Computable Upper Bounds for Unifilar Finite-State Channels

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

doi:10.1109/ISIT.2019.8849776

Computable Upper Bounds for Unifilar Finite-State Channels

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

Department of Electrical & Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

In this paper, we study the capacity of unifilar finite-state channels. We derive upper bounds that are based on the dual capacity bounding technique using test distributions with memory on directed Q-graphs. The bounds hold for any choice of graph-based test distribution and result in a multi-letter expression. The computability of the upper bound is shown via a novel dynamic programming formulation that can be efficiently evaluated. We further show that the bounds can be simplified to simple single-letter expressions by solving the corresponding Bellman equation explicitly. In particular, for the Ising and Trapdoor channels, we provide simple analytic upper bounds which outperform all previous bounds from the literature.

Original language	English
Title of host publication	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers
Pages	1892-1896
Number of pages	5
ISBN (Electronic)	9781538692912
DOIs	https://doi.org/10.1109/ISIT.2019.8849776
State	Published - 1 Jul 2019
Event	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 7 Jul 2019 → 12 Jul 2019

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2019-July
ISSN (Print)	2157-8095

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/Territory	France
City	Paris
Period	7/07/19 → 12/07/19

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.2019.8849776

Cite this

Huleihel, B., Sabag, O., Permuter, H. H., Kashyap, N., & Shamai Shitz, S. (2019). Computable Upper Bounds for Unifilar Finite-State Channels. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 1892-1896). Article 8849776 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT.2019.8849776

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abstract = "In this paper, we study the capacity of unifilar finite-state channels. We derive upper bounds that are based on the dual capacity bounding technique using test distributions with memory on directed Q-graphs. The bounds hold for any choice of graph-based test distribution and result in a multi-letter expression. The computability of the upper bound is shown via a novel dynamic programming formulation that can be efficiently evaluated. We further show that the bounds can be simplified to simple single-letter expressions by solving the corresponding Bellman equation explicitly. In particular, for the Ising and Trapdoor channels, we provide simple analytic upper bounds which outperform all previous bounds from the literature.",

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Huleihel, B, Sabag, O, Permuter, HH, Kashyap, N & Shamai Shitz, S 2019, Computable Upper Bounds for Unifilar Finite-State Channels. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849776, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers, pp. 1892-1896, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 7/07/19. https://doi.org/10.1109/ISIT.2019.8849776

Computable Upper Bounds for Unifilar Finite-State Channels. / Huleihel, Bashar; Sabag, Oron; Permuter, Haim H. et al.
2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers, 2019. p. 1892-1896 8849776 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - In this paper, we study the capacity of unifilar finite-state channels. We derive upper bounds that are based on the dual capacity bounding technique using test distributions with memory on directed Q-graphs. The bounds hold for any choice of graph-based test distribution and result in a multi-letter expression. The computability of the upper bound is shown via a novel dynamic programming formulation that can be efficiently evaluated. We further show that the bounds can be simplified to simple single-letter expressions by solving the corresponding Bellman equation explicitly. In particular, for the Ising and Trapdoor channels, we provide simple analytic upper bounds which outperform all previous bounds from the literature.

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Huleihel B, Sabag O, Permuter HH, Kashyap N, Shamai Shitz S. Computable Upper Bounds for Unifilar Finite-State Channels. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers. 2019. p. 1892-1896. 8849776. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2019.8849776

Computable Upper Bounds for Unifilar Finite-State Channels

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