Well-Rounded Lattices for Reliability and Security in Rayleigh Fading SISO Channels

TL;DR

This paper develops practical coset coding schemes for Rayleigh fading channels using well-rounded lattices, improving security and reliability by leveraging geometric and number-theoretic properties.

Contribution

It introduces a new class of coset codes based on well-rounded lattices, with precise analysis and simulation results for secure communication over Rayleigh fading channels.

Findings

New coset codes based on well-rounded lattices demonstrate improved performance.

Precise expressions for eavesdropper's decision probability enhance code design.

Number-theoretic results on ideal lattices support code construction.

Abstract

For many wiretap channel models asymptotically optimal coding schemes are known, but less effort has been put into actual realizations of wiretap codes for practical parameters. Bounds on the mutual information and error probability when using coset coding on a Rayleigh fading channel were recently established by Oggier and Belfiore, and the results in this paper build on their work. However, instead of using their ultimate inverse norm sum approximation, a more precise expression for the eavesdropper's probability of correct decision is used in order to determine a general class of good coset codes. The code constructions are based on well-rounded lattices arising from simple geometric criteria. In addition to new coset codes and simulation results, novel number-theoretic results on well-rounded ideal lattices are presented.