**Information theory**, a mathematical representation of the conditions and parameters affecting the transmission and processing of information. Most closely associated with the work of the American electrical engineer Claude Shannon in the mid-20th century, information theory is chiefly of interest to communication engineers, though some of the concepts have been adopted and used in such fields as psychology and linguistics.

Information theory overlaps heavily with communication theory, but it is more oriented toward the fundamental limitations on the processing and communication of information and less oriented toward the detailed operation of particular devices.

**Historical Background**

Interest in the concept of information grew directly from the creation of the telegraph and telephone. In 1844 the American inventor Samuel F.B. Morse built a telegraph line between Washington, D.C., and Baltimore, Maryland. Morse encountered many electrical problems when he sent signals through buried transmission lines, but inexplicably he encountered fewer problems when the lines were suspended on poles. This attracted the attention of many distinguished physicists, most notably the Scotsman William Thomson (Baron Kelvin).

In a similar manner, the invention of the telephone in 1875 by Alexander Graham Bell and its subsequent proliferation attracted further scientific notaries, such as Henri Poincaré, Oliver Heaviside, and Michael Pupin, to the problems associated with transmitting signals over wires. Much of their work was done using Fourier analysis, a technique described later in this article, but in all of these cases the analysis was dedicated to solving the practical engineering problems of communication systems.

The formal study of information theory did not begin until 1924, when Harry Nyquist, a researcher at Bell Laboratories, published a paper entitled “Certain Factors Affecting Telegraph Speed.” Nyquist realized that communication channels had maximum data transmission rates, and he derived a formula for calculating these rates in finite bandwidth noiseless channels. Another pioneer was Nyquist’s colleague R.V.L. Hartley, whose paper “Transmission of Information” (1928) established the first mathematical foundations for information theory.