Optimal Coding Functions for Pairwise Message Sharing on Finite-Field Multi-Way Relay Channels

TL;DR

This paper develops an optimal coding scheme for finite-field multi-way relay channels with pairwise message sharing, achieving capacity and generalizing previous results to any number of users.

Contribution

It introduces a new optimal function-decode-forward coding scheme that accounts for shared messages and proves it achieves the channel's capacity for any number of users.

Findings

Proposed an optimal coding scheme for pairwise message sharing.

Achieved the capacity region of the finite-field multi-way relay channel.

Generalized previous three-user results to any number of users.

Abstract

This paper considers the finite-field multi-way relay channel with pairwise message sharing, where multiple users exchange messages through a single relay and where the users may share parts of their source messages (meaning that some message parts are known/common to more than one user). In this paper, we design an optimal functional-decode-forward coding scheme that takes the shared messages into account. More specifically, we design an optimal function for the relay to decode (from the users on the uplink) and forward (back to the users on the downlink). We then show that this proposed function-decode-forward coding scheme can achieve the capacity region of the finite-field multi-way relay channel with pairwise message sharing. This paper generalizes our previous result for the case of three users to any number of users.