Capacity of the Gaussian Relay Channel with Correlated Noises to Within a Constant Gap

TL;DR

This paper demonstrates that the capacity of a Gaussian relay channel with correlated noises can be approximated within a constant gap using a modified noisy network coding strategy, highlighting the effectiveness of this approach over traditional relaying schemes.

Contribution

It introduces a correlation-dependent quantization scheme for noisy network coding that achieves near-capacity performance in correlated noise scenarios.

Findings

Modified noisy network coding achieves within 0.7925 bits of capacity.

Conventional compress-and-forward also achieves near-capacity.

Decode-and-forward and amplify-and-forward can have infinite gap in certain regimes.

Abstract

This paper studies the relaying strategies and the approximate capacity of the classic three-node Gaussian relay channel, but where the noises at the relay and at the destination are correlated. It is shown that the capacity of such a relay channel can be achieved to within a constant gap of $\hf \log_2 3 =0.7925$ bits using a modified version of the noisy network coding strategy, where the quantization level at the relay is set in a correlation dependent way. As a corollary, this result establishes that the conventional compress-and-forward scheme also achieves to within a constant gap to the capacity. In contrast, the decode-and-forward and the single-tap amplify-and-forward relaying strategies can have an infinite gap to capacity in the regime where the noises at the relay and at the destination are highly correlated, and the gain of the relay-to-destination link goes to infinity.