Secure degrees of freedom of the Gaussian diamond-wiretap channel

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.

The Wiretapped Diamond-Relay Channel

“…Let us first present the secure d.o.f. of the wiretapped diamond-relay channel when N = M , which was established in [31,Theorem 6].…”

“…is The achievability part of Theorem 2 when the location of wiretapped links is known can be easily proved by generalizing the proposed schemes in [31]. However, when the location of wiretapped links is unknown, it is not straightforward to extend the proposed schemes in [31] because their sub-schemes require asymmetric link d.o.f. and hence the amount of wiretapped information depends on the unknown location of wiretapped links.…”

“…In [31], for the diamond-relay channel where an eavesdropper can wiretap only the multiple-access portion of the channel, it is shown that transmitting common noise over the source-relay links facilitates more efficient jamming for both the case with full CSI and the case with no eavesdropper's CSI. For example, a key constituent scheme proposed in [31] for the case with no eavesdropper's CSI is computation for jamming (CoJ) where the source transmits a function of information and common noise symbols to two relays in order that the common noise symbols introduced to jam information symbols at the eavesdropper can be canceled at the destination through suitable precoding. When there are more than two relays, this scheme operates in a time-sharing basis in a way that only two source-relay links are utilized in each sub-scheme.…”

“…The legitimate terminals do not know which subset of source-relay links are revealed to the eavesdropper, except for the total number of such links. For achievability, we note that it is not straightforward to extend the proposed schemes in [31] because their sub-schemes require asymmetric link d.o.f. and hence the amount of wiretapped information varies over time according to the unknown location of wiretapped links.…”

On the Gaussian Multiple Access Wiretap Channel and the Gaussian Wiretap Channel With a Helper: Achievable Schemes and Upper Bounds

“…This approach has been used for example for wiretap channels in [22], [23], for relay networks [24] and for IC channels [25], [26]. It was also recently used in [27] for an s.d.o.f. analysis of the Gaussian diamond-wiretap channel, which is a multi-hop version of the G-MAC-WT.…”