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We can observe that as n goes to infinity, if <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====
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