3>
<a href="/facts/Genetics_compression_algorithms/MoEIlAyt">Genetics compression algorithms</a> are the latest generation of lossless algorithms that compress data (typically sequences of nucleotides) using both conventional compression algorithms and genetic algorithms adapted to the specific datatype. In 2012, a team of scientists from Johns Hopkins University published a genetic compression algorithm that does not use a reference genome for compression. HAPZIPPER was tailored for <a href="/facts/HapMap/L2ANDPC4">HapMap</a> data and achieves over 20-fold compression (95% reduction in file size), providing 2- to 4-fold better compression and is less computationally intensive than the leading general-purpose compression utilities. For this, Chanda, Elhaik, and Bader introduced MAF-based encoding (MAFE), which reduces the heterogeneity of the dataset by sorting SNPs by their minor allele frequency, thus homogenizing the dataset.<a class="footnote-ref" id="fnref:96" href="#fn:96">96</a> Other algorithms developed in 2009 and 2013 (DNAZip and GenomeZip) have compression ratios of up to 1200-fold—allowing 6 billion basepair diploid human genomes to be stored in 2.5 megabytes (relative to a reference genome or averaged over many genomes).<a class="footnote-ref" id="fnref:97" href="#fn:97">97</a><a class="footnote-ref" id="fnref:98" href="#fn:98">98</a> For a benchmark in genetics/genomics data compressors, see <a class="footnote-ref" id="fnref:99" href="#fn:99">99</a>

<h2 id="outlook-and-currently-unused-potential">Outlook and currently unused potential</h2>
It is estimated that the total amount of data that is stored on the world's storage devices could be further compressed with existing compression algorithms by a remaining average factor of 4.5:1.<a class="footnote-ref" id="fnref:100" href="#fn:100">100</a> It is estimated that the combined technological capacity of the world to store information provides 1,300 <a href="/facts/Exabytes/BNHUp9Qq">exabytes</a> of hardware digits in 2007, but when the corresponding content is optimally compressed, this only represents 295 exabytes of <a href="/facts/Shannon_information/EkUdL669">Shannon information</a>.<a class="footnote-ref" id="fnref:101" href="#fn:101">101</a>

<h2 id="see-also">See also</h2>

<ul><li><a href="/facts/HTTP_compression/clfoMHvy">HTTP compression</a></li>
<li><a href="/facts/Kolmogorov_complexity/L9ezq8pY">Kolmogorov complexity</a></li>
<li><a href="/facts/Minimum_description_length/em8tXqjf">Minimum description length</a></li>
<li><a href="/facts/Modulo-N_code/hcX6VRfu">Modulo-N code</a></li>
<li><a href="/facts/Motion_coding/ovDdeb9y">Motion coding</a></li>
<li><a href="/facts/Range_coding/36anhArm">Range coding</a></li>
<li><a href="/facts/Set_redundancy_compression/myB3avlf">Set redundancy compression</a></li>
<li><a href="/facts/Sub-band_coding/HWMqu3DR">Sub-band coding</a></li>
<li><a href="/facts/Universal_code_(data_compression)/9zn1cM2M">Universal code (data compression)</a></li>
<li><a href="/facts/Vector_quantization/rKNehCok">Vector quantization</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://dvd-hq.info/data_compression_3.php">"Part 3: Video compression"</a>, Data Compression Basics</li>
<li>Pierre Larbier, <a href="https://web.archive.org/web/20090905092232/http://extranet.ateme.com/download.php?file=1114">Using 10-bit AVC/H.264 Encoding with 4:2:2 for Broadcast Contribution</a>, Ateme, archived from <a href="http://extranet.ateme.com/download.php?file=1114">the original</a> on 2009-09-05</li>
<li><a href="https://web.archive.org/web/20170830224011/http://extranet.ateme.com/download.php?file=1194">Why does 10-bit save bandwidth (even when content is 8-bit)?</a> at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a> (archived 2017-08-30)</li>
<li><a href="https://web.archive.org/web/20170830224021/http://extranet.ateme.com/download.php?file=1196">Which compression technology should be used?</a> at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a> (archived 2017-08-30)</li>
<li><a href="http://media.wiley.com/product_data/excerpt/99/04705184/0470518499.pdf">Introduction to Compression Theory</a> (PDF), Wiley, <a href="https://web.archive.org/web/20070928023157/http://media.wiley.com/product_data/excerpt/99/04705184/0470518499.pdf">archived</a> (PDF) from the original on 2007-09-28</li>
<li><a href="http://tech.ebu.ch/docs/tech/tech3296.pdf">EBU subjective listening tests on low-bitrate audio codecs</a></li>
<li><a href="http://techgage.com/article/audio_archiving_guide_part_1_-_music_formats/">Audio Archiving Guide: Music Formats</a> (Guide for helping a user pick out the right codec)</li>
<li><a href="https://web.archive.org/web/20070928023157/http://mia.ece.uic.edu/~papers/WWW/MultimediaStandards/chapter7.pdf">MPEG 1&2 video compression intro (pdf format)</a> at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a> (archived September 28, 2007)</li>
<li><a href="http://wiki.hydrogenaud.io/index.php?title=Lossless_comparison">hydrogenaudio wiki comparison</a></li>
<li><a href="https://www.cs.cmu.edu/afs/cs/project/pscico-guyb/realworld/www/compression.pdf">Introduction to Data Compression</a> by Guy E Blelloch from <a href="/facts/CMU/3vxDJmTK">CMU</a></li>
<li><a href="http://www.monkeysaudio.com/theory.html">Explanation of lossless signal compression method used by most codecs</a></li>
<li><a href="https://web.archive.org/web/20100315021124/http://www.videsignline.com/howto/showArticle.jhtml?articleID=185301351">Videsignline – Intro to Video Compression</a> at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a> (archived 2010-03-15)</li>
<li><a href="https://web.archive.org/web/20130527124650/http://public.dhe.ibm.com/common/ssi/ecm/en/tsu12345usen/TSU12345USEN.PDF">Data Footprint Reduction Technology</a> at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a> (archived 2013-05-27)</li>
<li><a href="http://siliconmentor.blogspot.in/2014/12/what-is-run-length-coding-in-video.html">What is Run length Coding in video compression</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Wade, Graham (1994). Signal coding and processing (2 ed.). Cambridge University Press. p. 34. ISBN 978-0-521-42336-6. Retrieved 2011-12-22. The broad objective of source coding is to exploit or remove 'inefficient' redundancy in the PCM source and thereby achieve a reduction in the overall source rate R. <a href="978-0-521-42336-6" target="_blank">978-0-521-42336-6</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Mahdi, O.A.; Mohammed, M.A.; Mohamed, A.J. (November 2012). "Implementing a Novel Approach an Convert Audio Compression to Text Coding via Hybrid Technique" (PDF). International Journal of Computer Science Issues. 9 (6, No. 3): 53–59. Archived (PDF) from the original on 2013-03-20. Retrieved 6 March 2013. <a href="http://ijcsi.org/papers/IJCSI-9-6-3-53-59.pdf" target="_blank">http://ijcsi.org/papers/IJCSI-9-6-3-53-59.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Pujar, J.H.; Kadlaskar, L.M. (May 2010). "A New Lossless Method of Image Compression and Decompression Using Huffman Coding Techniques" (PDF). Journal of Theoretical and Applied Information Technology. 15 (1): 18–23. Archived (PDF) from the original on 2010-05-24. <a href="http://www.jatit.org/volumes/research-papers/Vol15No1/3Vol15No1.pdf" target="_blank">http://www.jatit.org/volumes/research-papers/Vol15No1/3Vol15No1.pdf</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Salomon, David (2008). A Concise Introduction to Data Compression. Berlin: Springer. ISBN 9781848000728. <a href="9781848000728" target="_blank">9781848000728</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Tank, M.K. (2011). "Implementation of Lempel-ZIV algorithm for lossless compression using VHDL". Thinkquest 2010: Proceedings of the First International Conference on Contours of Computing Technology. Berlin: Springer. pp. 275–283. doi:10.1007/978-81-8489-989-4_51. ISBN 978-81-8489-988-7. <a href="978-81-8489-988-7" target="_blank">978-81-8489-988-7</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Navqi, Saud; Naqvi, R.; Riaz, R.A.; Siddiqui, F. (April 2011). "Optimized RTL design and implementation of LZW algorithm for high bandwidth applications" (PDF). Electrical Review. 2011 (4): 279–285. Archived (PDF) from the original on 2013-05-20. <a href="http://pe.org.pl/articles/2011/4/68.pdf" target="_blank">http://pe.org.pl/articles/2011/4/68.pdf</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">Document Management - Portable document format - Part 1: PDF1.7 (1st ed.). Adobe Systems Incorporated. July 1, 2008. <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Stephen, Wolfram (2002). New Kind of Science. Champaign, IL: Wolfram Media. p. 1069. ISBN 1-57955-008-8. <a href="1-57955-008-8" target="_blank">1-57955-008-8</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Mahmud, Salauddin (March 2012). "An Improved Data Compression Method for General Data" (PDF). International Journal of Scientific & Engineering Research. 3 (3): 2. Archived (PDF) from the original on 2013-11-02. Retrieved 6 March 2013. <a href="http://www.ijser.org/researchpaper%5CAn-Improved-Data-Compression-Method-for-General-Data.pdf" target="_blank">http://www.ijser.org/researchpaper%5CAn-Improved-Data-Compression-Method-for-General-Data.pdf</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Lane, Tom. "JPEG Image Compression FAQ, Part 1". Internet FAQ Archives. Independent JPEG Group. Retrieved 6 March 2013. <a href="http://www.faqs.org/faqs/jpeg-faq/part1/" target="_blank">http://www.faqs.org/faqs/jpeg-faq/part1/</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">G. J. Sullivan; J.-R. Ohm; W.-J. Han; T. Wiegand (December 2012). "Overview of the High Efficiency Video Coding (HEVC) Standard". IEEE Transactions on Circuits and Systems for Video Technology. 22 (12). IEEE: 1649–1668. doi:10.1109/TCSVT.2012.2221191. S2CID 64404. <a href="/wiki/Gary_Sullivan_(engineer)" target="_blank">/wiki/Gary_Sullivan_(engineer)</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">"How to choose optimal archiving settings – WinRAR". <a href="https://www.winrar-france.fr/winrar_instructions_for_use/source/html/HELPArcOptimal.htm" target="_blank">https://www.winrar-france.fr/winrar_instructions_for_use/source/html/HELPArcOptimal.htm</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">"(Set compression Method) switch – 7zip". Archived from the original on 2022-04-09. Retrieved 2021-11-07. <a href="https://web.archive.org/web/20220409225619/https://sevenzip.osdn.jp/chm/cmdline/switches/method.htm" target="_blank">https://web.archive.org/web/20220409225619/https://sevenzip.osdn.jp/chm/cmdline/switches/method.htm</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">Wolfram, Stephen (2002). A New Kind of Science. Wolfram Media, Inc. p. 1069. ISBN 978-1-57955-008-0. <a href="978-1-57955-008-0" target="_blank">978-1-57955-008-0</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">Arcangel, Cory. "On Compression" (PDF). Archived (PDF) from the original on 2013-07-28. Retrieved 6 March 2013. <a href="http://www.coryarcangel.com/downloads/Cory-Arcangel-OnC.pdf" target="_blank">http://www.coryarcangel.com/downloads/Cory-Arcangel-OnC.pdf</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">Ahmed, Nasir (January 1991). "How I Came Up With the Discrete Cosine Transform". Digital Signal Processing. 1 (1): 4–5. Bibcode:1991DSP.....1....4A. doi:10.1016/1051-2004(91)90086-Z. <a href="/wiki/N._Ahmed" target="_blank">/wiki/N._Ahmed</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
<li id="fn:17">Nasir Ahmed; T. Natarajan; Kamisetty Ramamohan Rao (January 1974). "Discrete Cosine Transform" (PDF). IEEE Transactions on Computers. C-23 (1): 90–93. doi:10.1109/T-C.1974.223784. S2CID 149806273. Archived (PDF) from the original on 2016-12-08. <a href="/wiki/N._Ahmed" target="_blank">/wiki/N._Ahmed</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></li>
<li id="fn:18">CCITT Study Group VIII und die Joint Photographic Experts Group (JPEG) von ISO/IEC Joint Technical Committee 1/Subcommittee 29/Working Group 10 (1993), "Annex D – Arithmetic coding", Recommendation T.81: Digital Compression and Coding of Continuous-tone Still images – Requirements and guidelines (PDF), pp. 54 ff, retrieved 2009-11-07 <a href="https://www.w3.org/Graphics/JPEG/itu-t81.pdf" target="_blank">https://www.w3.org/Graphics/JPEG/itu-t81.pdf</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></li>
<li id="fn:19">Mahmud, Salauddin (March 2012). "An Improved Data Compression Method for General Data" (PDF). International Journal of Scientific & Engineering Research. 3 (3): 2. Archived (PDF) from the original on 2013-11-02. Retrieved 6 March 2013. <a href="http://www.ijser.org/researchpaper%5CAn-Improved-Data-Compression-Method-for-General-Data.pdf" target="_blank">http://www.ijser.org/researchpaper%5CAn-Improved-Data-Compression-Method-for-General-Data.pdf</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></li>
<li id="fn:20">Marak, Laszlo. "On image compression" (PDF). University of Marne la Vallee. Archived from the original (PDF) on 28 May 2015. Retrieved 6 March 2013. <a href="https://web.archive.org/web/20150528012028/http://www.ujoimro.com/resources/Laszlo_Marak_image_compression.pdf" target="_blank">https://web.archive.org/web/20150528012028/http://www.ujoimro.com/resources/Laszlo_Marak_image_compression.pdf</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></li>
<li id="fn:21">Mahoney, Matt. "Rationale for a Large Text Compression Benchmark". Florida Institute of Technology. Retrieved 5 March 2013. <a href="http://cs.fit.edu/~mmahoney/compression/rationale.html" target="_blank">http://cs.fit.edu/~mmahoney/compression/rationale.html</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></li>
<li id="fn:22">Shmilovici A.; Kahiri Y.; Ben-Gal I.; Hauser S. (2009). "Measuring the Efficiency of the Intraday Forex Market with a Universal Data Compression Algorithm" (PDF). Computational Economics. 33 (2): 131–154. CiteSeerX 10.1.1.627.3751. doi:10.1007/s10614-008-9153-3. S2CID 17234503. Archived (PDF) from the original on 2009-07-09. <a href="http://www.eng.tau.ac.il/~bengal/28.pdf" target="_blank">http://www.eng.tau.ac.il/~bengal/28.pdf</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></li>
<li id="fn:23">I. Ben-Gal (2008). "On the Use of Data Compression Measures to Analyze Robust Designs" (PDF). IEEE Transactions on Reliability. 54 (3): 381–388. doi:10.1109/TR.2005.853280. S2CID 9376086. <a href="http://www.eng.tau.ac.il/~bengal/Journal%20Paper.pdf" target="_blank">http://www.eng.tau.ac.il/~bengal/Journal%20Paper.pdf</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></li>
<li id="fn:24">D. Scully; Carla E. Brodley (2006). "Compression and Machine Learning: A New Perspective on Feature Space Vectors". Data Compression Conference (DCC'06). p. 332. doi:10.1109/DCC.2006.13. ISBN 0-7695-2545-8. S2CID 12311412. <a href="0-7695-2545-8" target="_blank">0-7695-2545-8</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></li>
<li id="fn:25">Gary Adcock (January 5, 2023). "What Is AI Video Compression?". massive.io. Retrieved 6 April 2023. <a href="https://massive.io/file-transfer/what-is-ai-video-compression/" target="_blank">https://massive.io/file-transfer/what-is-ai-video-compression/</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></li>
<li id="fn:26">Mentzer, Fabian; Toderici, George; Tschannen, Michael; Agustsson, Eirikur (2020). "High-Fidelity Generative Image Compression". arXiv:2006.09965 [eess.IV]. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></li>
<li id="fn:27">"What is Unsupervised Learning? | IBM". www.ibm.com. 23 September 2021. Retrieved 2024-02-05. <a href="https://www.ibm.com/topics/unsupervised-learning" target="_blank">https://www.ibm.com/topics/unsupervised-learning</a> <a href="#fnref:27" class="footnote-back-ref">↩</a></li>
<li id="fn:28">"Differentially private clustering for large-scale datasets". blog.research.google. 2023-05-25. Retrieved 2024-03-16. <a href="https://blog.research.google/2023/05/differentially-private-clustering-for.html" target="_blank">https://blog.research.google/2023/05/differentially-private-clustering-for.html</a> <a href="#fnref:28" class="footnote-back-ref">↩</a></li>
<li id="fn:29">Edwards, Benj (2023-09-28). "AI language models can exceed PNG and FLAC in lossless compression, says study". Ars Technica. Retrieved 2024-03-07. <a href="https://arstechnica.com/information-technology/2023/09/ai-language-models-can-exceed-png-and-flac-in-lossless-compression-says-study/" target="_blank">https://arstechnica.com/information-technology/2023/09/ai-language-models-can-exceed-png-and-flac-in-lossless-compression-says-study/</a> <a href="#fnref:29" class="footnote-back-ref">↩</a></li>
<li id="fn:30">"Language Modeling Is Compression". arxiv.org. Retrieved 2025-01-30. <a href="https://arxiv.org/html/2309.10668v2#S3" target="_blank">https://arxiv.org/html/2309.10668v2#S3</a> <a href="#fnref:30" class="footnote-back-ref">↩</a></li>
<li id="fn:31">Korn, D.; et al. (July 2002). "RFC 3284: The VCDIFF Generic Differencing and Compression Data Format". Internet Engineering Task Force. Retrieved 5 March 2013. <a href="http://tools.ietf.org/html/rfc3284" target="_blank">http://tools.ietf.org/html/rfc3284</a> <a href="#fnref:31" class="footnote-back-ref">↩</a></li>
<li id="fn:32">Korn, D.G.; Vo, K.P. (1995). B. Krishnamurthy (ed.). Vdelta: Differencing and Compression. Practical Reusable Unix Software. New York: John Wiley & Sons, Inc. <a href="#fnref:32" class="footnote-back-ref">↩</a></li>
<li id="fn:33">Claude Elwood Shannon (1948). Alcatel-Lucent (ed.). "A Mathematical Theory of Communication" (PDF). Bell System Technical Journal. 27 (3–4): 379–423, 623–656. doi:10.1002/j.1538-7305.1948.tb01338.x. hdl:11858/00-001M-0000-002C-4314-2. Archived (PDF) from the original on 2011-05-24. Retrieved 2019-04-21. <a href="/wiki/Claude_Elwood_Shannon" target="_blank">/wiki/Claude_Elwood_Shannon</a> <a href="#fnref:33" class="footnote-back-ref">↩</a></li>
<li id="fn:34">David Albert Huffman (September 1952), "A method for the construction of minimum-redundancy codes" (PDF), Proceedings of the IRE, vol. 40, no. 9, pp. 1098–1101, doi:10.1109/JRPROC.1952.273898, archived (PDF) from the original on 2005-10-08 <a href="/wiki/David_Albert_Huffman" target="_blank">/wiki/David_Albert_Huffman</a> <a href="#fnref:34" class="footnote-back-ref">↩</a></li>
<li id="fn:35">Pratt, W.K.; Kane, J.; Andrews, H.C. (1969). "Hadamard transform image coding". Proceedings of the IEEE. 57: 58–68. doi:10.1109/PROC.1969.6869. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:35" class="footnote-back-ref">↩</a></li>
<li id="fn:36">Ahmed, Nasir (January 1991). "How I Came Up With the Discrete Cosine Transform". Digital Signal Processing. 1 (1): 4–5. Bibcode:1991DSP.....1....4A. doi:10.1016/1051-2004(91)90086-Z. <a href="/wiki/N._Ahmed" target="_blank">/wiki/N._Ahmed</a> <a href="#fnref:36" class="footnote-back-ref">↩</a></li>
<li id="fn:37">"T.81 – DIGITAL COMPRESSION AND CODING OF CONTINUOUS-TONE STILL IMAGES – REQUIREMENTS AND GUIDELINES" (PDF). CCITT. September 1992. Retrieved 12 July 2019. <a href="https://www.w3.org/Graphics/JPEG/itu-t81.pdf" target="_blank">https://www.w3.org/Graphics/JPEG/itu-t81.pdf</a> <a href="#fnref:37" class="footnote-back-ref">↩</a></li>
<li id="fn:38">"The JPEG image format explained". BT.com. BT Group. 31 May 2018. Archived from the original on 5 August 2019. Retrieved 5 August 2019. <a href="https://web.archive.org/web/20190805194553/https://home.bt.com/tech-gadgets/photography/what-is-a-jpeg-11364206889349" target="_blank">https://web.archive.org/web/20190805194553/https://home.bt.com/tech-gadgets/photography/what-is-a-jpeg-11364206889349</a> <a href="#fnref:38" class="footnote-back-ref">↩</a></li>
<li id="fn:39">Baraniuk, Chris (15 October 2015). "Copy protections could come to JPEGs". BBC News. BBC. Retrieved 13 September 2019. <a href="https://www.bbc.co.uk/news/technology-34538705" target="_blank">https://www.bbc.co.uk/news/technology-34538705</a> <a href="#fnref:39" class="footnote-back-ref">↩</a></li>
<li id="fn:40">"What Is a JPEG? The Invisible Object You See Every Day". The Atlantic. 24 September 2013. Retrieved 13 September 2019. <a href="https://www.theatlantic.com/technology/archive/2013/09/what-is-a-jpeg-the-invisible-object-you-see-every-day/279954/" target="_blank">https://www.theatlantic.com/technology/archive/2013/09/what-is-a-jpeg-the-invisible-object-you-see-every-day/279954/</a> <a href="#fnref:40" class="footnote-back-ref">↩</a></li>
<li id="fn:41">"The GIF Controversy: A Software Developer's Perspective". 27 January 1995. Retrieved 26 May 2015. <a href="https://mike.pub/19950127-gif-lzw" target="_blank">https://mike.pub/19950127-gif-lzw</a> <a href="#fnref:41" class="footnote-back-ref">↩</a></li>
<li id="fn:42">L. Peter Deutsch (May 1996). DEFLATE Compressed Data Format Specification version 1.3. IETF. p. 1. sec. Abstract. doi:10.17487/RFC1951. RFC 1951. Retrieved 2014-04-23. <a href="/wiki/L._Peter_Deutsch" target="_blank">/wiki/L._Peter_Deutsch</a> <a href="#fnref:42" class="footnote-back-ref">↩</a></li>
<li id="fn:43">Hoffman, Roy (2012). Data Compression in Digital Systems. Springer Science & Business Media. p. 124. ISBN 9781461560319. Basically, wavelet coding is a variant on DCT-based transform coding that reduces or eliminates some of its limitations. (...) Another advantage is that rather than working with 8 × 8 blocks of pixels, as do JPEG and other block-based DCT techniques, wavelet coding can simultaneously compress the entire image. <a href="9781461560319" target="_blank">9781461560319</a> <a href="#fnref:43" class="footnote-back-ref">↩</a></li>
<li id="fn:44">Taubman, David; Marcellin, Michael (2012). JPEG2000 Image Compression Fundamentals, Standards and Practice: Image Compression Fundamentals, Standards and Practice. Springer Science & Business Media. ISBN 9781461507994. <a href="9781461507994" target="_blank">9781461507994</a> <a href="#fnref:44" class="footnote-back-ref">↩</a></li>
<li id="fn:45">Unser, M.; Blu, T. (2003). "Mathematical properties of the JPEG2000 wavelet filters". IEEE Transactions on Image Processing. 12 (9): 1080–1090. Bibcode:2003ITIP...12.1080U. doi:10.1109/TIP.2003.812329. PMID 18237979. S2CID 2765169. <a href="http://infoscience.epfl.ch/record/63104" target="_blank">http://infoscience.epfl.ch/record/63104</a> <a href="#fnref:45" class="footnote-back-ref">↩</a></li>
<li id="fn:46">Sullivan, Gary (8–12 December 2003). "General characteristics and design considerations for temporal subband video coding". ITU-T. Video Coding Experts Group. Retrieved 13 September 2019. <a href="https://www.itu.int/wftp3/av-arch/video-site/0312_Wai/VCEG-U06.doc" target="_blank">https://www.itu.int/wftp3/av-arch/video-site/0312_Wai/VCEG-U06.doc</a> <a href="#fnref:46" class="footnote-back-ref">↩</a></li>
<li id="fn:47">Bovik, Alan C. (2009). The Essential Guide to Video Processing. Academic Press. p. 355. ISBN 9780080922508. <a href="9780080922508" target="_blank">9780080922508</a> <a href="#fnref:47" class="footnote-back-ref">↩</a></li>
<li id="fn:48">Swartz, Charles S. (2005). Understanding Digital Cinema: A Professional Handbook. Taylor & Francis. p. 147. ISBN 9780240806174. <a href="9780240806174" target="_blank">9780240806174</a> <a href="#fnref:48" class="footnote-back-ref">↩</a></li>
<li id="fn:49">Mahdi, O.A.; Mohammed, M.A.; Mohamed, A.J. (November 2012). "Implementing a Novel Approach an Convert Audio Compression to Text Coding via Hybrid Technique" (PDF). International Journal of Computer Science Issues. 9 (6, No. 3): 53–59. Archived (PDF) from the original on 2013-03-20. Retrieved 6 March 2013. <a href="http://ijcsi.org/papers/IJCSI-9-6-3-53-59.pdf" target="_blank">http://ijcsi.org/papers/IJCSI-9-6-3-53-59.pdf</a> <a href="#fnref:49" class="footnote-back-ref">↩</a></li>
<li id="fn:50">Cunningham, Stuart; McGregor, Iain (2019). "Subjective Evaluation of Music Compressed with the ACER Codec Compared to AAC, MP3, and Uncompressed PCM". International Journal of Digital Multimedia Broadcasting. 2019: 1–16. doi:10.1155/2019/8265301. <a href="https://doi.org/10.1155%2F2019%2F8265301" target="_blank">https://doi.org/10.1155%2F2019%2F8265301</a> <a href="#fnref:50" class="footnote-back-ref">↩</a></li>
<li id="fn:51">The Olympus WS-120 digital speech recorder, according to its manual, can store about 178 hours of speech-quality audio in .WMA format in 500 MB of flash memory. <a href="#fnref:51" class="footnote-back-ref">↩</a></li>
<li id="fn:52">Coalson, Josh. "FLAC Comparison". Retrieved 2020-08-23. <a href="https://xiph.org/flac/comparison.html" target="_blank">https://xiph.org/flac/comparison.html</a> <a href="#fnref:52" class="footnote-back-ref">↩</a></li>
<li id="fn:53">"Format overview". Retrieved 2020-08-23. <a href="https://xiph.org/flac/documentation_format_overview.html" target="_blank">https://xiph.org/flac/documentation_format_overview.html</a> <a href="#fnref:53" class="footnote-back-ref">↩</a></li>
<li id="fn:54">Jaiswal, R.C. (2009). Audio-Video Engineering. Pune, Maharashtra: Nirali Prakashan. p. 3.41. ISBN 9788190639675. <a href="9788190639675" target="_blank">9788190639675</a> <a href="#fnref:54" class="footnote-back-ref">↩</a></li>
<li id="fn:55">Faxin Yu; Hao Luo; Zheming Lu (2010). Three-Dimensional Model Analysis and Processing. Berlin: Springer. p. 47. ISBN 9783642126512. <a href="9783642126512" target="_blank">9783642126512</a> <a href="#fnref:55" class="footnote-back-ref">↩</a></li>
<li id="fn:56">Jaiswal, R.C. (2009). Audio-Video Engineering. Pune, Maharashtra: Nirali Prakashan. p. 3.41. ISBN 9788190639675. <a href="9788190639675" target="_blank">9788190639675</a> <a href="#fnref:56" class="footnote-back-ref">↩</a></li>
<li id="fn:57">US patent 2605361, C. Chapin Cutler, "Differential Quantization of Communication Signals", issued 1952-07-29
 <a href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US2605361" target="_blank">https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US2605361</a> <a href="#fnref:57" class="footnote-back-ref">↩</a></li>
<li id="fn:58">Cummiskey, P.; Jayant, N. S.; Flanagan, J. L. (1973). "Adaptive Quantization in Differential PCM Coding of Speech". Bell System Technical Journal. 52 (7): 1105–1118. doi:10.1002/j.1538-7305.1973.tb02007.x. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:58" class="footnote-back-ref">↩</a></li>
<li id="fn:59">Cummiskey, P.; Jayant, Nikil S.; Flanagan, J. L. (1973). "Adaptive quantization in differential PCM coding of speech". The Bell System Technical Journal. 52 (7): 1105–1118. doi:10.1002/j.1538-7305.1973.tb02007.x. ISSN 0005-8580. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:59" class="footnote-back-ref">↩</a></li>
<li id="fn:60">Schroeder, Manfred R. (2014). "Bell Laboratories". Acoustics, Information, and Communication: Memorial Volume in Honor of Manfred R. Schroeder. Springer. p. 388. ISBN 9783319056609. <a href="9783319056609" target="_blank">9783319056609</a> <a href="#fnref:60" class="footnote-back-ref">↩</a></li>
<li id="fn:61">Gray, Robert M. (2010). "A History of Realtime Digital Speech on Packet Networks: Part II of Linear Predictive Coding and the Internet Protocol" (PDF). Found. Trends Signal Process. 3 (4): 203–303. doi:10.1561/2000000036. ISSN 1932-8346. Archived (PDF) from the original on 2010-07-04. <a href="https://ee.stanford.edu/~gray/lpcip.pdf" target="_blank">https://ee.stanford.edu/~gray/lpcip.pdf</a> <a href="#fnref:61" class="footnote-back-ref">↩</a></li>
<li id="fn:62">Schroeder, Manfred R. (2014). "Bell Laboratories". Acoustics, Information, and Communication: Memorial Volume in Honor of Manfred R. Schroeder. Springer. p. 388. ISBN 9783319056609. <a href="9783319056609" target="_blank">9783319056609</a> <a href="#fnref:62" class="footnote-back-ref">↩</a></li>
<li id="fn:63">Schroeder, Manfred R. (2014). "Bell Laboratories". Acoustics, Information, and Communication: Memorial Volume in Honor of Manfred R. Schroeder. Springer. p. 388. ISBN 9783319056609. <a href="9783319056609" target="_blank">9783319056609</a> <a href="#fnref:63" class="footnote-back-ref">↩</a></li>
<li id="fn:64">Nasir Ahmed; T. Natarajan; Kamisetty Ramamohan Rao (January 1974). "Discrete Cosine Transform" (PDF). IEEE Transactions on Computers. C-23 (1): 90–93. doi:10.1109/T-C.1974.223784. S2CID 149806273. Archived (PDF) from the original on 2016-12-08. <a href="/wiki/N._Ahmed" target="_blank">/wiki/N._Ahmed</a> <a href="#fnref:64" class="footnote-back-ref">↩</a></li>
<li id="fn:65">Guckert, John (Spring 2012). "The Use of FFT and MDCT in MP3 Audio Compression" (PDF). University of Utah. Archived (PDF) from the original on 2014-01-24. Retrieved 14 July 2019. <a href="http://www.math.utah.edu/~gustafso/s2012/2270/web-projects/Guckert-audio-compression-svd-mdct-MP3.pdf" target="_blank">http://www.math.utah.edu/~gustafso/s2012/2270/web-projects/Guckert-audio-compression-svd-mdct-MP3.pdf</a> <a href="#fnref:65" class="footnote-back-ref">↩</a></li>
<li id="fn:66">Luo, Fa-Long (2008). Mobile Multimedia Broadcasting Standards: Technology and Practice. Springer Science & Business Media. p. 590. ISBN 9780387782638. <a href="9780387782638" target="_blank">9780387782638</a> <a href="#fnref:66" class="footnote-back-ref">↩</a></li>
<li id="fn:67">Britanak, V. (2011). "On Properties, Relations, and Simplified Implementation of Filter Banks in the Dolby Digital (Plus) AC-3 Audio Coding Standards". IEEE Transactions on Audio, Speech, and Language Processing. 19 (5): 1231–1241. doi:10.1109/TASL.2010.2087755. S2CID 897622. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:67" class="footnote-back-ref">↩</a></li>
<li id="fn:68">Brandenburg, Karlheinz (1999). "MP3 and AAC Explained" (PDF). Archived (PDF) from the original on 2017-02-13. <a href="http://graphics.ethz.ch/teaching/mmcom12/slides/mp3_and_aac_brandenburg.pdf" target="_blank">http://graphics.ethz.ch/teaching/mmcom12/slides/mp3_and_aac_brandenburg.pdf</a> <a href="#fnref:68" class="footnote-back-ref">↩</a></li>
<li id="fn:69">Princen, J.; Johnson, A.; Bradley, A. (1987). "Subband/Transform coding using filter bank designs based on time domain aliasing cancellation". ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing. Vol. 12. pp. 2161–2164. doi:10.1109/ICASSP.1987.1169405. S2CID 58446992. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:69" class="footnote-back-ref">↩</a></li>
<li id="fn:70">Princen, J.; Bradley, A. (1986). "Analysis/Synthesis filter bank design based on time domain aliasing cancellation". IEEE Transactions on Acoustics, Speech, and Signal Processing. 34 (5): 1153–1161. doi:10.1109/TASSP.1986.1164954. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:70" class="footnote-back-ref">↩</a></li>
<li id="fn:71">"Ricardo Sametband, La Nación Newspaper "Historia de un pionero en audio digital"" (in Spanish). <a href="https://www.lanacion.com.ar/tecnologia/la-historia-de-un-pionero-del-audio-digital-nid187775" target="_blank">https://www.lanacion.com.ar/tecnologia/la-historia-de-un-pionero-del-audio-digital-nid187775</a> <a href="#fnref:71" class="footnote-back-ref">↩</a></li>
<li id="fn:72">Zwicker, Eberhard; et al. (1967). The Ear As A Communication Receiver. Melville, NY: Acoustical Society of America. Archived from the original on 2000-09-14. Retrieved 2011-11-11. <a href="https://web.archive.org/web/20000914080525/http://asa.aip.org/books/ear.html" target="_blank">https://web.archive.org/web/20000914080525/http://asa.aip.org/books/ear.html</a> <a href="#fnref:72" class="footnote-back-ref">↩</a></li>
<li id="fn:73">"Summary of some of Solidyne's contributions to Broadcast Engineering". Brief History of Solidyne. Buenos Aires: Solidyne. Archived from the original on 8 March 2013. Retrieved 6 March 2013. <a href="https://web.archive.org/web/20130308063719/http://www.solidynepro.com/indexahtmlp_Hist-ENG%2Ct.htm" target="_blank">https://web.archive.org/web/20130308063719/http://www.solidynepro.com/indexahtmlp_Hist-ENG%2Ct.htm</a> <a href="#fnref:73" class="footnote-back-ref">↩</a></li>
<li id="fn:74">"Anuncio del Audicom, AES Journal, July-August 1992, Vol 40, # 7/8, pag 647". <a href="http://www.aes.org/e-lib/browse.cfm?elib=19076" target="_blank">http://www.aes.org/e-lib/browse.cfm?elib=19076</a> <a href="#fnref:74" class="footnote-back-ref">↩</a></li>
<li id="fn:75">"File Compression Possibilities". A Brief guide to compress a file in 4 different ways. 17 February 2017. <a href="https://www.gadgetcouncil.com/compress-1GB-files-into-10-mb/" target="_blank">https://www.gadgetcouncil.com/compress-1GB-files-into-10-mb/</a> <a href="#fnref:75" class="footnote-back-ref">↩</a></li>
<li id="fn:76">Dmitriy Vatolin; et al. (Graphics & Media Lab Video Group) (March 2007). Lossless Video Codecs Comparison '2007 (PDF) (Report). Moscow State University. Archived (PDF) from the original on 2008-05-15. <a href="http://compression.ru/video/codec_comparison/pdf/msu_lossless_codecs_comparison_2007_eng.pdf" target="_blank">http://compression.ru/video/codec_comparison/pdf/msu_lossless_codecs_comparison_2007_eng.pdf</a> <a href="#fnref:76" class="footnote-back-ref">↩</a></li>
<li id="fn:77">Chen, Jie; Koc, Ut-Va; Liu, KJ Ray (2001). Design of Digital Video Coding Systems: A Complete Compressed Domain Approach. CRC Press. p. 71. ISBN 9780203904183. <a href="9780203904183" target="_blank">9780203904183</a> <a href="#fnref:77" class="footnote-back-ref">↩</a></li>
<li id="fn:78">Li, Jian Ping (2006). Proceedings of the International Computer Conference 2006 on Wavelet Active Media Technology and Information Processing: Chongqing, China, 29-31 August 2006. World Scientific. p. 847. ISBN 9789812709998. <a href="9789812709998" target="_blank">9789812709998</a> <a href="#fnref:78" class="footnote-back-ref">↩</a></li>
<li id="fn:79">"Video Coding". CSIP website. Center for Signal and Information Processing, Georgia Institute of Technology. Archived from the original on 23 May 2013. Retrieved 6 March 2013. <a href="https://web.archive.org/web/20130523194345/http://csip.ece.gatech.edu/drupal7/?q=technical-area%2Fvideo-coding" target="_blank">https://web.archive.org/web/20130523194345/http://csip.ece.gatech.edu/drupal7/?q=technical-area%2Fvideo-coding</a> <a href="#fnref:79" class="footnote-back-ref">↩</a></li>
<li id="fn:80">Faxin Yu; Hao Luo; Zheming Lu (2010). Three-Dimensional Model Analysis and Processing. Berlin: Springer. p. 47. ISBN 9783642126512. <a href="9783642126512" target="_blank">9783642126512</a> <a href="#fnref:80" class="footnote-back-ref">↩</a></li>
<li id="fn:81">Lane, Tom. "JPEG Image Compression FAQ, Part 1". Internet FAQ Archives. Independent JPEG Group. Retrieved 6 March 2013. <a href="http://www.faqs.org/faqs/jpeg-faq/part1/" target="_blank">http://www.faqs.org/faqs/jpeg-faq/part1/</a> <a href="#fnref:81" class="footnote-back-ref">↩</a></li>
<li id="fn:82">Faxin Yu; Hao Luo; Zheming Lu (2010). Three-Dimensional Model Analysis and Processing. Berlin: Springer. p. 47. ISBN 9783642126512. <a href="9783642126512" target="_blank">9783642126512</a> <a href="#fnref:82" class="footnote-back-ref">↩</a></li>
<li id="fn:83">Robinson, A. H.; Cherry, C. (1967). "Results of a prototype television bandwidth compression scheme". Proceedings of the IEEE. 55 (3). IEEE: 356–364. doi:10.1109/PROC.1967.5493. <a href="/wiki/Proceedings_of_the_IEEE" target="_blank">/wiki/Proceedings_of_the_IEEE</a> <a href="#fnref:83" class="footnote-back-ref">↩</a></li>
<li id="fn:84">Ghanbari, Mohammed (2003). Standard Codecs: Image Compression to Advanced Video Coding. Institution of Engineering and Technology. pp. 1–2. ISBN 9780852967102. <a href="9780852967102" target="_blank">9780852967102</a> <a href="#fnref:84" class="footnote-back-ref">↩</a></li>
<li id="fn:85">Nasir Ahmed; T. Natarajan; Kamisetty Ramamohan Rao (January 1974). "Discrete Cosine Transform" (PDF). IEEE Transactions on Computers. C-23 (1): 90–93. doi:10.1109/T-C.1974.223784. S2CID 149806273. Archived (PDF) from the original on 2016-12-08. <a href="/wiki/N._Ahmed" target="_blank">/wiki/N._Ahmed</a> <a href="#fnref:85" class="footnote-back-ref">↩</a></li>
<li id="fn:86">Reader, Cliff (2016-08-31). "Patent landscape for royalty-free video coding". In Tescher, Andrew G (ed.). Applications of Digital Image Processing XXXIX. Applications of Digital Image Processing XXXIX. Vol. 9971. San Diego, California: Society of Photo-Optical Instrumentation Engineers. pp. 99711B. Bibcode:2016SPIE.9971E..1BR. doi:10.1117/12.2239493. Archived from the original on 2016-12-08. Lecture recording, from 3:05:10. <a href="https://web.archive.org/web/20161208075738/https://www.youtube.com/watch?v=wi1BefrfTos" target="_blank">https://web.archive.org/web/20161208075738/https://www.youtube.com/watch?v=wi1BefrfTos</a> <a href="#fnref:86" class="footnote-back-ref">↩</a></li>
<li id="fn:87">"The History of Video File Formats Infographic — RealPlayer". 22 April 2012. <a href="http://www.real.com/resources/digital-video-file-formats/" target="_blank">http://www.real.com/resources/digital-video-file-formats/</a> <a href="#fnref:87" class="footnote-back-ref">↩</a></li>
<li id="fn:88">Ghanbari, Mohammed (2003). Standard Codecs: Image Compression to Advanced Video Coding. Institution of Engineering and Technology. pp. 1–2. ISBN 9780852967102. <a href="9780852967102" target="_blank">9780852967102</a> <a href="#fnref:88" class="footnote-back-ref">↩</a></li>
<li id="fn:89">"Patent statement declaration registered as H261-07". ITU. Retrieved 11 July 2019. <a href="https://www.itu.int/net4/ipr/details_ps.aspx?sector=ITU-T&id=H261-07" target="_blank">https://www.itu.int/net4/ipr/details_ps.aspx?sector=ITU-T&id=H261-07</a> <a href="#fnref:89" class="footnote-back-ref">↩</a></li>
<li id="fn:90">"The History of Video File Formats Infographic — RealPlayer". 22 April 2012. <a href="http://www.real.com/resources/digital-video-file-formats/" target="_blank">http://www.real.com/resources/digital-video-file-formats/</a> <a href="#fnref:90" class="footnote-back-ref">↩</a></li>
<li id="fn:91">"MPEG-2 Patent List" (PDF). MPEG LA. Archived (PDF) from the original on 2019-05-29. Retrieved 7 July 2019. <a href="https://www.mpegla.com/wp-content/uploads/m2-att1.pdf" target="_blank">https://www.mpegla.com/wp-content/uploads/m2-att1.pdf</a> <a href="#fnref:91" class="footnote-back-ref">↩</a></li>
<li id="fn:92">"The History of Video File Formats Infographic — RealPlayer". 22 April 2012. <a href="http://www.real.com/resources/digital-video-file-formats/" target="_blank">http://www.real.com/resources/digital-video-file-formats/</a> <a href="#fnref:92" class="footnote-back-ref">↩</a></li>
<li id="fn:93">"The History of Video File Formats Infographic — RealPlayer". 22 April 2012. <a href="http://www.real.com/resources/digital-video-file-formats/" target="_blank">http://www.real.com/resources/digital-video-file-formats/</a> <a href="#fnref:93" class="footnote-back-ref">↩</a></li>
<li id="fn:94">"MPEG-4 Visual - Patent List" (PDF). MPEG LA. Archived (PDF) from the original on 2019-07-06. Retrieved 6 July 2019. <a href="https://www.mpegla.com/wp-content/uploads/m4v-att1.pdf" target="_blank">https://www.mpegla.com/wp-content/uploads/m4v-att1.pdf</a> <a href="#fnref:94" class="footnote-back-ref">↩</a></li>
<li id="fn:95">"AVC/H.264 – Patent List" (PDF). MPEG LA. Retrieved 6 July 2019. <a href="https://www.mpegla.com/wp-content/uploads/avc-att1.pdf" target="_blank">https://www.mpegla.com/wp-content/uploads/avc-att1.pdf</a> <a href="#fnref:95" class="footnote-back-ref">↩</a></li>
<li id="fn:96">Chanda P, Bader JS, Elhaik E (27 Jul 2012). "HapZipper: sharing HapMap populations just got easier". Nucleic Acids Research. 40 (20): e159. doi:10.1093/nar/gks709. PMC 3488212. PMID 22844100. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3488212" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3488212</a> <a href="#fnref:96" class="footnote-back-ref">↩</a></li>
<li id="fn:97">Christley S, Lu Y, Li C, Xie X (Jan 15, 2009). "Human genomes as email attachments". Bioinformatics. 25 (2): 274–5. doi:10.1093/bioinformatics/btn582. PMID 18996942. <a href="https://doi.org/10.1093%2Fbioinformatics%2Fbtn582" target="_blank">https://doi.org/10.1093%2Fbioinformatics%2Fbtn582</a> <a href="#fnref:97" class="footnote-back-ref">↩</a></li>
<li id="fn:98">Pavlichin DS, Weissman T, Yona G (September 2013). "The human genome contracts again". Bioinformatics. 29 (17): 2199–202. doi:10.1093/bioinformatics/btt362. PMID 23793748. <a href="https://doi.org/10.1093%2Fbioinformatics%2Fbtt362" target="_blank">https://doi.org/10.1093%2Fbioinformatics%2Fbtt362</a> <a href="#fnref:98" class="footnote-back-ref">↩</a></li>
<li id="fn:99">Hosseini, Morteza; Pratas, Diogo; Pinho, Armando (2016). "A Survey on Data Compression Methods for Biological Sequences". Information. 7 (4): 56. doi:10.3390/info7040056. <a href="https://doi.org/10.3390%2Finfo7040056" target="_blank">https://doi.org/10.3390%2Finfo7040056</a> <a href="#fnref:99" class="footnote-back-ref">↩</a></li>
<li id="fn:100">"Data Compression via Logic Synthesis" (PDF). <a href="https://infoscience.epfl.ch/record/188645/files/06742961.pdf" target="_blank">https://infoscience.epfl.ch/record/188645/files/06742961.pdf</a> <a href="#fnref:100" class="footnote-back-ref">↩</a></li>
<li id="fn:101">Hilbert, Martin; López, Priscila (1 April 2011). "The World's Technological Capacity to Store, Communicate, and Compute Information". Science. 332 (6025): 60–65. Bibcode:2011Sci...332...60H. doi:10.1126/science.1200970. PMID 21310967. S2CID 206531385. <a href="https://doi.org/10.1126%2Fscience.1200970" target="_blank">https://doi.org/10.1126%2Fscience.1200970</a> <a href="#fnref:101" class="footnote-back-ref">↩</a></li>
</ol>

Data compression open-in-new

Data compression