On the applications of the minimum mean p-th error (MMPE) to information theoretic quantities

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 the minimum mean p-th error (MMPE) estimation problem: estimating a random vector in the presence of additive white Gaussian noise (AWGN) in order to minimize an Lp norm of the estimation error. The MMPE generalizes the classical minimum mean square error (MMSE) estimation problem. This paper derives basic properties of the optimal MMPE estimator and MMPE functional. Optimal estimators are found for several inputs of interests, such as Gaussian and binary symbols. Under an appropriate p-th moment constraint, the Gaussian input is shown to be asymptotically the hardest to estimate for any p ≥ 1. By using a conditional version of the MMPE, the famous 'MMSE single-crossing point' bound is shown to hold for the MMPE too for all p ≥ 1, up to a multiplicative constant. Finally, the paper develops connections between the conditional differential entropy and the MMPE, which leads to a tighter version of the Ozarow-Wyner lower bound on the rate achieved by discrete inputs on AWGN channels.

Original languageEnglish (US)
Title of host publication2016 IEEE Information Theory Workshop, ITW 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages66-70
Number of pages5
ISBN (Electronic)9781509010905
DOIs
StatePublished - Oct 21 2016
Event2016 IEEE Information Theory Workshop, ITW 2016 - Cambridge, United Kingdom
Duration: Sep 11 2016Sep 14 2016

Publication series

Name2016 IEEE Information Theory Workshop, ITW 2016

Other

Other2016 IEEE Information Theory Workshop, ITW 2016
CountryUnited Kingdom
CityCambridge
Period9/11/169/14/16

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Software
  • Signal Processing

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    Dytso, A., Bustin, R., Tuninetti, D., Devroye, N., Poor, H. V., & Shamai, S. (2016). On the applications of the minimum mean p-th error (MMPE) to information theoretic quantities. In 2016 IEEE Information Theory Workshop, ITW 2016 (pp. 66-70). [7606797] (2016 IEEE Information Theory Workshop, ITW 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITW.2016.7606797