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that capacity is maximized mutual information.

The result of these steps is that . As the block length goes to infinity, we obtain is bounded away from 0 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

A strong converse theorem, proven by Wolfowitz in 1957, states that,

:

for some finite positive constant . While the weak converse states that the error probability is bounded away from zero as goes to infinity,

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