TY - GEN

T1 - On communications through a Gaussian noise channel with an MMSE disturbance constraint

AU - Dytso, Alex

AU - Bustin, Ronit

AU - Tuninetti, Daniela

AU - Devroye, Natasha

AU - Poor, H. Vincent

AU - Shamai, Shlomo

N1 - Funding Information:
The work of Alex Dytso, Daniela Tuninetti and Natasha Devroye was partially funded by NSF under award 1422511. The work of Ronit Bustin was supported in part by the Women Postdoctoral Sholarship of Israel's Council for Higher Education (VATAT) 2014-2015. The work of H. Vincent Poor and Ronit Bustin was partially supported by NSF under awards CCF-1420575 and ECCS-1343210. The work of Shlomo Shamai was supported by the Israel Science Foundation and the S. and N. Grand Research Fund. The contents of this article are solely the responsibility of the authors and do not necessarily represent the official views of the funding agencies.
Publisher Copyright:
© 2016 IEEE.

PY - 2017/3/27

Y1 - 2017/3/27

N2 - 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.

AB - 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.

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U2 - 10.1109/ITA.2016.7888177

DO - 10.1109/ITA.2016.7888177

M3 - Conference contribution

AN - SCOPUS:84985952678

T3 - 2016 Information Theory and Applications Workshop, ITA 2016

BT - 2016 Information Theory and Applications Workshop, ITA 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2016 Information Theory and Applications Workshop, ITA 2016

Y2 - 31 January 2016 through 5 February 2016

ER -