An Upper Bound on the Number of Mass Points in the Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel

Semih Yagli, Alex Dytso, H. Vincent Poor, Shlomo Shamai Shitz

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

Abstract

This paper studies an n-dimensional additive Gaussian noise channel with a peak-power-constrained input. It is well known that, in this case, the capacity-achieving input distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of shells of the optimal input distribution nor a bound on it was available.This paper provides an alternative proof of the finiteness of the number shells of the capacity-achieving input distribution and produces the first firm upper bound on the number of shells, paving an alternative way for approaching many such problems. In particular, for every dimension n, it is shown that the number of shells is given by O(A2) where A is the constraint on the input amplitude. Moreover, this paper also provides bounds on the number of points for the case of n = 1 with an additional power constraint.

Original languageEnglish (US)
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1907-1911
Number of pages5
ISBN (Electronic)9781538692912
DOIs
StatePublished - Jul 2019
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: Jul 7 2019Jul 12 2019

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
CountryFrance
CityParis
Period7/7/197/12/19

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

Fingerprint Dive into the research topics of 'An Upper Bound on the Number of Mass Points in the Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel'. Together they form a unique fingerprint.

  • Cite this

    Yagli, S., Dytso, A., Poor, H. V., & Shamai Shitz, S. (2019). An Upper Bound on the Number of Mass Points in the Capacity Achieving Distribution for the Amplitude Constrained Additive Gaussian Channel. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 1907-1911). [8849318] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849318