Noisy-channel coding theorem: Difference between revisions

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{{redirect|Shannon's theorem|text=Shannon's name is also associated with the [[sampling 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 data (digital [[information]]) nearly error-free up to a computable maximum rate through the channel. This result was presented by [[Claude Shannon]] in 1948 and was based in part on earlier work and ideas of [[Harry Nyquist]] and [[Ralph Hartley]].

The '''Shannon limit''' or '''Shannon capacity''' of a communication channel refers to the maximum [[Code rate|rate]] of error-free data that can theoretically be transferred over the channel if the link is subject to random data transmission errors, for a particular noise level. It was first described by Shannon (1948), and shortly after published in a book by Shannon and [[Warren Weaver]] entitled ''[[The Mathematical Theory of Communication]]'' (1949). This founded the modern discipline of [[information theory]].