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

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

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

6 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publicationProceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1646-1650
Number of pages5
ISBN (Electronic)9781509018062
DOIs
StatePublished - Aug 10 2016
Externally publishedYes
Event2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain
Duration: Jul 10 2016Jul 15 2016

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2016-August
ISSN (Print)2157-8095

Other

Other2016 IEEE International Symposium on Information Theory, ISIT 2016
CountrySpain
CityBarcelona
Period7/10/167/15/16

All Science Journal Classification (ASJC) codes

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

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    Dytso, A., Bustin, R., Tuninetti, D., Devroye, N., Poor, H. V., & Shitz, S. S. (2016). On the minimum mean p-th error in Gaussian noise channels and its applications. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory (pp. 1646-1650). [7541578] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2016.7541578