A Mathematical Theory of Communication

Short description: 1948 scholarly article by Claude Shannon

A Mathematical Theory of Communication

1949 full book edition

Author| Claude E. Shannon
Country| United States
Language| English
Subject| Communication theory

Publication date

| 1948

"A Mathematical Theory of Communication" is an article by mathematician Claude 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]

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]

## Contents

* 1 Publication
* 2 Contents
* 3 See also
* 4 References
* 5 External links

## 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.[12]

## Contents

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.

## See also

* List of computer books

## References

1. ↑ "A Mathematical Theory of Communication". Bell System Technical Journal 27 (3): 379–423. July 1948. doi:10.1002/j.1538-7305.1948.tb01338.x. http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf. "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. ↑ "A Mathematical Theory of Communication". Bell System Technical Journal 27 (4): 623–656. October 1948. doi:10.1002/j.1538-7305.1948.tb00917.x.
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. https://archive.org/details/informationtheor00yeun.
5. ↑ The Mathematical Theory of Communication. University of Illinois Press. 1949. http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf.
6. ↑ Yan, Zheng (2020) (in en). Publishing Journal Articles: A Scientific Guide for New Authors Worldwide. Cambridge University Press. pp. 7. ISBN 978-1-108-27742-6. https://books.google.com/books?id=eEgFEAAAQBAJ&pg=PA7.
7. ↑ Goodman, Rob; Soni, Jimmy (2018). "Genius in Training" (in en-US). https://alumni.umich.edu/michigan-alum/genius-in-training/.
8. ↑ "Claude Shannon: Reluctant Father of the Digital Age" (in en). 2001-07-01. https://www.technologyreview.com/2001/07/01/235669/claude-shannon-reluctant-father-of-the-digital-age/.
9. ↑ Gleick, James (2011) (in en). The Information: A History, a Theory, a Flood (1st ed.). New York: Vintage Books. pp. 3–4. ISBN 978-1-4000-9623-7. https://books.google.com/books?id=WAKWDwAAQBAJ&pg=PA3.
10. ↑ Watson, Peter (2018) (in en). Convergence: The Idea at the Heart of Science. New York London Toronto Sydney New Delhi: Simon & Schuster. pp. 392. ISBN 978-1-4767-5434-5. https://books.google.com/books?id=gC6MDAAAQBAJ&pg=PA392.
11. ↑ Nicolelis, Miguel A. L. (2020) (in en). The True Creator of Everything: How the Human Brain Shaped the Universe as We Know it. New Haven: Yale University Press. pp. 34. ISBN 978-0-300-24463-2. OCLC on1090423259. https://books.google.com/books?id=my7EDwAAQBAJ&pg=PA34.
12. ↑ "The Mathematical Theory of Communication". https://monoskop.org/images/b/be/Shannon_Claude_E_Weaver_Warren_The_Mathematical_Theory_of_Communication_1963.pdf.

## External links

* (PDF) "A Mathematical Theory of Communication" by C. E. Shannon (reprint with corrections) hosted by the Harvard Mathematics Department, at Harvard University
* Original publications:  (in en) The Bell System Technical Journal 1948-07: Vol 27 Iss 3. AT & T Bell Laboratories. 1948-07-01. pp. 379–423. https://archive.org/details/sim_att-technical-journal_1948-07_27_3/page/n2/. ,  (in en) The Bell System Technical Journal 1948-10: Vol 27 Iss 4. AT & T Bell Laboratories. 1948-10-01. pp. 623–656. https://archive.org/details/sim_att-technical-journal_1948-10_27_4/page/623/.
* Khan Academy video about "A Mathematical Theory of Communication"

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