"A Mathematical Theory of Communication" is an article by

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

Claude E. Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of th ...

published in ''

Bell System Technical Journal The ''Bell Labs Technical Journal'' was the in-house scientific journal for scientists of Bell Labs, published yearly by the IEEE society. The journal was originally established as ''The Bell System Technical Journal'' (BSTJ) in New York by the Am ...

'' in 1948. It was renamed ''The Mathematical Theory of Communication'' in the 1949 book of the same name, 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, as it gave rise to the field of

information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...

, with ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Pri ...

'' referring to the paper as the "

Magna Carta (Medieval Latin for "Great Charter"), sometimes spelled Magna Charta, is a royal charter of rights agreed to by King John of England at Runnymede, near Windsor, on 15 June 1215. First drafted by the Archbishop of Canterbury, Cardin ...

of the

Information Age The Information Age is a historical period that began in the mid-20th century. It is characterized by a rapid shift from traditional industries, as established during the Industrial Revolution, to an economy centered on information technology ...

", while the electrical engineer

Robert G. Gallager Robert Gray Gallager (born May 29, 1931) is an American electrical engineer known for his work on information theory and communications networks. Gallager was elected a member of the National Academy of Engineering (NAE) in 1979 for contributi ...

called the paper a "blueprint for the digital era". Historian

James Gleick James Gleick (; born August 1, 1954) is an American author and historian of science whose work has chronicled the cultural impact of modern technology. Recognized for his writing about complex subjects through the techniques of narrative nonficti ...

rated the paper as the most important development of 1948, placing the

transistor A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...

second in the same time period, with Gleick emphasizing that the paper by Shannon was "even more profound and more fundamental" than the transistor. It is also noted that "as did relativity and quantum theory, information theory radically changed the way scientists look at the universe". The paper also formally introduced the term "

bit The bit is the most basic unit of information in computing and digital communication. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as ...

" and serves as its theoretical foundation.

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'' (), which was published as a

paperback A paperback (softcover, softback) book is one with a thick paper or paperboard cover, also known as wrappers, and often held together with adhesive, glue rather than stitch (textile arts), stitches or Staple (fastener), staples. In contrast, ...

in 1963 (). The book contains an additional article by

Warren Weaver Warren Weaver (July 17, 1894 – November 24, 1978) was an American scientist, mathematician, and science administrator. He is widely recognized as one of the pioneers of machine translation and as an important figure in creating support for scie ...

, providing an overview of the theory for a more general audience.

This work is known for introducing the concepts of

channel capacity Channel capacity, in electrical engineering, computer science, and information theory, is the theoretical maximum rate at which information can be reliably transmitted over a communication channel. Following the terms of the noisy-channel coding ...

as well as the

noisy channel coding theorem In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete ...

. 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 A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing, information theory and biology. In ...

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 In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential states or possible outcomes. This measures the expected amount of information needed ...

, redundancy and the

source coding theorem In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for data whose source is an independent identically-distributed random variable, and the opera ...

, and introduced the term

(which Shannon credited to

John Tukey John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distributi ...

) as a unit of information. It was also in this paper that the

Shannon–Fano coding In the field of data compression, Shannon–Fano coding, named after Claude Shannon and Robert Fano, is one of two related techniques for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured). * Shann ...

technique was proposed – a technique developed in conjunction with

Robert Fano Roberto Mario "Robert" Fano (11 November 1917 – 13 July 2016) was an Italian-American computer scientist and professor of electrical engineering and computer science at the Massachusetts Institute of Technology. He became a student and working ...

References

External links

(PDF) "A Mathematical Theory of Communication" by C. E. Shannon
(reprint with corrections) hosted by th
Harvard Mathematics Department
at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

** Original publications: ,
Khan Academy video about "A Mathematical Theory of Communication"
{{DEFAULTSORT:Mathematical Theory of Communication 1963 non-fiction books Information theory Computer science books Mathematics books Mathematics papers Works originally published in American magazines 1948 documents Works originally published in science and technology magazines Texts related to the history of the Internet Claude Shannon

Publication

Contents

References

External links