On the Capacity of Networks with Correlated Sources

TL;DR

This paper investigates how well entropy functions can characterize correlations among sources in network capacity problems, proposing the use of auxiliary variables for improved accuracy.

Contribution

It introduces a method using auxiliary random variables to better approximate source correlations via entropy functions.

Findings

Entropy functions can be made more accurate with carefully chosen auxiliary variables.

The approach improves the characterization of source dependencies in network capacity analysis.

Provides a framework for extending linear programming bounds to correlated sources.

Abstract

Characterizing the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterizing all information inequalities. The majority of computable outer bounds in the literature are relaxations of the Linear Programming bound which involves entropy functions of random variables related to the sources and link messages. When sources are not independent, the problem is even more complicated. Extension of linear programming bounds to networks with correlated sources is largely open. Source dependence is usually specified via a joint probability distribution, and one of the main challenges in extending linear programming bounds is the difficulty (or impossibility) of characterizing arbitrary dependencies via entropy functions. This paper tackles the problem by answering the question of how well entropy functions can characterize correlation among sources. We show that by using carefully chosen auxiliary random variables, the characterization can be fairly "accurate".