Capacity Theorems for the AWGN Multi-Way Relay Channel

TL;DR

This paper establishes capacity theorems for the L-user AWGN multi-way relay channel, showing that a new functional-decode-forward strategy achieves capacity at high SNR for multiple users, improving upon existing methods.

Contribution

It introduces a functional-decode-forward coding strategy that achieves the capacity of the multi-way relay channel at high SNR, extending the understanding of optimal communication strategies.

Findings

Functional-decode-forward achieves capacity for L >= 3 at high SNR.

Complete-decode-forward is optimal at low SNR (<= 0 dB).

The proposed strategy asymptotically achieves capacity as SNR increases.

Abstract

The L-user additive white Gaussian noise multi-way relay channel is considered, where multiple users exchange information through a single relay at a common rate. Existing coding strategies, i.e., complete-decode-forward and compress-forward are shown to be bounded away from the cut-set upper bound at high signal-to-noise ratios (SNR). It is known that the gap between the compress-forward rate and the capacity upper bound is a constant at high SNR, and that between the complete-decode-forward rate and the upper bound increases with SNR at high SNR. In this paper, a functional-decode-forward coding strategy is proposed. It is shown that for L >= 3, complete-decode-forward achieves the capacity when SNR <= 0 dB, and functional-decode-forward achieves the capacity when SNR >= 0 dB. For L=$, functional-decode-forward achieves the capacity asymptotically as SNR increases.