Truong, Lan V (2023) Replica Analysis of the Linear Model with Markov or Hidden Markov Signal Priors. IEEE Transactions on Information Theory, 69 (12). pp. 7953-7975. DOI https://doi.org/10.1109/tit.2023.3299490
Truong, Lan V (2023) Replica Analysis of the Linear Model with Markov or Hidden Markov Signal Priors. IEEE Transactions on Information Theory, 69 (12). pp. 7953-7975. DOI https://doi.org/10.1109/tit.2023.3299490
Truong, Lan V (2023) Replica Analysis of the Linear Model with Markov or Hidden Markov Signal Priors. IEEE Transactions on Information Theory, 69 (12). pp. 7953-7975. DOI https://doi.org/10.1109/tit.2023.3299490
Abstract
This paper estimates free energy, average mutual information, and minimum mean square error (MMSE) of a linear model under two assumptions: (1) the source is generated by a Markov chain, (2) the source is generated via a hidden Markov model. Our estimates are based on the replica method in statistical physics. We show that under the posterior mean 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 decoder where the state distribution follows the left Perron-Frobenius eigenvector with unit Manhattan norm 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 achieved by the Metropolis–Hastings algorithm or some well-known approximate message passing algorithms in the research literature.
Item Type: | Article |
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Uncontrolled Keywords: | Compressed sensing; Free energy; Hidden Markov model; Linear model; Linear regression; Markov chain; Maximum a posteriori estimation; Minimum mean square error; Replica method; Statistical Physics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 19 Sep 2023 16:09 |
Last Modified: | 03 Feb 2024 23:28 |
URI: | http://repository.essex.ac.uk/id/eprint/36352 |
Available files
Filename: Replica_Markov_Final.pdf