Capacity of the Gaussian Two-Pair Two-Way Relay Channel to Within 1/2 Bit

TL;DR

This paper demonstrates that the capacity of the Gaussian two-pair two-way relay channel can be approached within 1/2 bit using a hybrid coding scheme and strategic power allocation, regardless of channel conditions.

Contribution

It introduces a novel hybrid coding scheme and message-reassembling strategy that achieve near-capacity performance for the Gaussian two-pair TWRC under arbitrary conditions.

Findings

Capacity is achievable within 1/2 bit for all channel conditions.

Hybrid coding scheme effectively combines Gaussian, lattice, and superposition coding.

Power allocation is crucial for approaching channel capacity.

Abstract

This paper studies the transceiver design of the Gaussian two-pair two-way relay channel (TWRC), where two pairs of users exchange information through a common relay in a pairwise manner. Our main contribution is to show that the capacity of the Gaussian two-pair TWRC is achievable to within 1/2 bit for arbitrary channel conditions. In the proof, we develop a hybrid coding scheme involving Gaussian random coding, nested lattice coding, superposition coding, and network-coded decoding. Further, we present a message-reassembling strategy to decouple the coding design for the user-to-relay and relay-to-user links, so as to provide flexibility to fully exploit the channel randomness. Finally, judicious power allocation at the relay is necessary to approach the channel capacity under various channel conditions.