Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels

Mohamed Taoufiq Damir, Alex Karrila, Laia Amoros, Oliver Gnilke, David Karpuk, Camilla Hollanti

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error probability are controlled by the average flatness factor of the eavesdropper's lattice, which we further interpret geometrically. It is concluded that the minimization of the (average) flatness factor of the eavesdropper's lattice leads to the study of well-rounded lattices, which are shown to be among the optimal in order to achieve these minima. Constructions of some well-rounded lattices are also provided.

Original languageEnglish
JournalIEEE Transactions on Information Theory
DOIs
Publication statusE-pub ahead of print - 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • Coset codes
  • flatness factor
  • information theoretic security
  • lattices
  • multiple-input multiple-output (MIMO) channels
  • number fields
  • physical layer security
  • Rayleigh fast-fading channels
  • single-input single-output (SISO) channels
  • well-rounded lattices
  • wiretap channels

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