MMSE dimension

Yihong Wu, Sergio Verdú

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

3 Scopus citations


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
Number of pages5
StatePublished - 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


Other2010 IEEE International Symposium on Information Theory, ISIT 2010
Country/TerritoryUnited States
CityAustin, TX

All Science Journal Classification (ASJC) codes

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


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