Feedback capacity of the compound channel

Brooke Shrader, Haim Permuter

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


In this work, we find the capacity of a compound finite-state channel (FSC) with time-invariant deterministic feedback. We consider the use of fixed length block codes over the compound channel. Our achievability result includes a proof of the existence of a universal decoder for the family of FSCs with feedback. As a consequence of our capacity result, we show that feedback does not increase the capacity of the compound Gilbert-Elliot channel. Additionally, we show that for a stationary and uniformly ergodic Markovian channel, if the compound channel capacity is zero without feedback then it is zero with feedback. Finally, we use our result on the FSC to show that the feedback capacity of the memoryless compound channel is given by infθ maxQX I(X;Y θ).

Original languageEnglish
Pages (from-to)3629-3644
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - 12 Aug 2009


  • Causal conditioning probability
  • Code-trees
  • Compound channel
  • Directed information
  • Feedback capacity
  • Finite-state channel (FSC)
  • Gilbert-Elliot channel
  • Pinsker's inequality
  • Sanov's theorem
  • Types of code-trees
  • Universal decoder

ASJC Scopus subject areas

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


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