Functional properties of MMSE

Yihong Wu, Sergio Verdu

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

19 Scopus citations

Abstract

We show that the minimum mean-square error (MMSE) of estimating the input based on the channel output is a concave functional of the input-output joint distribution, and its various regularity properties are explored. In particular, the MMSE in Gaussian channels is shown to be weakly continuous in the input distribution and Lipschitz continuous with respect to the quadratic Wasserstein distance for peak-limited inputs. Regularity properties of mutual information are also obtained and some connections with rate-distortion theory are also drawn.

Original languageEnglish (US)
Title of host publication2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Pages1453-1457
Number of pages5
DOIs
StatePublished - Aug 23 2010
Event2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States
Duration: Jun 13 2010Jun 18 2010

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8103

Other

Other2010 IEEE International Symposium on Information Theory, ISIT 2010
CountryUnited States
CityAustin, TX
Period6/13/106/18/10

All Science Journal Classification (ASJC) codes

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

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  • Cite this

    Wu, Y., & Verdu, S. (2010). Functional properties of MMSE. In 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings (pp. 1453-1457). [5513606] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2010.5513606