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The paper proposes Monte Carlo algorithms for the computation of theinformation rate of two-dimensional source/channel models. The focus of thepaper is on binary-input channels with constraints on the allowed inputconfigurations. The problem of numerically computing the information rate, andeven the noiseless capacity, of such channels has so far remained largelyunsolved. Both problems can be reduced to computing a Monte Carlo estimate of apartition function. The proposed algorithms use tree-based Gibbs sampling andmultilayer (multitemperature) importance sampling. The viability of theproposed algorithms is demonstrated by simulation results.

Monte Carlo Algorithms for the Partition Function and Information Rates of Two-Dimensional Channels