TY - GEN

T1 - On the minimum mean p-th error in Gaussian noise channels and its applications

AU - Dytso, Alex

AU - Bustin, Ronit

AU - Tuninetti, Daniela

AU - Devroye, Natasha

AU - Poor, H. Vincent

AU - Shitz, Shlomo Shamai

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 scholarship 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 (ISF). 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 - 2016/8/10

Y1 - 2016/8/10

N2 - The problem of estimating an arbitrary random variable from its observation corrupted by additive white Gaussian noise, where the cost function is taken to be the minimum mean p-th error (MMPE), is considered. The classical minimum mean square error (MMSE) is a special case of the MMPE. Several bounds and properties of the MMPE are derived and discussed. As applications of the new MMPE bounds, this paper presents: (a) a new upper bound for the MMSE that complements the 'single-crossing point property' for all SNR values below a certain value at which the MMSE is known, (b) an improved characterization of the phase-transition phenomenon which manifests, in the limit as the length of the capacity achieving code goes to infinity, as a discontinuity of the MMSE, and (c) new bounds on the second derivative of mutual information, or the first derivative of MMSE, that tighten previously known bounds.

AB - The problem of estimating an arbitrary random variable from its observation corrupted by additive white Gaussian noise, where the cost function is taken to be the minimum mean p-th error (MMPE), is considered. The classical minimum mean square error (MMSE) is a special case of the MMPE. Several bounds and properties of the MMPE are derived and discussed. As applications of the new MMPE bounds, this paper presents: (a) a new upper bound for the MMSE that complements the 'single-crossing point property' for all SNR values below a certain value at which the MMSE is known, (b) an improved characterization of the phase-transition phenomenon which manifests, in the limit as the length of the capacity achieving code goes to infinity, as a discontinuity of the MMSE, and (c) new bounds on the second derivative of mutual information, or the first derivative of MMSE, that tighten previously known bounds.

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U2 - 10.1109/ISIT.2016.7541578

DO - 10.1109/ISIT.2016.7541578

M3 - Conference contribution

AN - SCOPUS:84985991413

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1646

EP - 1650

BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016

Y2 - 10 July 2016 through 15 July 2016

ER -