Information rate is the average entropy per symbol. https://en.wikipedia.org/w/index.php?title=Information_theory&oldid=1002438403, Short description is different from Wikidata, Articles with too many examples from May 2020, Wikipedia articles with style issues from May 2020, Creative Commons Attribution-ShareAlike License. In practice many channels have memory. "Whatever came up, he engaged it with joy, and he attacked it with some surprising resource — which might be some new kind of technical concept or a hammer and saw with some scraps of wood," Dr. Minsky said. The American mathematician and computer scientist who conceived and laid the foundations for information theory. ( 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. 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. y His later work on chess-playing machines and an electronic mouse that could run a maze helped create the field of artificial intelligence, the effort to make machines that think. One early commercial application of information theory was in the field of seismic oil exploration. If is the set of all messages {x1, ..., xn} that X could be, and p(x) is the probability of some 2 After attending primary and secondary school in his neighboring hometown of Gaylord, he earned bachelors degrees in both electrical engineering and mathematics from the University of Michigan. While at M.I.T., he worked with Dr. Vannevar Bush on one of the early calculating machines, the "differential analyzer," which used a precisely honed system of shafts, gears, wheels and disks to solve equations in calculus. This task will allow us to propose, in Section 10, a formal reading of the concept of Shannon information, according to which the epistemic and the physical views are different possible models of the formalism. The rate of a source of information is related to its redundancy and how well it can be compressed, the subject of source coding. for any logarithmic base. p He gained his PhD from MIT in the subject, but he made substantial contributions to the theory and practice of computing. Other important information theoretic quantities include Rényi entropy (a generalization of entropy), differential entropy (a generalization of quantities of information to continuous distributions), and the conditional mutual information. Il étudie le génie électrique et les mathématiques à l'université du Michigan dont il est diplômé en 19362. If, however, each bit is independently equally likely to be 0 or 1, 1000 shannons of information (more often called bits) have been transmitted. The goal was to find the fundamental limits of communication operations and signal processing through an operation like data compression. Nondiscrimination Policy | 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. x 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. 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. His Collected Papers, published in 1993, contains 127 publications on topics ranging from communications to computing, and juggling to “mind-reading” machines. {\displaystyle i} When Shannon was a student electronic computers didn't exist. 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. And his ability to combine abstract thinking with a practical approach — he had a penchant for building machines — inspired a generation of computer scientists. 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). , while Bob believes (has a prior) that the distribution is x Yet, unfortunately, he is virtually unknown to the public. . Any process that generates successive messages can be considered a source of information. A basic property of the mutual information is that. . | The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering. Read important changes and updates to the 2020 activities of the IEEE Information Theory Society due to the COVID-19 pandemic at: Home | lim X Of course, Babbagehad described the basic design of a stored program computer in the 180… Shannon's main result, the noisy-channel coding theorem showed that, in the limit of many channel uses, the rate of information that is asymptotically achievable is equal to the channel capacity, a quantity dependent merely on the statistics of the channel over which the messages are sent.[2]. 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). Dr. Marvin Minsky of M.I.T., who as a young theorist worked closely with Dr. Shannon, was struck by his enthusiasm and enterprise. 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). He was also the first recipient of the Harvey Prize (1972), the Kyoto Prize (1985), and the Shannon Award (1973). P For stationary sources, these two expressions give the same result.[11]. , , This is an introduction to Shannon's Information Theory. Information theory leads us to believe it is much more difficult to keep secrets than it might first appear. . However, these theorems only hold in the situation where one transmitting user wishes to communicate to one receiving user. 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. ( Claude Shannon first proposed the information theory in 1948. However, such channels often fail to produce exact reconstruction of a signal; noise, periods of silence, and other forms of signal corruption often degrade quality. 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. Synopsis. Between these two extremes, information can be quantified as follows. 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. Information theory also has applications in Gambling and information theory, black holes, and bioinformatics. ) 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. Use of this website signifies your agreement to the IEEE Terms and Conditions. . Information theory studies the quantification, storage, and communication of information. , where pi is the probability of occurrence of the i-th possible value of the source symbol. Next, Shannon set … Intuitively, the entropy HX of a discrete random variable X is a measure of the amount of uncertainty associated with the value of X when only its distribution is known. {\displaystyle p(x)} Information theoretic security refers to methods such as the one-time pad that are not vulnerable to such brute force attacks. Let p(y|x) be the conditional probability distribution function of Y given X. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering. In addition, for any rate R > C, it is impossible to transmit with arbitrarily small block error. is the distribution underlying some data, when, in reality, In a blockbuster paper in 1948, Claude Shannon introduced the notion of a "bit" and laid the foundation for the information age. There were a few mechanical analog computers that could be used to calculate trajectories and tide tables, but nothing that could be described as a digital computer. That is, knowing Y, we can save an average of I(X; Y) bits in encoding X compared to not knowing Y. Claude E. Shannon. i Pierce, JR. "An introduction to information theory: symbols, signals and noise". An accomplished unicyclist, he was famous for cycling the halls of Bell Labs at night, juggling as he went. in 1940. i 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. 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. X {\displaystyle p(X)} In what follows, an expression of the form p log p is considered by convention to be equal to zero whenever p = 0. . , Prior to this paper, limited information-theoretic ideas had been developed at Bell Labs, all implicitly assuming events of equal probability. ) The mutual information of X relative to Y is given by: where SI (Specific mutual Information) is the pointwise mutual information. Contact | On April 30, 1916, American mathematician, electrical engineer, and cryptographer Claude Elwood Shannon was born, the “father of information theory “, whose groundbreaking work ushered in the Digital Revolution.Of course Shannon is famous for having founded information theory with one landmark paper published in 1948.But he is also credited with founding both digital computer and … − 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. of Shannon’s theory, the epistemic and the physical interpretations, will be emphasized in Section 9. Shannon defined the quantity of information produced by a source--for example, the quantity in a message--by a formula similar to the equation that … These codes can be roughly subdivided into data compression (source coding) and error-correction (channel coding) techniques. This is justified because A property of entropy is that it is maximized when all the messages in the message space are equiprobable p(x) = 1/n; i.e., most unpredictable, in which case H(X) = log n. The special case of information entropy for a random variable with two outcomes is the binary entropy function, usually taken to the logarithmic base 2, thus having the shannon (Sh) as unit: The joint entropy of two discrete random variables X and Y is merely the entropy of their pairing: (X, Y). Information theory is the scientific study of the quantification, storage, and communication of information. , This is appropriate, for example, when the source of information is English prose. 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