Data compression

"Source coding" redirects here. For the term in computer programming, see Source code. In computer science and information theory, data compression or source coding is the process of encoding information using fewer bits (or other information-bearing units) than an unencoded representation would use, through use of specific encoding schemes. In computing, data deduplication is a specialized data compression technique for eliminating coarse-grained redundant data, typically to improve storage utilization. Compression is useful because it helps reduce the consumption of expensive resources, such as hard disk space or transmission bandwidth. On the downside, compressed data must be decompressed to be used, and this extra processing may be detrimental to some applications. For instance, a compression scheme for video may require expensive hardware for the video to be decompressed fast enough to be viewed as it is being decompressed (the option of decompressing the video in full before watching it may be inconvenient, and requires storage space for the decompressed video). The design of data compression schemes therefore involves trade-offs among various factors, including the degree of compression, the amount of distortion introduced (if using a lossy compression scheme), and the computational resources required to compress and uncompress the data. Contents 1 Lossless versus lossy compression 2 Example algorithms and applications 2.1 Lossy 2.2 Lossless 3 Theory 3.1 Machine learning 3.2 Data differencing 4 See also 4.1 Data compression topics 4.2 Compression algorithms 4.2.1 Lossless data compression 4.2.2 Lossy data compression 4.2.3 Example implementations 4.3 Corpora 5 References 6 External links // Lossless versus lossy compression Main articles: Lossless data compression and lossy data compression Lossless compression algorithms usually exploit statistical redundancy in such a way as to represent the sender's data more concisely without error. Lossless compression is possible because most real-world data has statistical redundancy. For example, in English text, the letter 'e' is much more common than the letter 'z', and the probability that the letter 'q' will be followed by the letter 'z' is very small. Another kind of compression, called lossy data compression or perceptual coding, is possible if some loss of fidelity is acceptable. Generally, a lossy data compression will be guided by research on how people perceive the data in question. For example, the human eye is more sensitive to subtle variations in luminance than it is to variations in color. JPEG image compression works in part by "rounding off" some of this less-important information. Lossy data compression provides a way to obtain the best fidelity for a given amount of compression. In some cases, transparent (unnoticeable) compression is desired; in other cases, fidelity is sacrificed to reduce the amount of data as much as possible. Lossless compression schemes are reversible so that the original data can be reconstructed, while lossy schemes accept some loss of data in order to achieve higher compression. However, lossless data compression algorithms will always fail to compress some files; indeed, any compression algorithm will necessarily fail to compress any data containing no discernible patterns. Attempts to compress data that has been compressed already will therefore usually result in an expansion, as will attempts to compress all but the most trivially encrypted data. In practice, lossy data compression will also come to a point where compressing again does not work, although an extremely lossy algorithm, like for example always removing the last byte of a file, will always compress a file up to the point where it is empty. An example of lossless vs. lossy compression is the following string: 25.888888888 This string can be compressed as: 25.[9]8 Interpreted as, "twenty five point 9 eights", the original string is perfectly recreated, just written in a smaller form. In a lossy system, using 26 instead, the exact original data is lost, at the benefit of a shorter representation. Example algorithms and applications The above is a very simple example of run-length encoding, wherein large runs of consecutive identical data values are replaced by a simple code with the data value and length of the run. This is an example of lossless data compression. It is often used to optimize disk space on office computers, or better use the connection bandwidth in a computer network. For symbolic data such as spreadsheets, text, executable programs, etc., losslessness is essential because changing even a single bit cannot be tolerated (except in some limited cases). For visual and audio data, some loss of quality can be tolerated without losing the essential nature of the data. By taking advantage of the limitations of the human sensory system, a great deal of space can be saved while producing an output which is nearly indistinguishable from the original. These lossy data compression methods typically offer a three-way tradeoff between compression speed, compressed data size and quality loss. Lossy Lossy image compression is used in digital cameras, to increase storage capacities with minimal degradation of picture quality. Similarly, DVDs use the lossy MPEG-2 Video codec for video compression. In lossy audio compression, methods of psychoacoustics are used to remove non-audible (or less audible) components of the signal. Compression of human speech is often performed with even more specialized techniques, so that "speech compression" or "voice coding" is sometimes distinguished as a separate discipline from "audio compression". Different audio and speech compression standards are listed under audio codecs. Voice compression is used in Internet telephony for example, while audio compression is used for CD ripping and is decoded by audio players. Lossless The Lempel-Ziv (LZ) compression methods are among the most popular algorithms for lossless storage. DEFLATE is a variation on LZ which is optimized for decompression speed and compression ratio, therefore compression can be slow. DEFLATE is used in PKZIP, gzip and PNG. LZW (Lempel-Ziv-Welch) is used in GIF images. Also noteworthy are the LZR (LZ-Renau) methods, which serve as the basis of the Zip method. LZ methods utilize 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 Huffman encoded (e.g. SHRI, LZX). A current LZ-based coding scheme that performs well is LZX, used in Microsoft's CAB format. The very best compressors use probabilistic models, in which predictions are coupled to an algorithm called arithmetic coding. Arithmetic coding, invented by Jorma Rissanen, and turned into a practical method by Witten, Neal, and Cleary, achieves superior compression to the better-known Huffman algorithm, and lends itself especially well to adaptive data compression tasks where the predictions are strongly context-dependent. Arithmetic coding is used in the bilevel image-compression standard JBIG, and the document-compression standard DjVu. The text entry system, Dasher, is an inverse-arithmetic-coder. Theory The theoretical background of compression is provided by information theory (which is closely related to algorithmic information theory) for lossless compression, and by rate–distortion theory for lossy compression. These fields of study were essentially created by Claude Shannon, who published fundamental papers on the topic in the late 1940s and early 1950s. Cryptography and coding theory are also closely related. The idea of data compression is deeply connected with statistical inference. Many lossless data compression systems can be viewed in terms of a four-stage model. Lossy data compression systems typically include even more stages, including, for example, prediction, frequency transformation, and quantization. Machine learning See also: Machine learning There is a close connection between machine learning and compression: a system that predicts the posterior probabilities of a sequence given its entire history can be used for optimal data compression (by using arithmetic coding on the output distribution), while 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 justification for data compression as a benchmark for "general intelligence".1 Data differencing Main article: Data differencing Data compression can be seen as a special case of data differencing23 – data differencing consists of producing a difference given a source and a target, with patching producing a target given a source and a difference, while data compression consists of producing a compressed file given a target, and decompression consists of producing a target given only a compressed file. Thus, 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 entropy (corresponding to data compression) as a special case of relative entropy (corresponding to data differencing) with no initial data. When one wishes to emphasize the connection, one may use the term differential compression to refer to data differencing. See also Data compression topics Algorithmic complexity theory Information entropy Self-extracting archive Image compression Speech coding Video compression Multimedia compression Minimum description length Minimum message length (two-part lossless compression designed for inference) List of archive formats Comparison of file archivers List of Unix programs Free file format HTTP compression Magic compression algorithm Data compression symmetry Dyadic distribution Compression algorithms Lossless data compression Data deduplication run-length encoding dictionary coders LZ77 & LZ78 LZW Statistical Lempel Ziv Burrows-Wheeler transform prediction by partial matching (also known as PPM) context mixing Dynamic Markov Compression (DMC) entropy encoding Huffman coding (simple entropy coding; commonly used as the final stage of compression) Adaptive Huffman coding Shannon-Fano coding arithmetic coding (more advanced) range encoding (same as arithmetic coding, but looked at in a slightly different way) Golomb coding (simple entropy coding for infinite input data with a geometric distribution) universal codes (entropy coding for infinite input data with an arbitrary distribution) Elias gamma coding Fibonacci coding Slepian-Wolf coding (SWC) (lossless distributed source coding (DSC)) Lossy data compression discrete cosine transform fractal compression fractal transform wavelet compression vector quantization linear predictive coding Modulo-N code for correlated data A-law Compander Mu-law Compander Wyner-Ziv coding (WZC) (lossy Distributed source coding (DSC)) Example implementations DEFLATE (a combination of LZ77 and Huffman coding) – used by ZIP, gzip and PNG files LZMA used by 7-Zip LZO (very fast LZ variation, speed oriented) LZX (an LZ77 family compression algorithm) liblzg (a minimal LZ77 based compression library) Unix compress utility (the .Z file format), and GIF use LZW Unix pack utility (the .z file format) used Huffman coding bzip2 (a combination of the Burrows-Wheeler transform and Huffman coding) PAQ (very high compression based on context mixing, but extremely slow; competing in the top of the highest compression competitions) JPEG (image compression using optional chroma downsampling, discrete cosine transform, quantization, then Huffman coding) MPEG (audio and video compression standards family in wide use, using DCT and motion-compensated prediction for video) MP3 (a part of the MPEG-1 standard for sound and music compression, using subbanding and MDCT, perceptual modeling, quantization, and Huffman coding) AAC (part of the MPEG-2 and MPEG-4 audio coding specifications, using MDCT, perceptual modeling, quantization, and Huffman coding) Vorbis (DCT based AAC-alike audio codec, designed with a focus on avoiding patent encumbrance) JPEG 2000 (image compression using wavelets, then quantization, then entropy coding) TTA (uses linear predictive coding for lossless audio compression) FLAC (linear predictive coding for lossless audio compression) Corpora Data collections, commonly used for comparing compression algorithms. Canterbury Corpus Calgary Corpus References ^ Rationale for a Large Text Compression Benchmark ^ RFC 3284 ^ Korn, D.G.; Vo, K.P. (1995), B. Krishnamurthy, ed., Vdelta: Differencing and Compression, Practical Reusable Unix Software, John Wiley & Sons  External links Introduction to Data Compression by Guy E Blelloch from CMU v · d · eData compression methods Lossless Theory Entropy · Complexity · Redundancy · Lossy Entropy encoding Shannon–Fano · Shannon–Fano–Elias · Huffman · Adaptive Huffman · Arithmetic · Range · Golomb · Universal (Gamma · Exp-Golomb · Fibonacci · Levenshtein) Dictionary RLE · Byte pair encoding · DEFLATE · Lempel–Ziv (LZ77/78 · LZSS · LZW · LZWL · LZO · LZMA · LZX · LZRW · LZJB · LZS · LZT · ROLZ) · Statistical Lempel Ziv Others CTW · BWT · PPM · DMC · Delta Audio Theory Companding · Convolution · Dynamic range · Latency · Sampling · Nyquist–Shannon theorem · Sound quality Audio codec parts LPC (LAR · LSP) · WLPC · CELP · ACELP · A-law · μ-law · ADPCM · DPCM · MDCT · Fourier transform · Psychoacoustic model Others Bit rate (CBR · ABR · VBR) · Speech compression · Sub-band coding Image Terms Color space · Pixel · Chroma subsampling · Compression artifact · Image resolution Methods RLE · Fractal · Wavelet · EZW · SPIHT · LP · DCT · Chain code · KLT Others Test images · PSNR quality measure · Quantization Video Terms Video characteristics · Frame · Frame rate · Interlace · Frame types · Video quality · Video resolution Video codec parts Motion compensation · DCT · Quantization Others Video codecs · Rate distortion theory · Bit rate (CBR · ABR · VBR) Timeline of information theory, data compression, and error-correcting codes See Compression formats for formats and Compression software implementations for codecs v · d · eMultimedia compression and container formats Video ISO/IEC MJPEG · Motion JPEG 2000 · MPEG-1 · MPEG-2 (Part 2) · MPEG-4 (Part 2/ASP · Part 10/AVC) · HEVC ITU-T H.120 · H.261 · H.262 · H.263 · H.264 · HEVC Others AVS · Bink · CineForm · Cinepak · Dirac · DV · Indeo · Microsoft Video 1 · OMS Video · Pixlet · RealVideo · RTVideo · SheerVideo · Smacker · Sorenson Video & Sorenson Spark · Theora · VC-1 · VC-2 · VC-3 · VP3 · VP6 · VP7 · VP8 · WMV Audio ISO/IEC MPEG-1 Layer III (MP3) · MPEG-1 Layer II (Multichannel) · MPEG-1 Layer I · AAC · HE-AAC · MPEG Surround · MPEG-4 ALS · MPEG-4 SLS · MPEG-4 DST · MPEG-4 HVXC · MPEG-4 CELP ITU-T G.711 · G.718 · G.719 · G.722 · G.722.1 · G.722.2 · G.723 · G.723.1 · G.726 · G.728 · G.729 · G.729.1 Others AC-3 · AMR · AMR-WB · AMR-WB+ · Apple Lossless · ATRAC · CELT · DRA · DTS · EVRC · EVRC-B · FLAC · GSM-HR · GSM-FR · GSM-EFR · iLBC · iSAC · Monkey's Audio · TTA (True Audio) · MT9 · A-law · μ-law · Musepack · Nellymoser · OptimFROG · OSQ · QCELP · RealAudio · RTAudio · SD2 · SHN · SILK · Siren · SMV · Speex · SVOPC · TwinVQ · VMR-WB · Vorbis · WavPack · WMA Image ISO/IEC/ITU-T JPEG · JPEG 2000 · JPEG XR · lossless JPEG · JBIG · JBIG2 · PNG Others APNG · BMP · DjVu · EXR · GIF · ICER · ILBM · MNG · PCX · PGF · TGA · QTVR · TIFF · WBMP · WebP Containers ISO/IEC MPEG-PS · MPEG-TS · ISO base media file format · MPEG-4 Part 14 · Motion JPEG 2000 · MPEG-21 Part 9 ITU-T H.222.0 · T.802 Others 3GP and 3G2 · AMV · ASF · AIFF · AVI · AU · Bink · DivX Media Format · DPX · EVO · Flash Video · GXF · M2TS · Matroska · MXF · Ogg · QuickTime File Format · RealMedia · REDCODE RAW · RIFF · Smacker · MOD and TOD · VOB · WAV · WebM See Compression methods for methods and Compression software implementations for codecs v · d · eData compression software implementations Archivers with compression (Comparison) Free software 7-Zip · Ark · File Roller · FreeArc · Info-ZIP · KGB Archiver · PAQ · PeaZip · The Unarchiver · tar · UPX · Xarchiver · Zipeg Freeware DGCA · Filzip · IZArc · LHA · StuffIt Expander (decompression only)  · TUGZip · UHarc/WinUHA · ZipGenius Commercial ARC · ALZip · Archive Utility · ARJ · BetterZip · JAR · MacBinary · PKZIP/SecureZIP · PowerArchiver · StuffIt · WinAce · WinRAR · WinZip Lossless data compression* Free software bzip2 · compress · gzip · lzip · lzop · rzip · xz Audio compression (Comparison) Lossy Freeware Advanced Audio Coder (FAAC) · Helix DNA Producer · l3enc · LAME · TooLAME · libavcodec · libcelt · libspeex · Musepack · libvorbis · Windows Media Encoder Lossless FLAC · ALAC · libavcodec · Monkey's Audio · TTA (True Audio) · mp4als · OptimFROG · WavPack Video compression (Comparison) Lossy MPEG-4 ASP 3ivx · DivX · Nero Digital · FFmpeg · HDX4 · Xvid H.264/MPEG-4 AVC CoreAVC · Blu-code · DivX · FFmpeg · Nero Digital  · QuickTime · x264 Others CineForm · Cinepak · DNxHD · Helix DNA Producer · Indeo · libavcodec · Schrödinger (Dirac) · SBC · Sorenson · VP7 · libtheora · libvpx · Windows Media Encoder Lossless FFV1  · Huffyuv · Lagarith · MSU Lossless · SheerVideo * Non-archiving See Compression methods for methods and Compression formats for formats