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Rényi Resolvability and Its Applications to the Wiretap Channel

  • Lei YuEmail author
  • Vincent Y. F. Tan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10681)

Abstract

The conventional channel resolvability problem refers to the determination of the minimum rate needed for an input process to approximate the output distribution of a channel in either the total variation distance or the relative entropy. In this paper, we use the (normalized or unnormalized) Rényi divergence (with the Rényi parameter in [0,2]) to measure the level of approximation. We also provide asymptotic expressions for normalized Rényi divergence when the Rényi parameter is larger than or equal to 1 as well as (lower and upper) bounds for the case when the same parameter is smaller than 1. We characterize the minimum rate needed to ensure that the Rényi resolvability vanishes asymptotically. The optimal rates are the same for both the normalized and unnormalized cases. In addition, the minimum rate when the Rényi parameter no larger than 1 equals the minimum mutual information over all input distributions that induce the target output distribution similarly to the traditional case. When the Rényi parameter is larger than 1 the minimum rate is, in general, larger than the mutual information. We apply these results to the wiretap channel, and completely characterize the optimal tradeoff between the rates of the secret and non-secret messages when the leakage measure is given by the (unnormalized) Rényi divergence (which is a generalization of effective secrecy). This tradeoff differs from the conventional setting when the leakage is measured by the traditional mutual information.

Notes

Acknowledgements

The authors are supported by a Singapore National Research Foundation (NRF) National Cybersecurity R&D Grant (R-263-000-C74-281 and NRF2015NCR-NCR003-006).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringNational University of SingaporeSingaporeSingapore
  2. 2.Department of MathematicsNational University of SingaporeSingaporeSingapore

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