# A Mathematical Theory of Communication

"**A Mathematical Theory of Communication**" is an article by mathematician Claude E. Shannon published in *Bell System Technical Journal* in 1948.[1][2][3][4] It was renamed * The Mathematical Theory of Communication* in the 1949 book of the same name,[5] a small but significant title change after realizing the generality of this work.

## Publication

The article was the founding work of the field of information theory. It was later published in 1949 as a book titled *The Mathematical Theory of Communication* (ISBN 0-252-72546-8), which was published as a paperback in 1963 (ISBN 0-252-72548-4). The book contains an additional article by Warren Weaver, providing an overview of the theory for a more general audience.

## Contents

Shannon's article laid out the basic elements of communication:

- An information source that produces a message
- A transmitter that operates on the message to create a signal which can be sent through a channel
- A channel, which is the medium over which the signal, carrying the information that composes the message, is sent
- A receiver, which transforms the signal back into the message intended for delivery
- A destination, which can be a person or a machine, for whom or which the message is intended

It also developed the concepts of information entropy and redundancy, and introduced the term bit (which Shannon credited to John Tukey) as a unit of information. It was also in this paper that the Shannon–Fano coding technique was proposed – a technique developed in conjunction with Robert Fano.

## References

- Shannon, Claude Elwood (July 1948). "A Mathematical Theory of Communication" (PDF).
*Bell System Technical Journal*.**27**(3): 379–423. doi:10.1002/j.1538-7305.1948.tb01338.x. hdl:11858/00-001M-0000-002C-4314-2. Archived from the original (PDF) on 1998-07-15.The choice of a logarithmic base corresponds to the choice of a unit for measuring information. If the base 2 is used the resulting units may be called binary digits, or more briefly

*bits*, a word suggested by J. W. Tukey. - Shannon, Claude Elwood (October 1948). "A Mathematical Theory of Communication".
*Bell System Technical Journal*.**27**(4): 623–666. doi:10.1002/j.1538-7305.1948.tb00917.x. hdl:11858/00-001M-0000-002C-4314-2. - Ash, Robert B. (1966).
*Information Theory: Tracts in Pure & Applied Mathematics*. New York: John Wiley & Sons Inc. ISBN 0-470-03445-9. - Yeung, Raymond W. (2008). "The Science of Information".
*Information Theory and Network Coding*. Springer. doi:10.1007/978-0-387-79234-7_1. ISBN 978-0-387-79233-0. - Shannon, Claude Elwood; Weaver, Warren (1949).
*A Mathematical Theory of Communication*(PDF). University of Illinois Press. ISBN 0-252-72548-4. Archived from the original (PDF) on 1998-07-15.