On Linear Model with Markov Signal Priors

In this paper, we estimate free energy, average mutual information, and minimum mean square error (MMSE) of a linear model under the assumption that the source is generated by a Markov chain. Our estimates are based on the replica method in statistical physics. We show that under the MMSE estimator, the linear model with Markov sources or hidden Markov sources is decoupled into single input AWGN channels with state information available at both encoder and decoderwhere the state distribution follows the stationary distribution of the stochastic matrix of Markov chains. Numerical results show that the free energies and MSEs obtained via the replica method are closely approximate to their counterparts via MCMC simulations.