A Coordinate System for Gaussian Networks

TL;DR

This paper introduces a geometric coordinate system using Hermite polynomials to analyze non-Gaussian input distributions in Gaussian networks, revealing that non-Gaussian codes can outperform Gaussian ones and challenging existing conjectures.

Contribution

It proposes a novel Hermite polynomial-based coordinate system for analyzing non-Gaussian codes in Gaussian networks, advancing understanding of their potential advantages.

Findings

Non-Gaussian codes can achieve higher rates than Gaussian codes in certain Gaussian networks.

The strong Shamai-Laroia conjecture on the Gaussian ISI channel does not hold.

A new geometric tool for analyzing non-Gaussian distributions in Gaussian channels is introduced.

Abstract

This paper studies network information theory problems where the external noise is Gaussian distributed. In particular, the Gaussian broadcast channel with coherent fading and the Gaussian interference channel are investigated. It is shown that in these problems, non-Gaussian code ensembles can achieve higher rates than the Gaussian ones. It is also shown that the strong Shamai-Laroia conjecture on the Gaussian ISI channel does not hold. In order to analyze non-Gaussian code ensembles over Gaussian networks, a geometrical tool using the Hermite polynomials is proposed. This tool provides a coordinate system to analyze a class of non-Gaussian input distributions that are invariant over Gaussian networks.