The Capacity Region of Multiway Relay Channels Over Finite Fields with Full Data Exchange

TL;DR

This paper derives the capacity region for multi-way relay channels over finite fields, proposing a functional-decode-forward strategy that achieves capacity without feedback, applicable to various user rate configurations.

Contribution

The paper introduces a capacity-achieving coding strategy for multi-way relay channels over finite fields, extending understanding of optimal communication schemes in such networks.

Findings

Capacity region derived and characterized.

Functional-decode-forward achieves capacity.

Feedback does not increase capacity.

Abstract

The multi-way relay channel is a multicast network where L users exchange data through a relay. In this paper, the capacity region of a class of multi-way relay channels is derived, where the channel inputs and outputs take values over finite fields. The cut-set upper bound to the capacity region is derived and is shown to be achievable by our proposed functional-decode-forward coding strategy. More specifically, for the general case where the users can transmit at possibly different rates, functional-decode-forward, combined with rate splitting and joint source-channel decoding, is proved to achieve the capacity region; while for the case where all users transmit at a common rate, rate splitting and joint source-channel decoding are not required to achieve the capacity. That the capacity-achieving coding strategies do not utilize the users' received signals in the users' encoding functions implies that feedback does not increase the capacity region of this class of multi-way relay channels.