Secure Degrees of Freedom of the Gaussian Diamond-Wiretap Channel

TL;DR

This paper determines the exact secure degrees of freedom for the Gaussian diamond-wiretap channel, considering different CSI scenarios, and introduces new techniques for balancing message and noise transmission to enhance security.

Contribution

It establishes the exact secure degrees of freedom for the Gaussian diamond-wiretap channel and introduces novel methods for balancing message and noise signals under different CSI conditions.

Findings

Exact secure degrees of freedom are characterized for both full and no eavesdropper CSI cases.

New techniques for message and noise balancing improve secure communication.

Methods are adaptable to Gaussian non-fading channels.

Abstract

In this paper, we consider the Gaussian diamond-wiretap channel that consists of an orthogonal broadcast channel from a source to two relays and a Gaussian fast-fading multiple access-wiretap channel from the two relays to a legitimate destination and an eavesdropper. For the multiple access part, we consider both the case with full channel state information (CSI) and the case with no eavesdropper's CSI, at the relays and the legitimate destination. For both the cases, we establish the exact secure degrees of freedom and generalize the results for multiple relays. For the converse part, we introduce a new technique of capturing the trade-off between the message rate and the amount of individual randomness injected at each relay. In the achievability part, we show (i) how to strike a balance between sending message symbols and common noise symbols from the source to the relays in the broadcast component and (ii) how to combine artificial noise-beamforming and noise-alignment techniques at the relays in the multiple access component. In the case with full CSI, we propose a scheme where the relays simultaneously beamform common noise signals in the null space of the legitimate destination's channel, and align them with the message signals at the eavesdropper. In the case with no eavesdropper's CSI, we present a scheme that efficiently utilizes the broadcast links by incorporating computation between the message and common noise symbols at the source. Finally, most of our achievability and converse techniques can also be adapted to the Gaussian (non-fading) channel model.