Noisy-channel coding theorem: Difference between revisions

Revision as of 15:42, 7 March 2020

Revision as of 08:17, 16 March 2020

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

:has the following property. For any <math>\epsilon>0</math> and <math>R<C</math>, for large enough <math>N</math>, there exists a code of length <math>N</math> and rate &ge;<math>\geq ''R''</math> and a decoding algorithm, such that the maximal probability of block error is &le;<math>\leq &\epsilon;</math>.

:2. If a probability of bit error <math>p_b</math> is acceptable, rates up to <math>R(p_b)</math> are achievable, where