Asymptotics of Noisy Constrained Channel Capacity

In this paper, we generalize a result by E. Ordentlich and T. Weissman. (2004) and derive an asymptotic formula for the entropy rate of a hidden Markov chain, observed when a Markov chain passes through a binary symmetric channel. And we prove an asymptotic formula for the capacity of a binary symmetric channel with input process supported on an irreducible finite type constraint.