Noisy-channel coding theorem

Information theory
Entropy Differential entropy Conditional entropy Joint entropy Mutual information Directed information Conditional mutual information Relative entropy Entropy rate Limiting density of discrete points
Asymptotic equipartition property Rate–distortion theory
Shannon's source coding theorem Channel capacity Noisy-channel coding theorem Shannon–Hartley theorem
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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 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.