The Entropy of a Binary Hidden Markov Process

Abstract

The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter epsilon. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion coefficients up to second order in epsilon. Using a conjecture we extend the calculation to 11th order and discuss the convergence of the resulting series.

References in corpus (3)

• Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG
• Utilizing hidden Markov processes as a new tool for experimental physics
• Is a multiple excitation of a single atom equivalent to a single excitation of an ensemble of atoms?

Cited by in corpus (16)

• Hidden Markov models for stochastic thermodynamics
• Back-stepping, hidden substeps, and conditional dwell times in molecular motors
• Asymptotics of input-constrained binary symmetric channel capacity
• Taylor series expansions for the entropy rate of Hidden Markov Processes
• When memory pays: Discord in hidden Markov models
• Entropy of Hidden Markov Processes via Cycle Expansion
• On Maximum a Posteriori Estimation of Hidden Markov Processes
• Active Inference for Binary Symmetric Hidden Markov Models
• Statistical Physics Analysis of Maximum a Posteriori Estimation for Multi-channel Hidden Markov Models
• Phase transition for parameter learning of Hidden Markov Models
• Recovering the state sequence of hidden Markov models using mean-field approximations
• Asymptotics of Entropy Rate in Special Families of Hidden Markov Chains
• A Randomized Approach to the Capacity of Finite-State Channels
• Limit Theorems in Hidden Markov Models
• On analytic properties of entropy rate
• The entropy rate of the binary symmetric channel in the rare transitions regime