Information theory in random fields

Abstract

A random field is a family of random variables with a multidimensional parameter set. Random fields provide mathematical models for distributed sources of information. Channels that link an input and an output random field also are of interest.

First, we describe in detail a celebrated result of random field theory to the effect that a random field has the Markov property if and only if it is a Gibbs state with a nearest neighbor potential. Next we lower bound the zero-error capacity of a certain binary random field channel by developing an efficient zero-error coding scheme. Finally, we consider algorithms for computing the stationary distribution of a time evolution mechanism. These algorithms, which have long been employed in mathematical statistical mechanics, also play a central role in simulated annealing.