A Multiway Relay Channel with Balanced Sources

TL;DR

This paper investigates the joint source-channel coding problem for finite-field multiway relay channels, providing bounds, conditions for optimality, and characterizations for a class of sources, with applications to storage.

Contribution

It introduces tight bounds and optimality conditions for a class of sources in multiway relay channels, and characterizes this class using mutual information measures.

Findings

Bounds are tight for all sources in class $ ext{P}^*$

Strict source-channel separation is optimal within $ ext{P}^*$

$ ext{P}^*$ is characterized by conditional mutual information

Abstract

We consider a joint source-channel coding problem on a finite-field multiway relay channel, and we give closed-form lower and upper bounds on the optimal source-channel rate. These bounds are shown to be tight for all discrete memoryless sources in a certain class $\mathcal{P}^*$, and we demonstrate that strict source-channel separation is optimal within this class. We show how to test whether a given source belongs to $\mathcal{P}^*$, we give a balanced-information regularity condition for $\mathcal{P}^*$, and we express $\mathcal{P}^*$ in terms of conditional multiple-mutual informations. Finally, we show that $\mathcal{P}^*$ is useful for a centralised storage problem.