Relay Strategies Based on Cross-Determinism for the Broadcast Relay Channel

TL;DR

This paper introduces a novel relay strategy based on cross-determinism for the Gaussian MIMO broadcast relay channel, achieving near-optimal sum capacity through advanced coding, beamforming, and quantization techniques.

Contribution

It proposes an asymptotically optimal quantize-and-forward relay strategy leveraging cross-determinism, and extends achievable rate regions using a three-stage dirty paper coding approach.

Findings

The proposed QF relay strategy is asymptotically sum-capacity-achieving.

Cross-determinism effectively measures quantization penalty.

The approach extends the achievable rate region for the MIMO broadcast relay channel.

Abstract

We consider a two-user Gaussian multiple-input multiple-output (MIMO) broadcast channel with a common multiple-antenna relay, and a shared digital (noiseless) link between the relay and the two destinations. For this channel, this paper introduces an asymptotically sum-capacity-achieving quantize-and-forward (QF) relay strategy. Our technique to design an asymptotically optimal relay quantizer is based on identifying a cross-deterministic relation between the relay observation, the source signal, and the destination observation. In a relay channel, an approximate cross deterministic relation corresponds to an approximately deterministic relation, where the relay observation is to some extent a deterministic function of the source and destination signals. We show that cross determinism can serve as a measure for quantization penalty. By identifying an analogy between a deterministic broadcast relay channel and a Gaussian MIMO relay channel, we propose a three-stage dirty paper coding strategy, along with receiver beamforming and quantization at the relay, to asymptotically achieve an extended achievable rate region for the MIMO broadcast channel with a common multiple-antenna relay.