On the Achievable Information Rates of Finite-State Input Two-Dimensional Channels with Memory

TL;DR

This paper introduces a simulation-based method to estimate the achievable information rates of finite-state 2-D channels with memory, connecting information theory with statistical mechanics and providing practical algorithms for complex channel models.

Contribution

It proposes a novel approach linking Shannon information rates with free energy concepts and uses generalized belief propagation for tractable approximation, enabling accurate rate estimation.

Findings

Accurately estimates information rates of 2-D ISI channels

Calculates rates for hexagonal cellular networks with binary inputs

Provides bounds previously unavailable for these channels

Abstract

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.