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

TL;DR

This paper introduces Monte Carlo algorithms utilizing Gibbs sampling and importance sampling to estimate the information rates and capacities of two-dimensional channels with input constraints, addressing previously unsolved computational challenges.

Contribution

The paper presents novel Monte Carlo algorithms specifically designed for calculating the information rate and capacity of constrained two-dimensional channels, a problem largely unsolved before.

Findings

Algorithms effectively estimate partition functions for 2D channels

Simulation results demonstrate the algorithms' viability

Approach advances computational methods for information theory

Abstract

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