Low and Upper Bound of Approximate Sequence for the Entropy Rate of   Binary Hidden Markov Processes
  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. 
Shuangping Chen, Jun Li, Mi Zhou
cs.IT math.IT