Analytical and numerical characterizations of shannon ordering for discrete memoryless channels

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3 Scopus citations


This paper studies several problems concerning channel inclusion, which is a partial ordering between discrete memoryless channels (DMCs) proposed by Shannon. Specifically, majorization-based conditions are derived for channel inclusion between certain DMCs. Furthermore, under general conditions, channel equivalence defined through Shannon ordering is shown to be the same as permutation of input and output symbols. 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. For the exploitation of this sparsity, an effective iterative algorithm is established based on modifying the orthogonal matching pursuit algorithm.

Original languageEnglish (US)
Article number6623108
Pages (from-to)72-83
Number of pages12
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 2014


  • Channel inclusion
  • convex optimization
  • majorization
  • partial ordering

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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