  The achievable information rate of finite-state input two-dimensional (2-D)
channels with memory is an open problem, which is relevant, e.g., for
inter-symbol-interference (ISI) channels and cellular multiple-access channels.
We propose a method for simulation-based computation of such information rates.
We first draw a connection between the Shannon-theoretic information rate and
the statistical mechanics notion of free energy. Since the free energy of such
systems is intractable, we approximate it using the cluster variation method,
implemented via generalized belief propagation. The derived, fully tractable,
algorithm is shown to provide a practically accurate estimate of the
information rate. In our experimental study we calculate the information rates
of 2-D ISI channels and of hexagonal Wyner cellular networks with binary
inputs, for which formerly only bounds were known.
