Computable Upper Bounds on the Capacity of Finite-State Channels

Bashar Huleihel, Oron Sabag, Haim H. Permuter*, Navin Kashyap, Shlomo Shamai Shitz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We consider the use of the well-known dual capacity bounding technique for deriving upper bounds on the capacity of indecomposable finite-state channels (FSCs) with finite input and output alphabets. In this technique, capacity upper bounds are obtained by choosing suitable test distributions on the sequence of channel outputs. We propose test distributions that arise from certain graphical structures called Q -graphs. As we show in this paper, the advantage of this choice of test distribution is that, for the important sub-classes of unifilar and input-driven FSCs, the resulting upper bounds can be formulated as a dynamic programming (DP) problem, which makes the bounds tractable. We illustrate this for several examples of FSCs, where we are able to solve the associated DP problems explicitly to obtain capacity upper bounds that either match or beat the best previously reported bounds. For instance, for the classical trapdoor channel, we improve the best known upper bound of 0.661 (due to Lutz (2014)) to 0.584, shrinking the gap to the best known lower bound of 0.572, all bounds being in units of bits per channel use.

Original languageAmerican English
Article number9462805
Pages (from-to)5674-5692
Number of pages19
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - Sep 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


  • Channel capacity
  • dual capacity bound
  • dynamic programming (DP)
  • finite state channels (FSCs)


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