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2- and 3-Modular lattice wiretap codes in small dimensions

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

A recent line of work on lattice codes for Gaussian wiretap channels introduced a new lattice invariant called secrecy gain as a code design criterion which captures the confusion that lattice coding produces at an eavesdropper. Following up the study of unimodular lattice wiretap codes (Lin and Oggier in IEEE Trans Inf Theory 59(6):3295–3303, 2013), this paper investigates 2- and 3-modular lattices which can be constructed from linear codes and compares them with unimodular lattices. Most even 2- and 3-modular lattices are found to have better performance (that is, a higher secrecy gain) than the best unimodular lattices in dimension \(n,\ 2\le n\le 23\). Odd 2-modular lattices are considered, too, and three lattices are found to outperform the best unimodular lattices.

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Notes

  1. A k-dimensional lattice can be defined in a more general setting by a free abelian group of rank k.

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Acknowledgments

The research of F. Lin and of F. Oggier for this work is supported by the Singapore National Research Foundation under the Research Grant NRF-RF2009-07. The research of P. Solé for this work is supported by Merlion project 1.02.10. The authors would like to thank Christine Bachoc for helpful discussions.

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Authors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive, NW, Calgary, T2N 1N4, Canada

    Fuchun Lin

  2. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore

    Frédérique Oggier

  3. Telecom ParisTech, CNRS, UMR 5141, Department Comelec, 46 rue Barrault, 75634, Paris cedex 13, France

    Patrick Solé

  4. Mathematics Department, King AbdulAziz University, Jeddah, Saudi Arabia

    Patrick Solé

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  1. Fuchun Lin
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  2. Frédérique Oggier
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  3. Patrick Solé
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Correspondence to Frédérique Oggier.

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Lin, F., Oggier, F. & Solé, P. 2- and 3-Modular lattice wiretap codes in small dimensions. AAECC 26, 571–590 (2015). https://doi.org/10.1007/s00200-015-0267-2

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  • DOI: https://doi.org/10.1007/s00200-015-0267-2

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