Noisy-channel coding theorem: Difference between revisions

Revision as of 21:43, 18 May 2006

Revision as of 21:47, 18 May 2006

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:::<math>\le \epsilon + 2^{-n(I(X;Y)-R-3\epsilon)}</math>

We can observe that as n goes to infinity, as long asif <math>R < I(X;Y)</math> for the channel, the probability of error will go to 0.

Finally, given that the average codebook is shown to be "good" we know that there exists a codebook whose performance is better than the average, and so satisfies our need for arbitrarily low error probability communicating across the noisy channel.

==== Converse for discrete memoryless channels====