On establishing the Shannon ordering for discrete memoryless channels

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Abstract

This paper studies several problems concerning channel inclusion, which is a partial ordering between discrete memoryless channels (DMCs) proposed by Shannon. Specifically, checkable conditions are derived for channel inclusion between DMCs with certain special structure, and these conditions are related to the mathematical theory of majorization. The conditions for channel inclusion between binary erasure channel (BEC) and binary symmetric channel (BSC) are also derived, which are shown to be equivalent to those for channel output degradation. Furthermore, the determination of channel inclusion is considered as a convex optimization problem, and the sparsity of the weights related to the representation of the worse DMC in terms of the better one is revealed when channel inclusion holds between two DMCs.

Original languageEnglish (US)
Title of host publication2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
Pages865-869
Number of pages5
DOIs
StatePublished - Oct 22 2012
Event2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States
Duration: Jul 1 2012Jul 6 2012

Publication series

NameIEEE International Symposium on Information Theory - Proceedings

Other

Other2012 IEEE International Symposium on Information Theory, ISIT 2012
CountryUnited States
CityCambridge, MA
Period7/1/127/6/12

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ASJC Scopus subject areas

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

Cite this

Zhang, Y., & Tepedelenlioglu, C. (2012). On establishing the Shannon ordering for discrete memoryless channels. In 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012 (pp. 865-869). [6284684] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2012.6284684