Logarithmic Sobolev inequalities and strong data processing theorems for discrete channels

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

Abstract

The noisiness of a channel can be measured by comparing suitable functionals of the input and output distributions. For instance, if we fix a reference input distribution, then the worst-case ratio of output relative entropy to input relative entropy for any other input distribution is bounded by one, by the data processing theorem. However, for a fixed reference input distribution, this quantity may be strictly smaller than one, giving so-called strong data processing inequalities (SDPIs). This paper shows that the problem of determining both the best constant in an SDPI and any input distributions that achieve it can be addressed using so-called logarithmic Sobolev inequalities, which relate input relative entropy to certain measures of input-output correlation. Another contribution is a proof of equivalence between SDPIs and a limiting case of certain strong data processing inequalities for the Rényi divergence.

Original languageEnglish (US)
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages419-423
Number of pages5
DOIs
StatePublished - Dec 19 2013
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: Jul 7 2013Jul 12 2013

Publication series

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

Other

Other2013 IEEE International Symposium on Information Theory, ISIT 2013
CountryTurkey
CityIstanbul
Period7/7/137/12/13

ASJC Scopus subject areas

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

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  • Cite this

    Raginsky, M. (2013). Logarithmic Sobolev inequalities and strong data processing theorems for discrete channels. In 2013 IEEE International Symposium on Information Theory, ISIT 2013 (pp. 419-423). [6620260] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2013.6620260