MMSE dimension

Yihong Wu, Sergio Verdu

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

2 Scopus citations

Abstract

If N is standard Gaussian, the minimum mean-square error (MMSE) of estimating X based on √snrX + N vanishes at least as fast as 1/snr as snr → ∞. We define the MMSE dimension of X as thelimit as snr → ∞ of the product of snr and the MMSE. For discrete, absolutely continuous or mixed X we show that the MMSE dimension equals Renyi's information dimension. However, for singular X, we show that the product of snr and MMSE oscillates around information dimension periodically in snr (dB). We also show that discrete side information does not reduce MMSE dimension. These results extend considerably beyond Gaussian N under various technical conditions.

Original languageEnglish (US)
Title of host publication2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Pages1463-1467
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). MMSE dimension. In 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings (pp. 1463-1467). [5513599] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2010.5513599