论文标题
用马尔可夫或隐藏的马尔可夫信号先验对线性模型进行副本分析
Replica Analysis of the Linear Model with Markov or Hidden Markov Signal Priors
论文作者
论文摘要
本文估算了两个假设下的线性模型的自由能，平均共同信息和最小平方误差（MMSE）：（1）源是由马尔可夫链生成的，（2）源是通过隐藏的马尔可夫模型生成的。我们的估计基于统计物理学的副本方法。我们表明，在后平均值估计器下，带有马尔可夫源或隐藏的马尔可夫源的线性模型将其脱离到单输入AWGN通道中，并在编码器和解码器上可获得的状态信息，其中状态分布遵循Markov Chains of Markov Chains of Markov Chains的左Perron-Ferron-Frobenius Eigenius eigenius eigenius eigenius eigenius eigenius eigenius v。数值结果表明，通过复制方法获得的自由能和MSE与大都市杂货算法或一些众所周知的近似消息传递研究文献中的算法相近。
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.
