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

TL;DR

This paper explores the use of well-rounded lattices to optimize coset codes for Gaussian and fading wiretap channels, focusing on minimizing information leakage and decoding errors through geometric lattice properties.

Contribution

It introduces the concept of well-rounded lattices as optimal structures for wiretap coding, providing bounds, geometric interpretations, and constructions for these lattices.

Findings

Well-rounded lattices minimize the flatness factor, reducing information leakage.

Bounds on eavesdropper's decoding probability are linked to lattice flatness.

Constructed examples of well-rounded lattices demonstrate practical applicability.

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.