Security in The Gaussian Interference Channel: Weak and Moderately Weak Interference Regimes

TL;DR

This paper introduces a new lattice-based encoding scheme for secure communication over the Gaussian interference channel in weak regimes, achieving reliable and confidential transmission at finite SNR and outperforming previous methods.

Contribution

A novel lattice and asymmetric compute-and-forward scheme for secure interference channels that maintains confidentiality at finite SNR and scales optimally with SNR.

Findings

Lower bound on secure rates scales linearly with log(SNR)

Scheme outperforms i.i.d. Gaussian random codes

Achieves asymptotic optimality in the considered regimes

Abstract

We consider a secure communication scenario through the two-user Gaussian interference channel: each transmitter (user) has a confidential message to send reliably to its intended receiver while keeping it secret from the other receiver. Prior work investigated the performance of two different approaches for this scenario; i.i.d. Gaussian random codes and real alignment of structured codes. While the latter achieves the optimal sum secure degrees of freedom (s.d.o.f.), its extension to finite SNR regimes is challenging. In this paper, we propose a new achievability scheme for the weak and the moderately weak interference regimes, in which the reliability as well as the confidentiality of the transmitted messages are maintained at any finite SNR value. Our scheme uses lattice structure, structured jamming codewords, and lattice alignment in the encoding and the asymmetric compute-and-forward strategy in the decoding. We show that our lower bound on the sum secure rates scales linearly with log(SNR) and hence, it outperforms i.i.d. Gaussian random codes. Furthermore, we show that our achievable result is asymptotically optimal. Finally, we provide a discussion on an extension of our scheme to K>2 users.