On the capacity of ergodic channels: A large deviation analysis

The convergence behavior of capacity of ergodic channels is of great importance for the performance analysis of communication systems. This paper presents a fundamental study on the convergence rate of capacity of ergodic channels on the basis of large deviation theory. It can be revealed that both the probability that the information capacity differs from the ergodic capacity by more than δ(δ > 0) and the outage probability of information capacity decrease at a rate which is asymptotic to that of an exponential decaying function in the number of times of channel use N which are proposed in Theorem 1, Property 1 and 2. To verify the theoretical results, a case study of investigating the rate function for a Rayleigh fading channel is presented. The simulations show that the convergence rate of capacity of ergodic channel coincides with the Theorem and Properties. The achievability of capacity under the assumption of finite channel use is discussed as well.