“A Mathematical Theory of Communication” is Claude Shannon’s 1948 paper that founded information theory. It appeared in the Bell System Technical Journal in two parts, in the July and October 1948 issues, while Shannon was working at Bell Telephone Laboratories.
The paper recast communication as an exact engineering problem. Shannon set aside the meaning of messages, writing that the “semantic aspects of communication are irrelevant to the engineering problem,” and focused on the task of selecting and reproducing a message chosen from a set of possibilities. From this he built a general model of a source, a channel, and a receiver that applied to any form of signal.
Within that framework the paper introduced the concepts that define the field. It named the bit as the basic unit of information, writing that if base 2 is used “the resulting units may be called binary digits, or more briefly bits, a word suggested by J. W. Tukey.” It defined entropy as the measure of the information produced by a source, and it introduced channel capacity, the greatest rate at which information can be sent reliably over a noisy channel.
The 1948 paper is one of the most influential scientific works of the twentieth century. Its results on compression, capacity, and reliable transmission underlie modern digital communication and storage, and its ideas spread far beyond engineering into fields such as statistics, biology, and computer science.