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

Mohammad Mahdi Mahvari; Gerhard Kramer

doi:10.1109/TIT.2023.3293311

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

Mohammad Mahdi Mahvari
, Gerhard Kramer

Chair of Communications Engineering

Technical University of Munich

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	6231-6250
Number of pages	20
Journal	IEEE Transactions on Information Theory
Volume	69
Issue number	10
DOIs	https://doi.org/10.1109/TIT.2023.3293311
State	Published - 1 Oct 2023

Keywords

Additive Gaussian noise
Bernstein's theorem
random vectors
stability
statistical independence

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10.1109/TIT.2023.3293311

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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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AU - Kramer, Gerhard

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AB - 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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KW - random vectors

KW - stability

KW - statistical independence

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

Abstract

Keywords

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