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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 book of the same name,[5] a small but significant title change after realizing the generality of this work.



Shannon's diagram of a general communications system, which shows the process that produces a message.

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.


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.


  1. ^ Shannon, Claude E. (July 1948). "A Mathematical Theory of Communication". 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.
  2. ^ Shannon, Claude E. (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.
  3. ^ Robert B. Ash. Information Theory. New York: Interscience, 1965. ISBN 0-470-03445-9. New York: Dover 1990. ISBN 0-486-66521-6, p. v
  4. ^ Yeung, R. W. (2008). "The Science of Information". Information Theory and Network Coding. pp. 1–01. doi:10.1007/978-0-387-79234-7_1. ISBN 978-0-387-79233-0.
  5. ^ Claude E. Shannon, Warren Weaver. The Mathematical Theory of Communication. Univ of Illinois Press, 1949. ISBN 0-252-72548-4

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