Capacity of the vector Gaussian channel in the small amplitude regime

Alex Dytso, H. Vincent Poor, Shlomo Shamai Shitz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

This paper studies the capacity of an ndimensional vector Gaussian noise channel subject to the constraint that an input must lie in the ball of radius R centered at the origin. It is known that in this setting the optimizing input distribution is supported on a finite number of concentric spheres. However, the number, the positions and the probabilities of the spheres are generally unknown. This paper characterizes necessary and sufficient conditions on the constraint R such that the input distribution supported on a single sphere is optimal. The maximum R ¯ n, such that using only a single sphere is optimal, is shown to be a solution of an integral equation. Moreover, it is shown that R ¯ n scales as √n and the exact limit of √R ¯n/ √n is found.

Original languageEnglish (US)
Title of host publication2018 IEEE Information Theory Workshop, ITW 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781538635995
DOIs
StatePublished - Jan 15 2019
Event2018 IEEE Information Theory Workshop, ITW 2018 - Guangzhou, China
Duration: Nov 25 2018Nov 29 2018

Publication series

Name2018 IEEE Information Theory Workshop, ITW 2018

Conference

Conference2018 IEEE Information Theory Workshop, ITW 2018
CountryChina
CityGuangzhou
Period11/25/1811/29/18

All Science Journal Classification (ASJC) codes

  • Information Systems

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    Dytso, A., Poor, H. V., & Shitz, S. S. (2019). Capacity of the vector Gaussian channel in the small amplitude regime. In 2018 IEEE Information Theory Workshop, ITW 2018 [8613508] (2018 IEEE Information Theory Workshop, ITW 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITW.2018.8613508