To feed or not to feed back

Himanshu Asnani, Haim Permuter, Tsachy Weissman

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

Abstract

We establish results assessing the fundamental limits on reliable communication over Finite State Channels (FSCs), when the encoder and the decoder can control the availability or the quality of the feedback. The instantaneous feedback is a function of a cost constrained action taken by the encoder, a cost constrained action taken by the decoder, and the channel output. Achievability is through construction of a sequence of convergent achievable rates, using a simple scheme based on code tree generation, that generates channel input symbols along with encoder and decoder actions. For a given block length N, we give an upper bound on the maximum achievable rate. For stationary indecomposable channels without intersymbol interference (ISI), the capacity is given as the limit of normalized directed information between the input and output sequence, maximized over an appropriate set of causally conditioned distributions. As important special cases, we characterize (a) the framework of to feed or not to feed back where either the encoder or the decoder takes binary actions to determine whether current channel output will be fed back to the encoder, with a constraint on the fraction of channel outputs that are fed back, (b) the capacity of coding on the backward link in FSCs, i.e., when the decoder sends limited-rate instantaneous coded noise-free feedback on the backward link.

Original languageAmerican English
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages159-163
Number of pages5
DOIs
StatePublished - 26 Oct 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: 31 Jul 20115 Aug 2011

Publication series

NameIEEE International Symposium on Information Theory - Proceedings

Conference

Conference2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Country/TerritoryRussian Federation
CitySt. Petersburg
Period31/07/115/08/11

All Science Journal Classification (ASJC) codes

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

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