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We demonstrate an efficient formula to compute the entropy rate $H(\mu)$ of ahidden Markov process with $q$ output symbols where at least one symbol isunambiguously received. Using an approximation to $H(\mu)$ to the first $N$terms we give a $O(Nq^3$) algorithm to compute the entropy rate of the hiddenMarkov model. We use the algorithm to estimate the entropy rate when theparameters of the hidden Markov model are unknown.In the case of $q =2$ theprocess is the output of the Z-channel and we use this fact to give bounds onthe capacity of the Gilbert channel.

An efficient algorithm for the entropy rate of a hidden Markov model with unambiguous symbols