On entropy-constrained Gaussian channel capacity via the moment problem

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autores principales: Girish, Adway, Shamai, Shlomo, Telatar, Emre
Formato: Preprint
Publicado: 2025
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866908341867905024
author Girish, Adway
Shamai, Shlomo
Telatar, Emre
author_facet Girish, Adway
Shamai, Shlomo
Telatar, Emre
contents We study the capacity of the power-constrained additive Gaussian channel with an entropy constraint at the input. In particular, we characterize this capacity in the low signal-to-noise ratio regime at small entropy. This follows as a corollary of the following general result on a moment matching problem: We show that for any continuous random variable with finite moments, the largest number of initial moments that can be matched by a discrete random variable of sufficiently small but positive entropy is three.
format Preprint
id arxiv_https___arxiv_org_abs_2501_13814
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On entropy-constrained Gaussian channel capacity via the moment problem
Girish, Adway
Shamai, Shlomo
Telatar, Emre
Information Theory
Probability
We study the capacity of the power-constrained additive Gaussian channel with an entropy constraint at the input. In particular, we characterize this capacity in the low signal-to-noise ratio regime at small entropy. This follows as a corollary of the following general result on a moment matching problem: We show that for any continuous random variable with finite moments, the largest number of initial moments that can be matched by a discrete random variable of sufficiently small but positive entropy is three.
title On entropy-constrained Gaussian channel capacity via the moment problem
topic Information Theory
Probability
url https://arxiv.org/abs/2501.13814