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

TL;DR

This paper analyzes the three-user finite field multi-way relay channel with correlated sources, deriving achievable rates using Slepian-Wolf coding and functional-decode-forward strategies for reliable communication.

Contribution

It extends the understanding of multi-way relay channels by characterizing achievable rates with correlated sources and finite field adder channels.

Findings

Achievable rate regions are derived for specific source/channel classes.

Slepian-Wolf source coding combined with functional-decode-forward is effective.

The results generalize previous work to correlated sources and noisy channels.

Abstract

The three-user finite field multi-way relay channel with correlated sources is considered. The three users generate possibly correlated messages, and each user is to transmit its message to the two other users reliably in the Shannon sense. As there is no direct link among the users, communication is carried out via a relay, and the link from the users to the relay and those from the relay to the users are finite field adder channels with additive noise of arbitrary distribution. The problem is to determine the set of all possible achievable rates, defined as channel uses per source symbol for reliable communication. For two classes of source/channel combinations, the solution is obtained using Slepian-Wolf source coding combined with functional-decode-forward channel coding.