Bounds on rate distortion with feed forward for stationary and ergodic sources

Iddo Naiss, Haim H. Permuter

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

1 Scopus citations

Abstract

THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. Consider the rate distortion problem of discrete-time, ergodic, and stationary sources with feed forward at the receiver. We derive a sequence of achievable and computable rates that converge to the feed forward rate distortion. For ergodic and stationary sources, we show that for any n, the rate Rn(D) = 1/n min I(X̂n → Xn) is achievable, where the minimization is taken over the transition conditioning probability p(x̂nxn) such that double strok E sign[d(Xn, X̂n) ≤D. The limit of Rn(D) exists and is the feed forward rate distortion. We follow Gallager's proof where there is no feed forward, and, with appropriate modification, obtain our result. We provide an algorithm for calculating R n(D) using the alternating minimization procedure, and present several numerical examples.

Original languageEnglish
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages385-389
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
ISSN (Print)2157-8104

Conference

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

Keywords

  • Alternating minimization procedure
  • Blahut-Arimoto algorithm
  • Causal conditioning
  • Concatenating code trees
  • Directed information
  • Ergodic and stationary sources
  • Ergodic modes
  • Geometric programming
  • Rate distortion with feed forward

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