The Three-User Finite-Field Multi-Way Relay Channel with Correlated Sources

TL;DR

This paper investigates the optimal communication rate in a three-user finite-field multi-way relay channel with correlated sources, combining source and channel coding techniques to achieve reliable data exchange.

Contribution

It introduces a new coding scheme for correlated sources where common information equals mutual information, optimizing the source-channel rate.

Findings

Derived minimum source-channel rate for specific source-channel classes

Proposed a new coding scheme for sources with equal common and mutual information

Achieved reliable communication with optimized resource usage

Abstract

This paper studies the three-user finite-field multi-way relay channel, where the users exchange messages via a relay. The messages are arbitrarily correlated, and the finite-field channel is linear and is subject to additive noise of arbitrary distribution. The problem is to determine the minimum achievable source-channel rate, defined as channel uses per source symbol needed for reliable communication. We combine Slepian-Wolf source coding and functional-decode-forward channel coding to obtain the solution for two classes of source and channel combinations. Furthermore, for correlated sources that have their common information equal their mutual information, we propose a new coding scheme to achieve the minimum source-channel rate.