Stability of Bernstein's Theorem and Soft Doubling for Vector Gaussian Channels

Mohammad Mahdi Mahvari; Gerhard Kramer

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arXiv · 2212.04484

Stability of Bernstein's Theorem and Soft Doubling for Vector Gaussian Channels

Mohammad Mahdi Mahvari·Gerhard Kramer

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Abstract

The stability of Bernstein's characterization of Gaussian distributions is extended to vectors by utilizing characteristic functions. Stability is used to develop a soft doubling argument that establishes the optimality of Gaussian vectors for certain communications channels with additive Gaussian noise, including two-receiver broadcast channels. One novelty is that the argument does not require the existence of distributions that achieve capacity.

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Mohammad Mahdi Mahvari, Gerhard Kramer. 2022-12-08. Stability of Bernstein's Theorem and Soft Doubling for Vector Gaussian Channels. https://arxiv.org/abs/2212.04484

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