Graph-Based Encoders and Their Performance for Finite-State Channels with Feedback

Oron Sabag, Bashar Huleihel, Haim H. Permuter*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The capacity of unifilar finite-state channels in the presence of feedback is investigated. We derive a new evaluation method to extract graph-based encoders with their achievable rates, and to compute upper bounds to examine their performance. The evaluation method is built upon a recent methodology to derive simple bounds on the capacity using auxiliary directed graphs. While it is not clear whether the upper bound is convex, we manage to formulate it as a convex optimization problem using transformation of the argument with proper constraints. The lower bound is formulated as a non-convex optimization problem, yet, any feasible point to the optimization problem induces a graph-based encoder. In all examples, the numerical results show near-Tight upper and lower bounds that can be easily converted to analytic results. For the non-symmetric trapdoor channel and binary fading channels (BFCs), new capacity results are established by computing the corresponding bounds. For all other instances, including the Ising channel, the near-Tightness of the achievable rates is shown via a comparison with corresponding upper bounds. Finally, we show that any graph-based encoder implies a simple coding scheme that is based on the posterior matching principle and achieves the lower bound.

Original languageAmerican English
Article number8955863
Pages (from-to)2106-2117
Number of pages12
JournalIEEE Transactions on Communications
Volume68
Issue number4
DOIs
StatePublished - Apr 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1972-2012 IEEE.

Keywords

  • Channel capacity
  • Markov decision process (MDP)
  • convex optimization
  • feedback capacity
  • posterior matching (PM)

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