The Finite Field Multi-Way Relay Channel with Correlated Sources: Beyond Three Users

TL;DR

This paper extends the analysis of finite field multi-way relay channels with correlated sources from three users to more, establishing conditions under which achievable rates can be characterized and attained.

Contribution

It generalizes the ABCMI condition for more than three users and proves that achievable rates can be found and achieved with separate source-channel coding.

Findings

Achievable rates can be characterized for multi-user MWRC with correlated sources.

The generalized ABCMI condition applies to more than three users.

Separate source-channel coding attains the achievable rates under the ABCMI condition.

Abstract

The multi-way relay channel (MWRC) models cooperative communication networks in which many users exchange messages via a relay. In this paper, we consider the finite field MWRC with correlated messages. The problem is to find all achievable rates, defined as the number of channel uses required per reliable exchange of message tuple. For the case of three users, we have previously established that for a special class of source distributions, the set of all achievable rates can be found [Ong et al., ISIT 2010]. The class is specified by an almost balanced conditional mutual information (ABCMI) condition. In this paper, we first generalize the ABCMI condition to the case of more than three users. We then show that if the sources satisfy the ABCMI condition, then the set of all achievable rates is found and can be attained using a separate source-channel coding architecture.