Noisy-channel coding theorem: Difference between revisions

Revision as of 14:22, 17 August 2023

Revision as of 14:23, 17 August 2023

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'''Theorem''' (Shannon, 1948):

: 1. EveryFor every discrete memoryless channel, the [[channel capacity]], defined in terms of the [[mutual information]] <math>I(X; Y)</math> as

:: <math>\ C = \sup_{p_X} I(X;Y)</math><ref>For a description of the "sup" function, see [[Supremum]]</ref>