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The Arbitrarily Varying Relay Channel

Department of Electrical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel
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Parts of this work have been presented at the 2018 International Symposium on Information Theory, Vail, Colorado, 17–22 June 2018, and at the 56th Annual Allerton Conference on Communication, Control, and Computing, Monticelo, Illinoi, 3–5 October 2018. This work was supported by the Israel Science Foundation (grant No. 1285/16).
Entropy 2019, 21(5), 516; https://doi.org/10.3390/e21050516
Received: 26 March 2019 / Revised: 11 May 2019 / Accepted: 20 May 2019 / Published: 22 May 2019
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Abstract

We study the arbitrarily varying relay channel, which models communication with relaying in the presence of an active adversary. We establish the cutset bound and partial decode-forward bound on the random code capacity. We further determine the random code capacity for special cases. Then, we consider conditions under which the deterministic code capacity is determined as well. In addition, we consider the arbitrarily varying Gaussian relay channel with sender frequency division under input and state constraints. We determine the random code capacity, and establish lower and upper bounds on the deterministic code capacity. Furthermore, we show that as opposed to previous relay models, the primitive relay channel has a different behavior compared to the non-primitive relay channel in the arbitrarily varying scenario. View Full-Text
Keywords: arbitrarily varying channel; relay channel; decode-forward; Markov block code; minimax theorem; deterministic code; random code; symmetrizability arbitrarily varying channel; relay channel; decode-forward; Markov block code; minimax theorem; deterministic code; random code; symmetrizability
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Pereg, U.; Steinberg, Y. The Arbitrarily Varying Relay Channel. Entropy 2019, 21, 516.

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