Monotonic decrease of the non-Gaussianness of the sum of independent random variables:: A simple proof

被引：58

作者：

Tulino, Antonia M. ^{[1
]}

Verdu, Sergio

机构：

[1] Univ Naples Federico II, Dept Elect Engn, I-80125 Naples, Italy

[2] Princeton Univ, Dept Elect Engn, Princeton, NJ 08544 USA

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2006年 / 52卷 / 09期

基金：

美国国家科学基金会;

关键词：

central limit theorem; differential entropy; divergence; entropy power inequality; minimum mean-square error (MMSE); non-Gaussianness; relative entropy;

D O I：

10.1109/TIT.2006.880066

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 [计算机科学与技术];

摘要：

Artstein, Ball, Barthe, and Naor have recently shown that the non-Gaussianness (divergence with respect to a Gaussian random variable with identical first and second moments) of the sum of independent and identically distributed (i.i.d.) random variables is monotonically nonincreasing. We give a simplified proof using the relationship between non-Gaussianness and minimum mean-square error (MMSE) in Gaussian channels. As Artstein et at., we also deal with the more general setting of nonidentically distributed random variables.

引用

页码：4295 / 4297

页数：3

共 6 条

[1]

Solution of Shannon's problem on the monotonicity of entropy [J].