Improved computational efficiency in derivation of capacity regions in network information theory

Abstract

Derivation and description of capacity, or achievable rate regions in network information theory often involves auxiliary random variables. Unless the cardinalities of these random variables are bounded, the capacity region remains uncomputable, that is, there does not exist an algorithm that can compute the capacity region with a prescribed degree of accuracy. Reducing the cardinalities of these auxiliary random variables results in a major reduction in the amount of computation required to derive the capacity regions. In this paper we present improved upper bounds on the cardinality of the auxiliary random variables encountered in network information theory. Using these new bounds results in a reduction in the dimensionality of the space over which the optimization is performed and therefore considerably decreases the amount of computation required to describe the capacity region within a given accuracy.