Noisy-channel coding theorem: Difference between revisions

Revision as of 20:15, 8 May 2021

Revision as of 08:56, 1 July 2021

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#<math>\le 1 + P_e^{(n)}nR + nC</math> by the fact that capacity is maximized mutual information.

The result of these steps is that <math> P_e^{(n)} \ge 1 - \frac{1}{nR} - \frac{C}{R} </math>. As the block length <math>n</math> goes to infinity, we obtain <math> P_e^{(n)}</math> is bounded away from 010 if R is greater than C - we can get arbitrarily low rates of error only if R is less than C.

=== Strong converse for discrete memoryless channels ===