Sharp Variance-Entropy Comparison for Nonnegative Gaussian Quadratic Forms

被引:4
作者
Bartczak, Maciej [1 ]
Nayar, Piotr [1 ]
Zwara, Szymon [1 ]
机构
[1] Univ Warsaw, Fac Math Informat & Mech, PL-02097 Warsaw, Poland
关键词
Entropy; Gaussian chaos; quadratic form; gamma distribution; exponential random variables; channel capacity; INEQUALITY; PROBABILITIES; MOMENTS;
D O I
10.1109/TIT.2021.3113281
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this article we study weighted sums of n i.i.d. Gamma(alpha) random variables with nonnegative weights. We show that for n >= 1/alpha the sum with equal coefficients maximizes differential entropy when variance is fixed. As a consequence, we prove that among nonnegative quadratic forms in n independent standard Gaussian random variables, a diagonal form with equal coefficients maximizes differential entropy, under a fixed variance. This provides a sharp lower bound for the relative entropy between a nonnegative quadratic form and a Gaussian random variable. Bounds on capacities of transmission channels subjects to n independent additive gamma noises are also derived.
引用
收藏
页码:7740 / 7751
页数:12
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