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A Mathematical Theory of Communication

Summary

"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. It has tens of thousands of citations, being one of the most influential and cited scientific papers of all time,[6] as it gave rise to the field of information theory, with Scientific American referring to the paper as the "Magna Carta of the Information Age",[7] while the electrical engineer Robert G. Gallager called the paper a "blueprint for the digital era".[8] Historian James Gleick rated the paper as the most important development of 1948, placing the transistor second in the same time period, with Gleick emphasizing that the paper by Shannon was "even more profound and more fundamental" than the transistor.[9]

A Mathematical Theory of Communication
1949 full book edition
AuthorClaude E. Shannon
LanguageEnglish
SubjectCommunication theory
Publication date
1948
Publication placeUnited States

It is also noted that "as did relativity and quantum theory, information theory radically changed the way scientists look at the universe".[10] The paper also formally introduced the term "bit" and serves as its theoretical foundation.[11]

Publication

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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.[12]

Contents

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Shannon's diagram of a general communications system, showing the process by which a message sent becomes the message received (possibly corrupted by noise)

This work is known for introducing the concepts of channel capacity as well as the noisy channel coding theorem.

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, redundancy and the source coding theorem, 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

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  1. ^ 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.
  2. ^ Shannon, Claude Elwood (October 1948). "A Mathematical Theory of Communication". Bell System Technical Journal. 27 (4): 623–656. doi:10.1002/j.1538-7305.1948.tb00917.x. hdl:11858/00-001M-0000-002C-4314-2.
  3. ^ Ash, Robert B. (1966). Information Theory: Tracts in Pure & Applied Mathematics. New York: John Wiley & Sons Inc. ISBN 0-470-03445-9.
  4. ^ Yeung, Raymond W. (2008). "The Science of Information". Information Theory and Network Coding. Springer. pp. 1–4. doi:10.1007/978-0-387-79234-7_1. ISBN 978-0-387-79233-0.
  5. ^ Shannon, Claude Elwood; Weaver, Warren (1949). The Mathematical Theory of Communication (PDF). University of Illinois Press. ISBN 0-252-72548-4. Archived from the original (PDF) on 1998-07-15. {{cite book}}: ISBN / Date incompatibility (help)
  6. ^ Yan, Zheng (2020). Publishing Journal Articles: A Scientific Guide for New Authors Worldwide. Cambridge University Press. p. 7. ISBN 978-1-108-27742-6.
  7. ^ Goodman, Rob; Soni, Jimmy (2018). "Genius in Training". Alumni Association of the University of Michigan. Retrieved 2023-10-31.
  8. ^ "Claude Shannon: Reluctant Father of the Digital Age". MIT Technology Review. 2001-07-01. Retrieved 2024-06-26.
  9. ^ Gleick, James (2011). The Information: A History, a Theory, a Flood (1st ed.). New York: Vintage Books. pp. 3–4. ISBN 978-1-4000-9623-7.
  10. ^ Watson, Peter (2018). Convergence: The Idea at the Heart of Science. New York London Toronto Sydney New Delhi: Simon & Schuster. p. 392. ISBN 978-1-4767-5434-5.
  11. ^ Nicolelis, Miguel A. L. (2020). The True Creator of Everything: How the Human Brain Shaped the Universe as We Know it. New Haven: Yale University Press. p. 34. ISBN 978-0-300-24463-2. OCLC 1090423259.
  12. ^ "The Mathematical Theory of Communication" (PDF). Monoskop Digital Libraries. Retrieved 2024-05-28.
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  • (PDF) "A Mathematical Theory of Communication" by C. E. Shannon (reprint with corrections) hosted by the Harvard Mathematics Department, at Harvard University
    • Original publications: The Bell System Technical Journal 1948-07: Vol 27 Iss 3. AT & T Bell Laboratories. 1948-07-01. pp. 379–423., The Bell System Technical Journal 1948-10: Vol 27 Iss 4. AT & T Bell Laboratories. 1948-10-01. pp. 623–656.
  • Khan Academy video about "A Mathematical Theory of Communication"

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