  We demonstrate an efficient formula to compute the entropy rate $H(\mu)$ of a
hidden Markov process with $q$ output symbols where at least one symbol is
unambiguously 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 hidden
Markov model. We use the algorithm to estimate the entropy rate when the
parameters of the hidden Markov model are unknown.In the case of $q =2$ the
process is the output of the Z-channel and we use this fact to give bounds on
the capacity of the Gilbert channel.
