The secrecy capacity of the arbitrarily varying wiretap channel under list decoding

Ahmed S. Mansour; Holger Boche; Rafael F. Schaefer

doi:10.3934/amc.2019002

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2019, Volume 13, Issue 1: 11-39. Doi: 10.3934/amc.2019002

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The secrecy capacity of the arbitrarily varying wiretap channel under list decoding

1.
Lehrstuhl für Theoretische Informationstechnik, Technische Universität München, 80290 München, Germany
2.
Information Theory and Applications Chair, Technische Universität Berlin, 10587 Berlin, Germany

This work was presented in part at IEEE-CNS, Philadelphia, USA, October 2016 [19] and at IEEE-SPAWC, Sapporo, Japan, July 2017 [20]

Received: March 31, 2017

Published: December 2018

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Abstract

We consider a communication scenario in which the channel undergoes two different classes of attacks at the same time: a passive eavesdropper and an active jammer. This scenario is modelled by the concept of arbitrarily varying wiretap channels (AVWCs). In this paper, we derive a full characterization of the list secrecy capacity of the AVWC, showing that the list secrecy capacity is equivalent to the correlated random secrecy capacity if the list size L is greater than the order of symmetrizability of the AVC between the transmitter and the legitimate receiver. Otherwise, it is zero. Our result indicates that for a sufficiently large list size L, list codes can overcome the drawbacks of correlated and uncorrelated codes and provide a stable secrecy capacity for AVWCs. Furthermore, we investigate the effect of relaxing the reliability and secrecy constraints by allowing a non-vanishing error probability and information leakage on the list size L. We found that we can construct a list code whose rate is close to the correlated secrecy capacity using a finite list size L that only depends on the average error probability requested. Finally, we point out that our capacity characterization is an important step in investigating the analytical properties of the capacity function such as: the continuity behavior, Turing computability and super-activation of parallel AVWCs.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Discrete memoryless arbitrarily varying wiretap channel $(\mathfrak{W},\mathfrak{V})$

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