Mutual information saddle points in channels of exponential family type

Todd P. Coleman, Maxim Raginsky

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

Abstract

This paper extends our prior work on "E-type" (exponential family type) channels. The channels considered here have transition kernels induced by an exponential family with a two-component sufficient statistic composed of an input-output distortion function and an output cost function. We demonstrate the existence of a mutual information saddle point in any E-type channel for which there exists a source distribution such that the induced output distribution is maximum-entropy under an output cost constraint. For additive-noise E-type channels, we provide necessary and sufficient conditions on the existence of saddle points which coincide with convolution divisibility of the additive noise law. This machinery generalizes many well-known saddle-point, capacity, and rate-distortion theorems, including those for the additive Gaussian and exponential-noise channels, and leads to a saddle point result on the non-additive exponential server timing channel, which appears to be new.

Original languageEnglish (US)
Title of host publication2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Pages1355-1359
Number of pages5
DOIs
StatePublished - Aug 23 2010
Externally publishedYes
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

ASJC Scopus subject areas

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

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  • Cite this

    Coleman, T. P., & Raginsky, M. (2010). Mutual information saddle points in channels of exponential family type. In 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings (pp. 1355-1359). [5513481] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2010.5513481