Data compression
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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.
As with any communication, compressed data communication only works when both the sender and receiver of the information understand the encoding scheme. For example, this text makes sense only if the receiver understands that it is intended to be interpreted as characters representing the English language. Similarly, compressed data can only be understood if the decoding method is known by the receiver.
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's 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.
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[edit] Lossless versus lossy 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 smaller file.
[edit] 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.
[edit] 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.
[edit] 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.
[edit] 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.
[edit] 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].
[edit] Data differencing
Data compression can be seen as a special case of data differencing[2][3] – 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.
[edit] See also
[edit] 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
[edit] Compression algorithms
[edit] Lossless data compression
- run-length encoding
- dictionary coders
- 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)
- 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)
- Slepian-Wolf coding(SWC)(lossless Distributed source coding(DSC))
[edit] Lossy data compression
- discrete cosine transform
- fractal compression
- 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))
[edit] 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)
- 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 a discrete cosine transform, then quantization, then Huffman coding)
- MPEG (audio and video compression standards family in wide use, using DCT and motion-compensated prediction for video)
- 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)
[edit] Corpora
Data collections, commonly used for comparing compression algorithms.
[edit] 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
[edit] External links
- Data Compression - Systematisation by T.Strutz
- Guide to compression formats
- Introduction to Data Compression by Guy E Blelloch from CMU
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