Entropy Rate for Hidden Markov Chains with rare transitions

TL;DR

This paper analyzes the entropy of Hidden Markov Chains derived from Markov Chains with rare transitions, passing through noisy channels, providing asymptotic estimates as transition rates approach zero.

Contribution

It introduces asymptotic estimates for the entropy of Hidden Markov Chains with rare transitions, advancing understanding of their informational properties.

Findings

Asymptotic entropy estimates as transition rates tend to zero

Characterization of entropy behavior in noisy channels

Insights into information loss in rare transition regimes

Abstract

We consider Hidden Markov Chains obtained by passing a Markov Chain with rare transitions through a noisy memoryless channel. We obtain asymptotic estimates for the entropy of the resulting Hidden Markov Chain as the transition rate is reduced to zero.