Compute-and-Forward Can Buy Secrecy Cheap

TL;DR

This paper introduces a novel lattice alignment scheme based on compute-and-forward for secure communication in Gaussian multiple access channels, effective at any finite SNR, outperforming traditional methods and matching high SNR results.

Contribution

A new finite SNR lattice alignment scheme for secure communication that outperforms random coding and aligns with high SNR theoretical results.

Findings

Secure sum rate scales with log(SNR)

Scheme outperforms random coding at finite SNR

Results match prior high SNR work

Abstract

We consider a Gaussian multiple access channel with $K$ transmitters, a (intended) receiver and an external eavesdropper. The transmitters wish to reliably communicate with the receiver while concealing their messages from the eavesdropper. This scenario has been investigated in prior works using two different coding techniques; the random i.i.d. Gaussian coding and the signal alignment coding. Although, the latter offers promising results in a very high SNR regime, extending these results to the finite SNR regime is a challenging task. In this paper, we propose a new lattice alignment scheme based on the compute-and-forward framework which works at any finite SNR. We show that our achievable secure sum rate scales with $\log(\mathrm{SNR})$ and hence, in most SNR regimes, our scheme outperforms the random coding scheme in which the secure sum rate does not grow with power. Furthermore, we show that our result matches the prior work in the infinite SNR regime. Additionally, we analyze our result numerically.