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Entropy units11/23/2023 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 S n = n log S, where S was the number of possible symbols, and n the number of symbols in a transmission. 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 the Boltzmann 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. Prior to this paper, limited information-theoretic ideas had been developed at Bell Labs, all implicitly assuming events of equal probability. Shannon's classic paper "A Mathematical Theory of Communication" in the Bell System Technical Journal in July and October 1948. The landmark event establishing the discipline of information theory and bringing it to immediate worldwide attention was the publication of Claude E. Main article: History of information theory See the article ban (unit) for a historical application. Concepts, methods and results from coding theory and information theory are widely used in cryptography and cryptanalysis. In the latter case, it took many years to find the methods Shannon's work proved were possible.Ī third class of information theory codes are cryptographic algorithms (both codes and ciphers). These codes can be roughly subdivided into data compression (source coding) and error-correction (channel coding) techniques. Ĭoding theory is concerned with finding explicit methods, called codes, for increasing the efficiency and reducing the error rate of data communication over noisy channels to near the channel capacity. 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. 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. Abstractly, information can be thought of as the resolution of uncertainty. Information theory studies the transmission, processing, extraction, and utilization of information. The theory has also found applications in other areas, including statistical inference, cryptography, neurobiology, perception, linguistics, the evolution and function of molecular codes ( bioinformatics), thermal physics, molecular dynamics, quantum computing, black holes, information retrieval, intelligence gathering, plagiarism detection, pattern recognition, anomaly detection and even art creation. 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. for ZIP files), and channel coding/ error detection and correction (e.g. Important sub-fields of information theory include source coding, algorithmic complexity theory, algorithmic information theory and information-theoretic security.Īpplications of fundamental topics of information theory include source coding/ data compression (e.g. Some other important measures in information theory are mutual information, channel capacity, error exponents, and relative entropy. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy, less uncertainty) than specifying the outcome from a roll of a die (with six equally likely outcomes). Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. : vii The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering.Ī key measure in information theory is entropy. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. Information theory is the mathematical study of the quantification, storage, and communication of information.
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