Timeline of information theory

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A timeline of events related to Red pog.svg   information theory, Orange pog.svg   quantum information theory and statistical physics, Green pog.svg   data compression, Purple pog.svg   error correcting codes and related subjects.

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In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information. Typically, a device that performs data compression is referred to as an encoder, and one that performs the reversal of the process (decompression) as a decoder.

<span class="mw-page-title-main">Huffman coding</span> Technique to compress data

In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".

Information theory is the mathematical study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering.

Lossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statistical redundancy. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though usually with greatly improved compression rates.

<span class="mw-page-title-main">Image compression</span> Reduction of image size to save storage and transmission costs

Image compression is a type of data compression applied to digital images, to reduce their cost for storage or transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic data compression methods which are used for other digital data.

In information theory, an entropy coding is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any lossless data compression method must have an expected code length greater than or equal to the entropy of the source.

In the field of data compression, Shannon–Fano coding, named after Claude Shannon and Robert Fano, is one of two related techniques for constructing a prefix code based on a set of symbols and their probabilities.

Lempel–Ziv–Welch (LZW) is a universal lossless data compression algorithm created by Abraham Lempel, Jacob Ziv, and Terry Welch. It was published by Welch in 1984 as an improved implementation of the LZ78 algorithm published by Lempel and Ziv in 1978. The algorithm is simple to implement and has the potential for very high throughput in hardware implementations. It is the algorithm of the Unix file compression utility compress and is used in the GIF image format.

LZ77 and LZ78 are the two lossless data compression algorithms published in papers by Abraham Lempel and Jacob Ziv in 1977 and 1978. They are also known as LZ1 and LZ2 respectively. These two algorithms form the basis for many variations including LZW, LZSS, LZMA and others. Besides their academic influence, these algorithms formed the basis of several ubiquitous compression schemes, including GIF and the DEFLATE algorithm used in PNG and ZIP.

<span class="mw-page-title-main">Coding theory</span> Study of the properties of codes and their fitness

Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data.

Adaptive coding refers to variants of entropy encoding methods of lossless data compression. They are particularly suited to streaming data, as they adapt to localized changes in the characteristics of the data, and don't require a first pass over the data to calculate a probability model. The cost paid for these advantages is that the encoder and decoder must be more complex to keep their states synchronized, and more computational power is needed to keep adapting the encoder/decoder state.

This is a list of information theory topics.

In cryptography, the McEliece cryptosystem is an asymmetric encryption algorithm developed in 1978 by Robert McEliece. It was the first such scheme to use randomization in the encryption process. The algorithm has never gained much acceptance in the cryptographic community, but is a candidate for "post-quantum cryptography", as it is immune to attacks using Shor's algorithm and – more generally – measuring coset states using Fourier sampling.

Algebraic geometry codes, often abbreviated AG codes, are a type of linear code that generalize Reed–Solomon codes. The Russian mathematician V. D. Goppa constructed these codes for the first time in 1982.

<span class="mw-page-title-main">Abraham Lempel</span> Israeli computer scientist (1936–2023)

Abraham Lempel was an Israeli computer scientist and one of the fathers of the LZ family of lossless data compression algorithms.

Lempel–Ziv–Storer–Szymanski (LZSS) is a lossless data compression algorithm, a derivative of LZ77, that was created in 1982 by James A. Storer and Thomas Szymanski. LZSS was described in article "Data compression via textual substitution" published in Journal of the ACM.

<span class="mw-page-title-main">Universal code (data compression)</span>

In data compression, a universal code for integers is a prefix code that maps the positive integers onto binary codewords, with the additional property that whatever the true probability distribution on integers, as long as the distribution is monotonic (i.e., p(i) ≥ p(i + 1) for all positive i), the expected lengths of the codewords are within a constant factor of the expected lengths that the optimal code for that probability distribution would have assigned. A universal code is asymptotically optimal if the ratio between actual and optimal expected lengths is bounded by a function of the information entropy of the code that, in addition to being bounded, approaches 1 as entropy approaches infinity.

The decisive event which established the discipline of information theory, and brought it to immediate worldwide attention, was the publication of Claude E. Shannon's classic paper "A Mathematical Theory of Communication" in the Bell System Technical Journal in July and October 1948.

Lempel–Ziv–Stac is a lossless data compression algorithm that uses a combination of the LZ77 sliding-window compression algorithm and fixed Huffman coding. It was originally developed by Stac Electronics for tape compression, and subsequently adapted for hard disk compression and sold as the Stacker disk compression software. It was later specified as a compression algorithm for various network protocols. LZS is specified in the Cisco IOS stack.

In information theory and communication, the Slepian–Wolf coding, also known as the Slepian–Wolf bound, is a result in distributed source coding discovered by David Slepian and Jack Wolf in 1973. It is a method of theoretically coding two lossless compressed correlated sources.

References

  1. 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.
  2. Nasir Ahmed. "How I Came Up With the Discrete Cosine Transform". Digital Signal Processing, Vol. 1, Iss. 1, 1991, pp. 4-5.
  3. Slepian, David S.; Wolf, Jack K. (July 1973). "Noiseless coding of correlated information sources". IEEE Transactions on Information Theory . 19 (4). IEEE: 471–480. doi:10.1109/TIT.1973.1055037. ISSN   0018-9448.