From finite-system entropy to entropy rate for a Hidden Markov Process

Abstract

A recent result presented the expansion for the entropy rate of a Hidden Markov Process (HMP) as a power series in the noise variable $\eps$. The coefficients of the expansion around the noiseless ($\eps = 0$) limit were calculated up to 11th order, using a conjecture that relates the entropy rate of a HMP to the entropy of a process of finite length (which is calculated analytically). In this communication we generalize and prove the validity of the conjecture, and discuss the theoretical and practical consequences of our new theorem.

References in corpus (1)

• Taylor series expansions for the entropy rate of Hidden Markov Processes

Cited by in corpus (7)

• Asymptotics of input-constrained binary symmetric channel capacity
• Entropy of Hidden Markov Processes via Cycle Expansion
• Analyticity of Entropy Rate of Continuous-State Hidden Markov Chains
• Entropy rate calculations of algebraic measures
• The entropy rate of the binary symmetric channel in the rare transitions regime
• Asymptotics of Entropy Rate in Special Families of Hidden Markov Chains
• Thermodynamics of the Binary Symmetric Channel