Capacity of Finite-State Channels With Delayed Feedback

Bashar Huleihel, Oron Sabag, Haim H. Permuter, Victoria Kostina

Research output: Contribution to journalArticlepeer-review


— In this paper, we investigate the capacity of finite-state channels (FSCs) in the presence of delayed feedback. We show that the capacity of a FSC with delayed feedback can be computed as that of a new FSC with instantaneous feedback and an extended state. Consequently, graph-based methods to obtain computable upper and lower bounds on the delayed feedback capacity of unifilar FSCs are proposed. Based on these methods, we establish that the capacity of the trapdoor channel with delayed feedback of two time instances is given by log2 (23 ). In addition, we derive an analytical upper bound on the delayed feedback capacity of the binary symmetric channel with a no consecutive ones input constraint. This bound also serves as a novel upper bound on its non-feedback capacity, which outperforms all previously known bounds. Lastly, we demonstrate that feedback does improve the capacity of the dicode erasure channel.

Original languageEnglish
Pages (from-to)16-29
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - 1 Jan 2024


  • Channel capacity
  • directed information
  • dual capacity upper bound
  • finite state channels (FSCs)

ASJC Scopus subject areas

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


Dive into the research topics of 'Capacity of Finite-State Channels With Delayed Feedback'. Together they form a unique fingerprint.

Cite this