The Gaussian Interference Relay Channel: Improved Achievable Rates and Sum Rate Upperbounds Using a Potent Relay

TL;DR

This paper advances the understanding of the Gaussian interference relay channel by proposing improved achievable strategies and upper bounds, especially with a potent relay, leading to tighter capacity estimates and insights into degrees of freedom.

Contribution

It introduces a generalized compress-and-forward strategy, a nested lattice compute-and-forward scheme, and a novel potent relay upper bound, enhancing capacity analysis of the GIFRC.

Findings

Generalized compress-and-forward improves achievable rates.

Nested lattice compute-and-forward outperforms other relaying schemes with weak direct links.

Sum capacity bounds are tighter with the potent relay model, matching known sum rates in many cases.

Abstract

We consider the Gaussian interference channel with an intermediate relay as a main building block for cooperative interference networks. On the achievability side, we consider compress-and-forward based strategies. Specifically, a generalized compress-and-forward strategy, where the destinations jointly decode the compression indices and the source messages, is shown to improve upon the compress-and-forward strategy which sequentially decodes the compression indices and source messages, and the recently proposed generalized hash-and-forward strategy. We also construct a nested lattice code based compute-and-forward relaying scheme, which outperforms other relaying schemes when the direct link is weak. In this case, it is shown that, with a relay, the interference link can be useful for decoding the source messages. Noting the need for upperbounding the capacity for this channel, we propose a new technique with which the sum rate can be bounded. In particular, the sum capacity is upperbounded by considering the channel when the relay node has abundant power and is named potent for that reason. For the Gaussian interference relay channel with potent relay, we study the strong and the weak interference regimes and establish the sum capacity, which, in turn, serve as upperbounds for the sum capacity of the GIFRC with finite relay power. Numerical results demonstrate that upperbounds are tighter than the cut-set bound, and coincide with known achievable sum rates for many scenarios of interest. Additionally, the degrees of freedom of the GIFRC are shown to be 2 when the relay has large power, achievable using compress-and-forward.