It is important in communication where it can be used to maximize the amount of information shared between sent and received signals. ( This innovation, credited as the advance that transformed circuit design “from an art to a science,” remains the basis for circuit and chip design to this day. In the latter case, it took many years to find the methods Shannon's work proved were possible. − . This page was last edited on 24 January 2021, at 13:22. q In this way, the extent to which Bob's prior is "wrong" can be quantified in terms of how "unnecessarily surprised" it is expected to make him. . 1 Shannon’s Information Theory Claude Shannon may be considered one of the most influential person of the 20th Century, as he laid out the foundation of the revolutionary information theory. Though analog computers like this turned out to be little more than footnotes in the history of the computer, Dr. Shannon quickly made his mark with digital electronics, a considerably more influential idea. Information theoretic concepts apply to cryptography and cryptanalysis. 1 "[15]:91, Concepts from information theory such as redundancy and code control have been used by semioticians such as Umberto Eco and Ferruccio Rossi-Landi to explain ideology as a form of message transmission whereby a dominant social class emits its message by using signs that exhibit a high degree of redundancy such that only one message is decoded among a selection of competing ones.[17]. These codes can be roughly subdivided into data compression (source coding) and error-correction (channel coding) techniques. | Shannon approached research with a sense of curiosity, humor, and fun. i For stationary sources, these two expressions give the same result.[11]. , x A basic property of this form of conditional entropy is that: Mutual information measures the amount of information that can be obtained about one random variable by observing another. for DSL). . Entropy is also commonly computed using the natural logarithm (base e, where e is Euler's number), which produces a measurement of entropy in nats per symbol and sometimes simplifies the analysis by avoiding the need to include extra constants in the formulas. Any process that generates successive messages can be considered a source of information. Harry Nyquist, "Certain Topics in Telegraph Transmission Theory", Transactions of AIEE, Vol. Shannon received both a master's degree in electrical engineering and his Ph.D. in mathematics from M.I.T. The field was fundamentally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. − In practice many channels have memory. Nonsense! . His theories laid the groundwork for the electronic communications networks that now lace the earth. i For example, if (X, Y) represents the position of a chess piece—X the row and Y the column, then the joint entropy of the row of the piece and the column of the piece will be the entropy of the position of the piece. souhaitée]. The mutual information of X relative to Y is given by: where SI (Specific mutual Information) is the pointwise mutual information. In other words, an eavesdropper would not be able to improve his or her guess of the plaintext by gaining knowledge of the ciphertext but not of the key. Information theory studies the quantification, storage, and communication of information. Information theory is closely associated with a collection of pure and applied disciplines that have been investigated and reduced to engineering practice under a variety of rubrics throughout the world over the past half-century or more: adaptive systems, anticipatory systems, artificial intelligence, complex systems, complexity science, cybernetics, informatics, machine learning, along with systems sciences of many descriptions. 2.- Shannon’s theory After graduating from the University of Michigan in 1936 with bachelor’s degrees in mathematics and electrical Of course, Babbagehad described the basic design of a stored program computer in the 180… In Shannon's revolutionary and groundbreaking paper, the work for which had been substantially completed at Bell Labs by the end of 1944, Shannon for the first time introduced the qualitative and quantitative model of communication as a statistical process underlying information theory, opening with the assertion that. x This implies that if X and Y are independent, then their joint entropy is the sum of their individual entropies. T his equation was published in the 1949 book The Mathematical Theory of Communication, co-written by Claude Shannon and Warren Weaver.An elegant way to … x It is important to realise that Shannon's Theory was created to find ways to optimise the physical encoding of information, to find fundamental limits on signal processing operations. Prior to this paper, limited information-theoretic ideas had been developed at Bell Labs, all implicitly assuming events of equal probability. lim "That was really his discovery, and from it the whole communications revolution has sprung.". In a blockbuster paper in 1948, Claude Shannon introduced the notion of a "bit" and laid the foundation for the information age. As noted by Ioan James, Shannon biographer for the Royal Society, “So wide were its repercussions that the theory was described as one of humanity’s proudest and rarest creations, a general scientific theory that could profoundly and rapidly alter humanity’s view of the world.” Shannon went on to develop many other important ideas whose impact expanded well beyond the field of “information theory” spawned by his 1948 paper. Under these constraints, we would like to maximize the rate of information, or the signal, we can communicate over the channel. Applications of fundamental topics of information theory include lossless data compression (e.g. Shannon, who died in 2001 at … Read important changes and updates to the 2020 activities of the IEEE Information Theory Society due to the COVID-19 pandemic at: Home | i Because of this, he is widely considered "the father of information theory". − Other bases are also possible, but less commonly used. A common unit of information is the bit, based on the binary logarithm. It's interesting how Information Theory, Las Vegas and Wall Street have been intertwined over the years. , (Here, I(x) is the self-information, which is the entropy contribution of an individual message, and X is the expected value.) This equation gives the entropy in the units of "bits" (per symbol) because it uses a logarithm of base 2, and this base-2 measure of entropy has sometimes been called the shannon in his honor. y , Claude Elwood Shannon was an American mathematician, cryptographer, and electrical engineer, who garnered fame when he conceptualised information theory with the landmark paper, ‘Mathematical Theory of Communication’, which he put out in 1948. In 1948, he published ‘The Mathematical Theory of Communication’, which is considered the most noted information theory. MP3s and JPEGs), and channel coding (e.g. ) [15]:171[16]:137 Nauta defined semiotic information theory as the study of "the internal processes of coding, filtering, and information processing. i Based on the probability mass function of each source symbol to be communicated, the Shannon entropy H, in units of bits (per symbol), is given by. = Its impact has been crucial to the success of the Voyager missions to deep space, the invention of the compact disc, the feasibility of mobile phones and the development of the Internet. Claude Shannon first proposed the information theory in 1948. One early commercial application of information theory was in the field of seismic oil exploration. p . Considered the founding father of the electronic communication age, Claude Shannon's work ushered in the Digital Revolution. Information theory and digital signal processing offer a major improvement of resolution and image clarity over previous analog methods. − Pierce, JR. "An introduction to information theory: symbols, signals and noise". Then the joint distribution of X and Y is completely determined by our channel and by our choice of f(x), the marginal distribution of messages we choose to send over the channel. Work in this field made it possible to strip off and separate the unwanted noise from the desired seismic signal. A brute force attack can break systems based on asymmetric key algorithms or on most commonly used methods of symmetric key algorithms (sometimes called secret key algorithms), such as block ciphers. x Although it is sometimes used as a 'distance metric', KL divergence is not a true metric since it is not symmetric and does not satisfy the triangle inequality (making it a semi-quasimetric). For more information about Shannon and his impact, see the article by Michelle Effros and H. Vincent Poor, Claude Shannon: His Work and Its Legacy, Published with the permission of the EMS Newsletter: reprinted from N°103 (March 2017) pp.29-34. Turing's information unit, the ban, was used in the Ultra project, breaking the German Enigma machine code and hastening the end of World War II in Europe. The goal was to find the fundamental limits of communication operations and signal processing through an operation like data compression. Contact | the channel is given by the condiation probability ( p x From Claude Shannon's 1948 paper, "A Mathematical Theory of Communication," which proposed the use of binary digits for coding information. His theories laid the groundwork for the electronic communications networks that now lace the earth. Indeed the diversity and directions of their perspectives and interests shaped the direction of Information Theory. Information theory is based on probability theory and statistics. Network information theory refers to these multi-agent communication models. Claude Shannon, the father of Information Theory You may not have heard of Claude Shannon, but his ideas made the modern information age possible. All such sources are stochastic. A class of improved random number generators is termed cryptographically secure pseudorandom number generators, but even they require random seeds external to the software to work as intended. The appropriate measure for this is the mutual information, and this maximum mutual information is called the channel capacity and is given by: This capacity has the following property related to communicating at information rate R (where R is usually bits per symbol). for any logarithmic base. {\displaystyle x\in \mathbb {X} } x This is justified because He created the field of Information Theory when he published a book "The Mathematical Theory… This is appropriate, for example, when the source of information is English prose. In a prize-winning masters thesis completed in the Department of Mathematics, Shannon proposed a method for applying a mathematical form of logic called Boolean algebra to the design of relay switching circuits. Il utilise notamment l'algèbre de Boole pour sa maîtrise soutenue en 1938 au Massachusetts Institute of Technology (MIT). | How to Submit to Web Site and Mailing List, Online: 2020 European School of Information Theory, Canceled: 2020 North American School of Information Theory, 2019 North American School of Information Theory, 2019 European School of Information Theory, 2018 North American School of Information Theory, 2018 IEEE European School of Information Theory (ESIT), May 7-11, 2017 North-American School of Information Theory, 2017 European School of Information Theory, 2016 European School of Information Theory, April 4-8, 2016, 2015 North American School of Information Theory, 2014 North American School of Information Theory, Journal on Selected Areas in Information Theory (JSAIT), JSAIT CFP: Sequential, Active, and Reinforcement Learning, Conversations on George Boole, the Legacy Interviews (2016), Aaron D. Wyner Distinguished Service Award, Communications Society & Information Theory Society Joint Paper Award, James L. Massey Research & Teaching Award for Young Scholars, Golden Jubilee Awards for Technological Innovation, BoG Meeting @ ISIT 2013, Istanbul, Turkey, BoG Meeting @ ISIT 2011, St. Petersburg, Russia, BoG Meeting, September 27, 2006, Monticello, Claude E. Shannon Award Selection Committee, Aaron D. Wyner Distinguished Service Award Selection Committee, James L. Massey Research and Teaching Award for Young Scholars Selection Committee, Thomas M. Cover Dissertation Award Committee, Information Theory Magazine Steering Committee, Journal on Selected Areas in Information Theory (JSAIT) Steering Committee, List of ITSOC Chapters and Joint Chapters, Report from IEEE TAB Ad Hoc Committee on Women and Under-represented Groups (WUG), TAB Committee on Diversity and Inclusion Charter, PhD Student in Machine Learning for Energy-Efficient Communication Systems, Postdoc in Information Theory for Energy-Efficient Communications, 55th Annual Conference on Information Sciences and Systems (CISS 2021), Rescheduled: 2020 IEEE Information Theory Workshop (ITW 2020) in Riva del Garda, 2021 IEEE International Symposium on Information Theory (ISIT). {\displaystyle \lim _{p\rightarrow 0+}p\log p=0} . Let p(y|x) be the conditional probability distribution function of Y given X. Claude Shannon: Born on the planet Earth (Sol III) in the year 1916 A.D. Generally regarded as the father of the information age, he formulated the notion of channel capacity in 1948 A.D. ⁡ In 1973, he recalled, he persuaded Shannon to give the first annual Shannon lecture at the International Information Theory Symposium, but Shannon almost backed out at the last minute. Coding theory is one of the most important and direct applications of information theory. . If Alice knows the true distribution Shannon died on Saturday, February 24, 2001 in Medford, Mass., after a long fight with Alzheimer's disease. Claude Shannon, American mathematician and electrical engineer who laid the theoretical foundations for digital circuits and information theory, a mathematical communication model. Shannon wanted to measure the amount of information you could transmit via various media. , , while Bob believes (has a prior) that the distribution is Accessibility | In 1941, Shannon took a position at Bell Labs, where he had spent several prior summers. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering. X These groundbreaking innovations provided the tools that ushered in the information age. A memoryless source is one in which each message is an independent identically distributed random variable, whereas the properties of ergodicity and stationarity impose less restrictive constraints. 2 Information theoretic security refers to methods such as the one-time pad that are not vulnerable to such brute force attacks. − in Proceedings of the IEEE90:2 (February 2002), pp 280-305. A simple model of the process is shown below: Here X represents the space of messages transmitted, and Y the space of messages received during a unit time over our channel. The entropy of a source that emits a sequence of N symbols that are independent and identically distributed (iid) is N ⋅ H bits (per message of N symbols). Based on the redundancy of the plaintext, it attempts to give a minimum amount of ciphertext necessary to ensure unique decipherability. ( is the correct distribution, the Kullback–Leibler divergence is the number of average additional bits per datum necessary for compression. The American mathematician and computer scientist who conceived and laid the foundations for information theory. 47 (April 1928), pp 617-644; repr. ( , Courtesy of MIT Museum. ( It is common in information theory to speak of the "rate" or "entropy" of a language. Il y explique comment construire des machines à relais en utilisant l'algèbre de Boole pour décrire l'état des relais (1 : fermé, 0 : ouvert)[réf. And his ability to combine abstract thinking with a practical approach — he had a penchant for building machines — inspired a generation of computer scientists. The latter is a property of the joint distribution of two random variables, and is the maximum rate of reliable communication across a noisy channel in the limit of long block lengths, when the channel statistics are determined by the joint distribution. Il obtient un PhD en mathématiques au MIT en 19402. Concepts, methods and results from coding theory and information theory are widely used in cryptography and cryptanalysis. 1 i ) The measure of sufficient randomness in extractors is min-entropy, a value related to Shannon entropy through Rényi entropy; Rényi entropy is also used in evaluating randomness in cryptographic systems. He was 84. While Shannon worked in a field for which no Nobel prize is offered, his work was richly rewarded by honors including the National Medal of Science (1966) and honorary degrees from Yale (1954), Michigan (1961), Princeton (1962), Edin- burgh (1964), Pittsburgh (1964), Northwestern (1970), Oxford (1978), East Anglia (1982), Carnegie-Mellon (1984), Tufts (1987), and the University of Pennsylvania (1991). ) His war-time work on secret communication systems was used to build the system over which Roosevelt and Churchill communicated during the war. ) y , Nondiscrimination Policy | The rate of a source of information is related to its redundancy and how well it can be compressed, the subject of source coding. A 0 Using a statistical description for data, information theory quantifies the number of bits needed to describe the data, which is the information entropy of the source. The unit of information was therefore the decimal digit, which has since sometimes been called the hartley in his honor as a unit or scale or measure of information. x In addition, for any rate R > C, it is impossible to transmit with arbitrarily small block error. , then Bob will be more surprised than Alice, on average, upon seeing the value of X. X It was originally proposed by Claude Shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper titled "A Mathematical Theory of Communication". p Claude Shannon is quite correctly described as a mathematician. . 1 He was also the first recipient of the Harvey Prize (1972), the Kyoto Prize (1985), and the Shannon Award (1973). i ( P The landmark event that 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. For any information rate R < C and coding error ε > 0, for large enough N, there exists a code of length N and rate ≥ R and a decoding algorithm, such that the maximal probability of block error is ≤ ε; that is, it is always possible to transmit with arbitrarily small block error. − A key measure in information theory is entropy. Information rate is the average entropy per symbol. A Mathematical Theory of Communication By C. E. SHANNON INTRODUCTION T HE recent development of various methods of modulation such as PCM and PPM which exchange bandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication. It can be subdivided into source coding theory and channel coding theory. Because entropy can be conditioned on a random variable or on that random variable being a certain value, care should be taken not to confuse these two definitions of conditional entropy, the former of which is in more common use. Ce domaine trouve son origine scientifique avec Claude Shannon qui en est le … y The Kullback–Leibler divergence (or information divergence, information gain, or relative entropy) is a way of comparing two distributions: a "true" probability distribution This division of coding theory into compression and transmission is justified by the information transmission theorems, or source–channel separation theorems that justify the use of bits as the universal currency for information in many contexts. For example, a logarithm of base 28 = 256 will produce a measurement in bytes per symbol, and a logarithm of base 10 will produce a measurement in decimal digits (or hartleys) per symbol. P For the more general case of a process that is not necessarily stationary, the average rate is, that is, the limit of the joint entropy per symbol. where pi is the probability of occurrence of the i-th possible value of the source symbol. , If Shannon … Other units include the nat, which is based on the natural logarithm, and the decimal digit, which is based on the common logarithm. x , The former quantity is a property of the probability distribution of a random variable and gives a limit on the rate at which data generated by independent samples with the given distribution can be reliably compressed. is the distribution underlying some data, when, in reality, Pseudorandom number generators are widely available in computer language libraries and application programs. {\displaystyle p(X)} When his results were finally de-classified and published in 1949, they revolutionized the field of cryptography. Connections between information-theoretic entropy and thermodynamic entropy, including the important contributions by Rolf Landauer in the 1960s, are explored in Entropy in thermodynamics and information theory. Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms - Examples of Entropy Increase? "For him, the harder a problem might seem, the better the chance to find something new.". That is, knowing Y, we can save an average of I(X; Y) bits in encoding X compared to not knowing Y. p For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a die (with six equally likely outcomes). {\displaystyle x^{i}=(x_{i},x_{i-1},x_{1-2},...,x_{1})} {\displaystyle q(X)} Important quantities of information are entropy, a measure of information in a single random variable, and mutual information, a measure of information in common between two random variables. Harry Nyquist's 1924 paper, Certain Factors Affecting Telegraph Speed, contains a theoretical section quantifying "intelligence" and the "line speed" at which it can be transmitted by a communication system, giving the relation W = K log m (recalling Boltzmann's constant), where W is the speed of transmission of intelligence, m is the number of different voltage levels to choose from at each time step, and K is a constant. . Information theory often concerns itself with measures of information of the distributions associated with random variables. Claude Elwood Shannon was born on … Another interpretation of the KL divergence is the "unnecessary surprise" introduced by a prior from the truth: suppose a number X is about to be drawn randomly from a discrete set with probability distribution . ) the mutual information, and the channel capacity of a noisy channel, including the promise of perfect loss-free communication given by the noisy-channel coding theorem; Data compression (source coding): There are two formulations for the compression problem: Error-correcting codes (channel coding): While data compression removes as much redundancy as possible, an error-correcting code adds just the right kind of redundancy (i.e., error correction) needed to transmit the data efficiently and faithfully across a noisy channel. In what follows, an expression of the form p log p is considered by convention to be equal to zero whenever p = 0. i ∈ . , + , p It was the result of crucial contributions made by many distinct individuals, from a variety of backgrounds, who took his ideas and expanded upon them. The last of these awards, named in his honor, is given by the Information Theory Society of the Institute of Electrical and Electronics Engineers (IEEE) and remains the highest possible honor in the community of researchers dedicated to the field that he invented. 1 Between these two extremes, information can be quantified as follows. 1 Claude Shannon, known as the ‘father of information theory’, was a celebrated American cryptographer, mathematician and electrical engineer. Shown above are the equations … y The theory has also found applications in other areas, including statistical inference,[1] cryptography, neurobiology,[2] perception,[3] linguistics, the evolution[4] and function[5] of molecular codes (bioinformatics), thermal physics,[6] quantum computing, black holes, information retrieval, intelligence gathering, plagiarism detection,[7] pattern recognition, anomaly detection[8] and even art creation. ( Ralph Hartley's 1928 paper, Transmission of Information, uses the word information as a measurable quantity, reflecting the receiver's ability to distinguish one sequence of symbols from any other, thus quantifying information as H = log Sn = n log S, where S was the number of possible symbols, and n the number of symbols in a transmission. This fundamental treatise both defined a mathematical notion by which information could be quantified and demonstrated that information could be delivered reliably over imperfect communication channels like phone lines or wireless connections. , 1 IEEE – All rights reserved. x x A basic property of the mutual information is that. Although related, the distinctions among these measures mean that a random variable with high Shannon entropy is not necessarily satisfactory for use in an extractor and so for cryptography uses. Il étudie le génie électrique et les mathématiques à l'université du Michigan dont il est diplômé en 19362. Mutual information can be expressed as the average Kullback–Leibler divergence (information gain) between the posterior probability distribution of X given the value of Y and the prior distribution on X: In other words, this is a measure of how much, on the average, the probability distribution on X will change if we are given the value of Y. In the case of communication of information over a noisy channel, this abstract concept was formalized in 1948 by Claude Shannon in a paper entitled A Mathematical Theory of Communication, in which information is thought of as a set of possible messages, and the goal is to send these messages over a noisy channel, and to have the receiver reconstruct the message with low probability of error, in spite of the channel noise. {\displaystyle q(x)} ZIP files), lossy data compression (e.g. {\displaystyle p(X)} Channel coding is concerned with finding such nearly optimal codes that can be used to transmit data over a noisy channel with a small coding error at a rate near the channel capacity. x La théorie de l'information, sans précision, est le nom usuel désignant la théorie de l'information de Shannon, qui est une théorie probabiliste permettant de quantifier le contenu moyen en information d'un ensemble de messages, dont le codage informatique satisfait une distribution statistique précise. A third class of information theory codes are cryptographic algorithms (both codes and ciphers). Namely, at time Seismic signal for stationary sources, these two extremes, information engineering, and electrical engineering in a amount... R > C, it took many years to find the fundamental limits of communication ’, was struck his! Groundwork for the benefit of humanity operation like data compression ( e.g include lossless data compression where! Graduate studies storage, and claude shannon information theory of information is that he had spent several prior summers improvement resolution! Attempts to give a minimum amount of time ethernet cable—is the primary of! His enthusiasm and enterprise, at 13:22, limited information-theoretic ideas had been developed at Bell at... And digital signal processing offer a major improvement of resolution and image clarity previous. Are widely used in cryptography and cryptanalysis of a random process, juggling as went. 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Own right outside information theory refers to these multi-agent communication models master 's degree in electrical engineering it to...