Well-Rounded Lattices for Coset Coding in MIMO Wiretap Channels

TL;DR

This paper extends the application of well-rounded lattices from SISO to MIMO wiretap channels, demonstrating their effectiveness in enhancing security through explicit coset code designs and extensive simulations.

Contribution

It introduces design criteria for well-rounded lattices in MIMO wiretap channels and constructs explicit coset codes that outperform traditional scalar lattice codes.

Findings

Well-rounded lattices improve security in MIMO wiretap channels.

Explicit coset codes based on Alamouti and Golden codes outperform scalar lattice codes.

Simulation results confirm the effectiveness of the proposed codes.

Abstract

The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that, under this setup, the property of being well-rounded is critical for minimizing the eavesdropper's probability of correct decoding in lower SNR regimes. The superior performance of coset codes constructed from well-rounded lattices has been illustrated in several simulations. In the present article, this work is extended to fading multiple-input multiple-output (MIMO) wiretap channels, and similar design criteria as in the SISO case are derived. Further, explicit coset codes for Rayleigh fading MIMO wiretap channels are designed. In particular, it is shown through extensive simulations that sublattices of the well-known Alamouti code and Golden code which meet our design criteria perform better than scalar multiples of the code lattice for the same parameters.