What is "information theory"

information theory \in`for*ma"tion the"o*ry\, n. (Math., Telecommunications) The science which studies the capacity of systems to contain and transmit information[2], and the factors such as noise and channel capacity that may affect the rate or accuracy of information transmission and reception.

n. (context mathematics English) A branch of applied mathematics and engineering involving the quantification of information sent over a communication channel, disregarding the meaning of the sent messages, exemplified by the http://en.wikipedia.org/wiki/Noisy-channel%20coding%20theorem.

n. (computer science) a statistical theory dealing with the limits and efficiency of information processing

Information theory studies the quantification, storage, and communication of information. It was originally proposed by Claude E. Shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper entitled " A Mathematical Theory of Communication". Now this theory has found applications in many other areas, including statistical inference, natural language processing, cryptography, neurobiology, the evolution and function of molecular codes, model selection in ecology, thermal physics, quantum computing, linguistics, plagiarism detection, pattern recognition, and anomaly detection.

A key measure in information theory is " entropy". Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. 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 (with six equally likely outcomes). Some other important measures in information theory are mutual information, channel capacity, error exponents, and relative entropy.

Applications of fundamental topics of information theory include lossless data compression (e.g. ZIP files), lossy data compression (e.g. MP3s and JPEGs), and channel coding (e.g. for Digital Subscriber Line (DSL)).

The field is at the intersection of mathematics, statistics, computer science, physics, neurobiology, and electrical engineering. 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, the development of the Internet, the study of linguistics and of human perception, the understanding of black holes, and numerous other fields. Important sub-fields of information theory include source coding, channel coding, algorithmic complexity theory, algorithmic information theory, information-theoretic security, and measures of information.