Near-Optimal Modulo-and-Forward Scheme for the Untrusted Relay Channel

TL;DR

This paper introduces a modulo-and-forward scheme with nested lattice encoding for untrusted relay channels, significantly improving secrecy capacity and diversity gain over traditional amplify-and-forward methods.

Contribution

It proposes a novel MF scheme that approaches the secrecy capacity within 1/2 bit and achieves full G-SDoF and G-SDG, outperforming AF schemes in untrusted relay channels.

Findings

MF scheme approaches secrecy capacity within 1/2 bit

Achieves full G-SDoF and G-SDG of order one

Outperforms AF scheme in security and diversity metrics

Abstract

This paper studies an untrusted relay channel, in which the destination sends artificial noise simultaneously with the source sending a message to the relay, in order to protect the source's confidential message. The traditional amplify-and-forward (AF) scheme shows poor performance in this situation because of the interference power dilemma: providing better security by using stronger artificial noise will decrease the confidential message power from the relay to the destination. To solve this problem, a modulo-and-forward (MF) operation at the relay with nested lattice encoding at the source is proposed. For this system with full channel state information at the transmitter (CSIT), theoretical analysis shows that the proposed MF scheme approaches the secrecy capacity within 1/2 bit for any channel realization, and hence achieves full generalized security degrees of freedom (G-SDoF). In contrast, the AF scheme can only achieve a small fraction of the G-SDoF. For this system without any CSIT, the total outage event, defined as either connection outage or secrecy outage, is introduced. Based on this total outage definition, analysis shows that the proposed MF scheme achieves the full generalized secure diversity gain (G-SDG) of order one. On the other hand, the AF scheme can only achieve a G-SDG of 1/2 at most.