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 - 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 -