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Data Compression


In computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use.

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.


Lossless versus lossy compression

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.

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 modern lossless compressors use probabilistic models, such as prediction by partial matching. The Burrows–Wheeler transform can also be viewed as an indirect form of statistical modeling.

In a further refinement of these techniques, statistical predictions can be 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. Coding theory is also 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

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".

Data differencing

Data compression can be viewed as a special case of data differencing – 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.

Technical Terms

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