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Computable Upper Bounds on the Capacity of Finite-State Channels

Huleihel, B and Sabag, O and Permuter, HH and Kashyap, N and Shamai Shitz, S (2021) Computable Upper Bounds on the Capacity of Finite-State Channels. In: IEEE Transactions on Information Theory, 67 (9). pp. 5674-5692.

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Official URL: https://doi.org/10.1109/TIT.2021.3091691


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.

Item Type: Journal Article
Publication: IEEE Transactions on Information Theory
Publisher: Institute of Electrical and Electronics Engineers Inc.
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Solar concentrators, Bounding techniques; Channel output; Finite state channels; Graphical structures; Input and outputs; Lower bounds; Trapdoor channel; Upper Bound, Dynamic programming
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 15 May 2023 10:02
Last Modified: 15 May 2023 10:02
URI: https://eprints.iisc.ac.in/id/eprint/81649

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