Entropy rate calculations of algebraic measures

摘要

Let K = {0, 1, …, q − 1}. We use a special class of translation invariant measures on K^Z called algebraic measures to study the entropy rate of a hidden Markov processes. We derive exact formulas for the entropy rate of a q state hidden Markov process derived from a specific noise model and show that the formula converges exponentially fast to the entropy rate.