  In the paper, the approximate sequence for entropy of some binary hidden
Markov models has been found to have two bound sequences, the low bound
sequence and the upper bound sequence. The error bias of the approximate
sequence is bound by a geometric sequence with a scale factor less than 1 which
decreases quickly to zero. It helps to understand the convergence of entropy
rate of generic hidden Markov models, and it provides a theoretical base for
estimating the entropy rate of some hidden Markov models at any accuracy.
