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information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...
,  
quantum information theory Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both t ...
and
statistical physics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
,  
data compression 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 compressi ...
,  
error correcting code In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The centra ...
s and related subjects. * 1872
Ludwig Boltzmann Ludwig Eduard Boltzmann ( ; ; 20 February 1844 – 5 September 1906) was an Austrian mathematician and Theoretical physics, theoretical physicist. His greatest achievements were the development of statistical mechanics and the statistical ex ...
presents his
H-theorem In classical statistical mechanics, the ''H''-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity ''H'' (defined below) to decrease in a nearly-ideal gas of molecules.L. Boltzmann,Weitere Studien über das Wär ...
, and with it the formula Σ''p''i log ''p''i for the entropy of a single gas particle * 1878 J. Willard Gibbs defines the
Gibbs entropy The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entrop ...
: the probabilities in the entropy formula are now taken as probabilities of the state of the ''whole'' system * 1924
Harry Nyquist Harry Nyquist (, ; February 7, 1889 – April 4, 1976) was a Swedish-American physicist and electronic engineer who made important contributions to communication theory. Personal life Nyquist was born in the village Nilsby of the parish Stora ...
discusses quantifying and the speed at which it can be transmitted by a communication system * 1927
John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...
defines the
von Neumann entropy In physics, the von Neumann entropy, named after John von Neumann, is a measure of the statistical uncertainty within a description of a quantum system. It extends the concept of Gibbs entropy from classical statistical mechanics to quantum statis ...
, extending the Gibbs entropy to quantum mechanics * 1928
Ralph Hartley Ralph Vinton Lyon Hartley (November 30, 1888 – May 1, 1970) was an American electronics researcher. He invented the Hartley oscillator and the Hartley transform, and contributed to the foundations of information theory. His legacy includes t ...
introduces Hartley information as the logarithm of the number of possible messages, with information being communicated when the receiver can distinguish one sequence of symbols from any other (regardless of any associated meaning) * 1929 Leó Szilárd analyses
Maxwell's demon Maxwell's demon is a thought experiment that appears to disprove the second law of thermodynamics. It was proposed by the physicist James Clerk Maxwell in 1867. In his first letter, Maxwell referred to the entity as a "finite being" or a "being ...
, showing how a Szilard engine can sometimes transform information into the extraction of useful work * 1940
Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. He was highly influential in the development of theoretical computer ...
introduces the deciban as a measure of information inferred about the German
Enigma machine The Enigma machine is a cipher device developed and used in the early- to mid-20th century to protect commercial, diplomatic, and military communication. It was employed extensively by Nazi Germany during World War II, in all branches of the W ...
cypher settings by the
Banburismus Banburismus was a Cryptanalysis, cryptanalytic process developed by Alan Turing at Bletchley Park in United Kingdom, Britain during the Second World War. It was used by Bletchley Park's Hut 8 to help break German ''Kriegsmarine'' (naval) message ...
process * 1944
Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of th ...
's theory of information is substantially complete * 1947 Richard W. Hamming invents
Hamming code In computer science and telecommunications, Hamming codes are a family of linear error-correcting codes. Hamming codes can detect one-bit and two-bit errors, or correct one-bit errors without detection of uncorrected errors. By contrast, the ...
s for error detection and correction (to protect patent rights, the result is not published until 1950) * 1948 Claude E. Shannon publishes ''
A Mathematical Theory of Communication "A Mathematical Theory of Communication" is an article by mathematician Claude E. Shannon published in '' Bell System Technical Journal'' in 1948. It was renamed ''The Mathematical Theory of Communication'' in the 1949 book of the same name, a s ...
'' * 1949 Claude E. Shannon publishes ''Communication in the Presence of Noise'' –
Nyquist–Shannon sampling theorem The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample r ...
and Shannon–Hartley law * 1949 Claude E. Shannon's ''
Communication Theory of Secrecy Systems "Communication Theory of Secrecy Systems" is a paper published in 1949 by Claude Shannon discussing cryptography from the viewpoint of information theory Information theory is the mathematical study of the quantification (science), quantifica ...
'' is declassified * 1949 Robert M. Fano publishes ''Transmission of Information''. M.I.T. Press, Cambridge, Massachusetts –
Shannon–Fano coding 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 (estimated or measured). * Shann ...
* 1949 – Leon G. Kraft discovers Kraft's inequality, which shows the limits of prefix codes * 1949 Marcel J. E. Golay introduces Golay codes for
forward error correction In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The centra ...
* 1951 Solomon Kullback and Richard Leibler introduce the
Kullback–Leibler divergence In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence), denoted D_\text(P \parallel Q), is a type of statistical distance: a measure of how much a model probability distribution is diff ...
* 1951 David A. Huffman invents Huffman encoding, a method of finding optimal prefix codes for
lossless 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 statisti ...
data compression 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 compressi ...
* 1953 August Albert Sardinas and George W. Patterson devise the
Sardinas–Patterson algorithm In coding theory, the Sardinas–Patterson algorithm is a classical algorithm for determining in polynomial time whether a given variable-length code is uniquely decodable, named after August Albert Sardinas and George W. Patterson, who published it ...
, a procedure to decide whether a given
variable-length code In coding theory, a variable-length code is a code which maps source symbols to a ''variable'' number of bits. The equivalent concept in computer science is '' bit string''. Variable-length codes can allow sources to be compressed and decompr ...
is uniquely decodable * 1954 Irving S. Reed and David E. Muller propose
Reed–Muller code Reed–Muller codes are error-correcting codes that are used in wireless communications applications, particularly in deep-space communication. Moreover, the proposed 5G standard relies on the closely related polar codes for error correction i ...
s * 1955 Peter Elias introduces
convolutional code In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of th ...
s * 1957
Eugene Prange Eugene August Prange (July 30, 1917 – February 12, 2006)Obituary
first discusses
cyclic code In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detecti ...
s * 1959 Alexis Hocquenghem, and independently the next year Raj Chandra Bose and Dwijendra Kumar Ray-Chaudhuri, discover
BCH code In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called a '' Galois field''). BCH codes were invented in ...
s * 1960 Irving S. Reed and Gustave Solomon propose Reed–Solomon codes * 1962 Robert G. Gallager proposes
low-density parity-check code Low-density parity-check (LDPC) codes are a class of error correction codes which (together with the closely-related turbo codes) have gained prominence in coding theory and information theory since the late 1990s. The codes today are widely us ...
s; they are unused for 30 years due to technical limitations * 1965 Dave Forney discusses
concatenated code In coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code. They were conceived in 1966 by Dave Forney as a solution to the problem of finding a code that has both expo ...
s * 1966
Fumitada Itakura is a Japanese scientist. He did pioneering work in statistical signal processing, and its application to speech analysis, synthesis and coding, including the development of the linear predictive coding (LPC) and line spectral pairs (LSP) metho ...
(
Nagoya University , abbreviated to or NU, is a Japanese national research university located in Chikusa-ku, Nagoya. It was established in 1939 as the last of the nine Imperial Universities in the then Empire of Japan, and is now a Designated National Universit ...
) and Shuzo Saito (
Nippon Telegraph and Telephone (NTT) is a Japanese telecommunications holding company headquartered in Tokyo, Japan. Ranked 55th in ''Fortune'' Global 500, NTT is the fourth largest telecommunications company in the world in terms of revenue, as well as the third largest pu ...
) develop
linear predictive coding Linear predictive coding (LPC) is a method used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital signal of speech in compressed form, using the information of a linear predictive model ...
(LPC), a form of
speech coding Speech coding is an application of data compression to digital audio signals containing speech. Speech coding uses speech-specific parameter estimation using audio signal processing techniques to model the speech signal, combined with generic da ...
* 1967
Andrew Viterbi Andrew James Viterbi (born Andrea Giacomo Viterbi, March 9, 1935) is an electrical engineer and businessman who co-founded Qualcomm Inc. and invented the Viterbi algorithm. He is the Presidential Chair Professor of Electrical Engineering at th ...
reveals the
Viterbi algorithm The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events. This i ...
, making decoding of convolutional codes practicable * 1968
Elwyn Berlekamp Elwyn Ralph Berlekamp (September 6, 1940 – April 9, 2019) was a professor of mathematics and computer science at the University of California, Berkeley.Berlekamp–Massey algorithm The Berlekamp–Massey algorithm is an algorithm that will find the shortest linear-feedback shift register (LFSR) for a given binary output sequence. The algorithm will also find the minimal polynomial of a linearly recurrent sequence in an ar ...
; its application to decoding BCH and Reed–Solomon codes is pointed out by James L. Massey the following year * 1968
Chris Wallace Christopher Wallace (born October 12, 1947) is an American broadcast journalist. He is known for his tough and wide-ranging interviews, for which he is often compared to his father, ''60 Minutes'' journalist Mike Wallace. Over his 60-year care ...
and David M. Boulton publish the first of many papers on Minimum Message Length ( MML) statistical and inductive inference * 1970 Valerii Denisovich Goppa introduces Goppa codes * 1972 Jørn Justesen proposes Justesen codes, an improvement of Reed–Solomon codes * 1972 Nasir Ahmed proposes the
discrete cosine transform A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequency, frequencies. The DCT, first proposed by Nasir Ahmed (engineer), Nasir Ahmed in 1972, is a widely ...
(DCT), which he develops with T. Natarajan and K. R. Rao in 1973; the DCT later became the most widely used
lossy compression In information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size ...
algorithm, the basis for multimedia formats such as
JPEG JPEG ( , short for Joint Photographic Experts Group and sometimes retroactively referred to as JPEG 1) is a commonly used method of lossy compression for digital images, particularly for those images produced by digital photography. The degr ...
,
MPEG The Moving Picture Experts Group (MPEG) is an alliance of working groups established jointly by International Organization for Standardization, ISO and International Electrotechnical Commission, IEC that sets standards for media coding, includ ...
and
MP3 MP3 (formally MPEG-1 Audio Layer III or MPEG-2 Audio Layer III) is a coding format for digital audio developed largely by the Fraunhofer Society in Germany under the lead of Karlheinz Brandenburg. It was designed to greatly reduce the amount ...
* 1973 David Slepian and Jack Wolf discover and prove the Slepian–Wolf coding limits for distributed
source coding 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 compressi ...
* 1976 Gottfried Ungerboeck gives the first paper on
trellis modulation Trellis coded modulation (TCM) is a modulation scheme that transmits information with high efficiency over band-limited channels such as telephone lines. Gottfried Ungerboeck invented trellis modulation while working for IBM in the 1970s, and fi ...
; a more detailed exposition in 1982 leads to a raising of analogue modem POTS speeds from 9.6 kbit/s to 33.6 kbit/s * 1976 – Richard Pasco and Jorma J. Rissanen develop effective
arithmetic coding Arithmetic coding (AC) is a form of entropy encoding used in lossless data compression. Normally, a String (computer science), string of characters is represented using a fixed number of bits per character, as in the American Standard Code for In ...
techniques * 1977 Abraham Lempel and Jacob Ziv develop Lempel–Ziv compression (
LZ77 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 Lempel-Ziv 1 (LZ1) and Lempel-Ziv 2 (LZ2) respectively. These two algorithms form the basis ...
) * 1982 Valerii Denisovich Goppa introduces algebraic geometry codes * 1989
Phil Katz Phillip Walter Katz (November 3, 1962 – April 14, 2000) was a computer programmer best known as the co-creator of the ZIP file format for data compression, and the author of PKZIP, a program for creating zip files that ran under DOS. ...
publishes the .zip format including DEFLATE (LZ77 + Huffman coding); later to become the most widely used archive container * 1993 Claude Berrou, Alain Glavieux and Punya Thitimajshima introduce Turbo codes * 1994
Michael Burrows Michael Burrows may refer to: * Michael Burrows (computer scientist), British computer scientist * Michael Burrows (artist), Australian singer-songwriter *Michael Burrows (bishop) Michael Andrew James Burrows (born 1961) is a bishop in the Church ...
and David Wheeler publish the
Burrows–Wheeler transform The Burrows–Wheeler transform (BWT) rearranges a character string into runs of similar characters, in a manner that can be reversed to recover the original string. Since compression techniques such as move-to-front transform and run-length enc ...
, later to find use in
bzip2 bzip2 is a free and open-source file compression program that uses the Burrows–Wheeler algorithm. It only compresses single files and is not a file archiver. It relies on separate external utilities such as tar for tasks such as handli ...
* 1995
Benjamin Schumacher Benjamin "Ben" Schumacher is an American theoretical physicist, working mostly in the field of quantum information theory. He discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in ...
coins the term
qubit In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical syste ...
and proves the quantum noiseless coding theorem * 2003 David J. C. MacKay shows the connection between information theory, inference and machine learning in his book. * 2006 Jarosław Duda introduces first
Asymmetric numeral systems Asymmetric numeral systems (ANS)J. Duda, K. Tahboub, N. J. Gadil, E. J. Delp''The use of asymmetric numeral systems as an accurate replacement for Huffman coding'' Picture Coding Symposium, 2015.J. Duda''Asymmetric numeral systems: entropy coding ...
entropy coding: since 2014 popular replacement of Huffman and
arithmetic coding Arithmetic coding (AC) is a form of entropy encoding used in lossless data compression. Normally, a String (computer science), string of characters is represented using a fixed number of bits per character, as in the American Standard Code for In ...
in compressors like Facebook Zstandard, Apple LZFSE,
CRAM Cram may refer to: * Cram (surname), a surname, and list of notable persons having the surname * Cram.com, a website for creating and sharing flashcards * ''Cram'' (Australian game show), a television show * ''Cram'' (game show), a TV game show ...
or
JPEG XL The JPEG XL Image Coding System is a royalty-free open standard for a image compression, compressed Raster graphics, raster image format. It defines a graphics file format and the abstract device for coding JPEG XL bitstreams. It is developed by t ...
* 2008 Erdal Arıkan introduces polar codes, the first practical construction of codes that achieves capacity for a wide array of channels


References

{{DEFAULTSORT:Timeline Of Information Theory
Information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...
Information theory Thermodynamics