Noisy-channel coding theorem: Difference between revisions

Revision as of 15:55, 2 March 2020

Revision as of 03:01, 3 March 2020

Line 10:

== Overview ==

Stated by [[Claude Shannon]] in 1948, the theorem describes the maximum possible efficiency of [[error-correcting code|error-correcting methods]] versus levels of noise interference and data corruption. Shannon's theorem has wide-ranging applications in both communications and [[data storage device|data storage]]. This theorem is of foundational importance to the modern field of [[information theory]]. Shannon only gave an outline of the proof. The first rigorous proof for the discrete case is due to [[Amiel Feinstein]]<ref>{{Cite journal|date=1954|others=Feinstein, Amiel.|title=A new basic theorem of information theory|urlhdl=https://dspace.mit.edu/handle/1721.1/4798|bibcode=1955PhDT........12F}}</ref> in 1954.

The Shannon theorem states that given a noisy channel with [[channel capacity]] ''C'' and information transmitted at a rate ''R'', then if <math>R < C</math> there exist [[code]]s that allow the [[probability of error]] at the receiver to be made arbitrarily small. This means that, theoretically, it is possible to transmit information nearly without error at any rate below a limiting rate, ''C''.