Noisy-channel coding theorem: Difference between revisions

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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)} \lege 1 - \frac{1}{nR} - \frac{C}{R} </math>. As the block length n goes to infinity, we obtain <math> P_e^{(n)}</math> is bounded away from 0 if R is greater than C - we can only get arbitrarily low rates of error if R is less than C.
 
== Channel coding theorem for non-stationary memoryless channels==