Entropy rate calculations of algebraic measures

Abstract

Let $K=\{0,1,...,q-1\}$. We use a special class of translation invariant measures on $K^{\mathbb{Z}}$ called algebraic measures to study the entropy rate of a hidden Markov processes. Under some irreducibility assumptions of the Markov transition matrix we derive exact formulas for the entropy rate of a general $q$ state hidden Markov process derived from a Markov source corrupted by a specific noise model. We obtain upper bounds on the error when using an approximation to the formulas and numerically compute the entropy rates of two and three state hidden Markov models.

References in corpus (2)

• From finite-system entropy to entropy rate for a Hidden Markov Process
• Efficient tests for equivalence of hidden Markov processes and quantum random walks