On communications through a Gaussian noise channel with an MMSE disturbance constraint

Alex Dytso, Ronit Bustin, Daniela Tuninetti, Natasha Devroye, H. Vincent Poor, Shlomo Shamai

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

3 Scopus citations

Abstract

This paper considers a Gaussian channel with one transmitter and two receivers. The goal is to maximize the communication rate at the intended/primary receiver subject to a disturbance constraint at the unintended/secondary receiver. The disturbance is measured in terms of minimum mean square error (MMSE) of the interference that the transmission to the primary receiver inflicts on the secondary receiver. The paper presents a new upper bound for the problem of maximizing the mutual information subject to an MMSE constraint. The new bound holds for vector inputs of any length and recovers a previously known limiting (when the length for vector input tends to infinity) expression from the work of Bustin et al. The key technical novelty is a new upper bound on MMSE. This new bound allows one to bound the MMSE for all signal-to-noise ratio (SNR) values below a certain SNR at which the MMSE is known (which corresponds to the disturbance constraint). This new bound complements the 'single-crossing point property' of the MMSE that upper bounds the MMSE for all SNR values above a certain value at which the MMSE value is known. The new MMSE upper bound provides a refined characterization of the phase-transition phenomenon which manifests, in the limit as the length of the vector input goes to infinity, as a discontinuity of the MMSE for the problem at hand. A matching lower bound, to within an additive gap of order O (log log 1/MMSE) (where MMSE is the disturbance constraint), is shown by means of the mixed inputs recently introduced by Dytso et al.

Original languageEnglish (US)
Title of host publication2016 Information Theory and Applications Workshop, ITA 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781509025299
DOIs
StatePublished - Mar 27 2017
Externally publishedYes
Event2016 Information Theory and Applications Workshop, ITA 2016 - La Jolla, United States
Duration: Jan 31 2016Feb 5 2016

Publication series

Name2016 Information Theory and Applications Workshop, ITA 2016

Other

Other2016 Information Theory and Applications Workshop, ITA 2016
CountryUnited States
CityLa Jolla
Period1/31/162/5/16

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications
  • Artificial Intelligence
  • Information Systems
  • Signal Processing

Fingerprint Dive into the research topics of 'On communications through a Gaussian noise channel with an MMSE disturbance constraint'. Together they form a unique fingerprint.

Cite this