Simulation-Based Estimation of the Partition Function and the Information Rate of Two-Dimensional Models

Monte Carlo methods are considered to compute, first, the partition function of graphical models, and second, the information rate of source/channel models, in both cases for factor graphs with cycles. The convergence of two basic Monte Carlo methods is improved by sampling only a cycle breaking subset of the variables and using exact sum-product computations for the remaining variables. The methods are demonstrated by their application to a two-dimensional Ising model and to a two-dimensional intersymbol interference channel.