Analyticity of Entropy Rate of Continuous-State Hidden Markov Chains

Abstract

We prove that under certain mild assumptions, the entropy rate of a hidden Markov chain, observed when passing a finite-state stationary Markov chain through a discrete-time continuous-output channel, is jointly analytic as a function of the input Markov chain parameters and the channel parameters. In particular, as consequences of the main theorems, we obtain analyticity for the entropy rate associated with representative channels: Cauchy and Gaussian.

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References in corpus (1)

• Asymptotics of input-constrained binary symmetric channel capacity