English

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

Information Theory 2020-07-31 v4 math.IT

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.

Keywords

Cite

@article{arxiv.1609.07723,
  title  = {Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels},
  author = {Mohamed Taoufiq Damir and Alex Karrila and Laia Amorós and Oliver Gnilke and David Karpuk and Camilla Hollanti},
  journal= {arXiv preprint arXiv:1609.07723},
  year   = {2020}
}

Comments

Partial results were published in ITW'16 (arXiv:1605.00419), ITNAC'16 (arXiv:1609.07666, arXiv:1606.06099), and SPAWC'18