The science of compressing and communicating information. It is a branch of applied mathematics and electrical engineering. Though originally the focus was on digital communications and computing, it now finds wide use in biology, physics and other sciences.
Information theory studies the quantification, storage, and communication of information. 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)). 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.
A key measure in information theory is entropy, which 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 die (with six equally likely outcomes). Some other important measures in information theory are mutual information, channel capacity, error exponents, and Kullback-Leibler divergence.
The field is at the intersection of mathematics, statistics, computer science, physics, neurobiology, and electrical engineering. The theory has also found applications in other areas, including statistical-inference, natural language processing, cryptography, neurobiology, human vision, the evolution and function of molecular codes (bioinformatics), model selection in statistics, thermal physics, quantum computing, linguistics, plagiarism detection, pattern-recognition, and anomaly detection. Important sub-fields of information theory include source coding, channel coding, algorithmic complexity theory, algorithmic information theory, information-theoretic security, and measures of information.
