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List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel

School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA
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This paper is an extended version of our paper published in the 2018 IEEE International Symposium on Information Theory (ISIT)
Entropy 2019, 21(6), 575; https://doi.org/10.3390/e21060575
Received: 11 April 2019 / Revised: 27 May 2019 / Accepted: 4 June 2019 / Published: 7 June 2019
(This article belongs to the Special Issue Information-Theoretic Security II)
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Abstract

In this paper, we determine the capacity of the Gaussian arbitrarily-varying channel with a (possibly stochastic) encoder and a deterministic list-decoder under the average probability of error criterion. We assume that both the legitimate and the adversarial signals are restricted by their power constraints. We also assume that there is no path between the adversary and the legitimate user but the adversary knows the legitimate user’s code. We show that for any list size L, the capacity is equivalent to the capacity of a point-to-point Gaussian channel with noise variance increased by the adversary power, if the adversary has less power than L times the transmitter power; otherwise, the capacity is zero. In the converse proof, we show that if the adversary has enough power, then the decoder can be confounded by the adversarial superposition of several codewords while satisfying its power constraint with positive probability. The achievability proof benefits from a novel variant of the Csiszár-Narayan method for the arbitrarily-varying channel.
Keywords: gaussian arbitrarily-varying channel; list-decoding; stochastic encoder; capacity gaussian arbitrarily-varying channel; list-decoding; stochastic encoder; capacity
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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Hosseinigoki, F.; Kosut, O. List-Decoding Capacity of the Gaussian Arbitrarily-Varying Channel. Entropy 2019, 21, 575.

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