On entropy-constrained Gaussian channel capacity via the moment problem

Adway Girish; Shlomo Shamai; Emre Telatar

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arXiv · 2501.13814

On entropy-constrained Gaussian channel capacity via the moment problem

Adway Girish·Shlomo Shamai·Emre Telatar

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Abstract

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.

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Adway Girish, Shlomo Shamai, Emre Telatar. 2025-01-23. On entropy-constrained Gaussian channel capacity via the moment problem. https://arxiv.org/abs/2501.13814

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