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Publication# Coding Along Hermite Polynomials for Gaussian Noise Channels

2009

Conference paper

Conference paper

Abstract

This paper shows that the capacity achieving input distribution for a fading Gaussian broadcast channel is not Gaussian in general. The construction of non-Gaussian distributions that strictly outperform Gaussian ones, for certain characterized fading distributions, is provided. The ability of analyzing non-Gaussian input distributions with closed form expressions is made possible in a local setting. It is shown that there exists a specific coordinate system, based on Hermite polynomials, which parametrizes Gaussian neighborhoods and which is particularly suitable to study the entropic operators encountered with Gaussian noise.

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