Capacity of a POST channel with and without feedback

Himanshu Asnani, Haim H. Permuter, Tsachy Weissman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations

Abstract

We consider finite state channels where the state of the channel is its previous output. We refer to such channels as POST (Previous Output is the STate) channels. Our focus is on a simple binary POST channel, with binary inputs and outputs where the state determines if the channel behaves as a Z or an S channel (of equal capacities). We show that the non feedback capacity equals the feedback capacity, despite the memory in the channel. The proof of this surprising result is based on showing that the induced output distribution, when maximizing the directed information in the presence of feedback, can also be achieved by an input distribution that is ignorant of the feedback. Indeed, we show that this is a necessary and sufficient condition for the feedback capacity to equal the non feedback capacity for any finite state channel.

Original languageEnglish
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2538-2542
Number of pages5
ISBN (Print)9781479904464
DOIs
StatePublished - 1 Jan 2013
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: 7 Jul 201312 Jul 2013

Publication series

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

Conference

Conference2013 IEEE International Symposium on Information Theory, ISIT 2013
Country/TerritoryTurkey
CityIstanbul
Period7/07/1312/07/13

Keywords

  • Causal conditioning
  • Convex optimization
  • Directed information
  • Feedback capacity
  • Finite state channel
  • KKT conditions

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