On Noisy Network Coding for a Gaussian Relay Chain Network with Correlated Noises

TL;DR

This paper examines the limitations of noisy network coding in Gaussian relay networks with correlated noises, showing it cannot always achieve near-capacity and proposing a combined strategy for better performance.

Contribution

It demonstrates the failure of noisy network coding to achieve constant-gap capacity in correlated noise scenarios and introduces a hybrid approach for improved bounds.

Findings

Noisy network coding fails to achieve constant-gap capacity with correlated noises.

A hybrid correlation-aware strategy can approach the cut-set bound within half a bit.

Correlated noise impacts the effectiveness of traditional noisy network coding methods.

Abstract

Noisy network coding, which elegantly combines the conventional compress-and-forward relaying strategy and ideas from network coding, has recently drawn much attention for its simplicity and optimality in achieving to within constant gap of the capacity of the multisource multicast Gaussian network. The constant-gap result, however, applies only to Gaussian relay networks with independent noises. This paper investigates the application of noisy network coding to networks with correlated noises. By focusing on a four-node Gaussian relay chain network with a particular noise correlation structure, it is shown that noisy network coding can no longer achieve to within constant gap to capacity with the choice of Gaussian inputs and Gaussian quantization. The cut-set bound of the relay chain network in this particular case, however, can be achieved to within half a bit by a simple concatenation of a correlation-aware noisy network coding strategy and a decode-and-forward scheme.