Information Bounds and Flatness Factor Approximation for Fading Wiretap MIMO Channels

TL;DR

This paper investigates secure lattice coding for fading MIMO channels, introducing bounds based on the flatness factor and providing a numerical approximation method that predicts lattice performance effectively.

Contribution

It presents a new analysis linking the flatness factor to security bounds and introduces a numerical approximation for the average flatness factor in fading channels.

Findings

The flatness factor bounds eavesdropper's probability and information leakage.

Numerical approximation of the average flatness factor is feasible and accurate.

The flatness factor effectively predicts lattice performance in fading channels.

Abstract

In this article, the design of secure lattice coset codes for general wireless channels with fading and Gaussian noise is studied. Recalling the eavesdropper's probability and information bounds, a variant of the latter is given from which it is explicitly seen that both quantities are upper bounded by (increasing functions of) the expected flatness factor of the faded lattice related to the eavesdropper. By making use of a recently developed approximation of the theta series of a lattice, it is further shown how the average flatness factor can be approximated numerically. In particular, based on the numerical computations, the average flatness factor not only bounds but also orders correctly the performance of different lattices.