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IEEE Communications Letters

The Gaussian Diamond-Wiretap Channel with Conferencing Relays

Si-Hyeon Lee, Ashish J. Khisti

Published Jan 1, 2016• 3 citations
Publisher

Abstract

In this letter, we consider the Gaussian diamond-wiretap channel with conferencing links between relays for the following three cases: 1) both conferencing links are confidential; 2) both conferencing links are public; and 3) one conferencing link is confidential, the other link is public, and the legitimate parties do not know which link is confidential or public. For all the cases, we establish the exact secure degrees of freedom (d.o.f.). Our results show that if at least one of conferencing links is confidential, the secure d.o.f. improves upon the case of no conferencing. In these cases of fully and partially confidential conferencing, it is shown to be sufficient to use the conferencing links only for transmitting noise symbols. On the other hand, if conferencing information is fully revealed to the eavesdropper, it is shown that there is no gain in secure d.o.f. due to conferencing, even if the conferencing information is also known to the legitimate destination.

DOI
10.1109/lcomm.2016.2558145

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In this letter, we consider the Gaussian diamond-wiretap channel with conferencing links between relays for the following three cases: 1) both conferencing links are confidential; 2) both conferencing links are public; and 3) one conferencing link is confidential, the other link is public, and the legitimate parties do not know which link is confidential or public. For all the cases, we establish the exact secure degrees of freedom (d.o.f.). Our results show that if at least one of conferencing links is confidential, the secure d.o.f. improves upon the case of no conferencing. In these cases of fully and partially confidential conferencing, it is shown to be sufficient to use the conferencing links only for transmitting noise symbols. On the other hand, if conferencing information is fully revealed to the eavesdropper, it is shown that there is no gain in secure d.o.f. due to conferencing, even if the conferencing information is also known to the legitimate destination.
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 this letter, we establish the secure degrees-of-freedom of the Gaussian diamond-wiretap channel with rate-limited relay cooperation, where the eavesdropper not only observes the relay transmission through another multiple access channel but also wiretaps some of communication links among relays. The legitimate parties do not know the location of wiretapped relay links nor the eavesdropper's channel state information. As an optimal relay cooperation strategy, a noise-forwarding scheme that does not incorporate secure network coding is adopted. Furthermore, we briefly outline how the scheme can be extended to incorporate the case when the source-relay links are also wiretapped.
In this thesis, the physical layer secrecy for several Gaussian network models are studied. We first establish the secure degrees of freedom (d.o.f.)~of helper-assisted Gaussian wiretap channel with shared keys between the transmitter and the helpers. As a natural extension, we next consider the Gaussian diamond wiretap channel where the relays can obtain common randomness from the source node. Secure d.o.f.~for the diamond wiretap channel is established and upper and lower bounds for the multi-relay case are also provided. We then study the diamond channel with conferencing links and investigate the effects of the conferencing links under Gaussian channel as well as binary adder MAC channel. Finally we discuss the artificial noise transmission for secrecy with constant-amplitude constraint for the beamforming vector. The effects of such constraint are examined and algorithms to solve for the beamforming vector are given.
In this paper, we study a diamond-relay channel where the source is connected toMrelays through orthogonal links and the relays transmit to the destination over a wireless multiple-access channel in the presence of an eavesdropper. The eavesdropper not only observes the relay transmissions through another multiple-access channel but also observes a certain number of source-relay links. The legitimate terminals know neither the eavesdropper's channel state information nor the location of source-relay links revealed to the eavesdropper except the total number of such links. For this wiretapped diamond-relay channel, we establish the optimal secure d.o.f. In the achievability part, our proposed scheme uses the source-relay links to transmit a judiciously constructed combination of message symbols, artificial noise symbols, and fictitious message symbols associated with secure network coding. The relays use a combination of beamforming and interference alignment in their transmission scheme. For the converse part, we take a genie-aided approach assuming that the location of wiretapped links is known.
We consider a practical scenario of the Gaussian multiantenna wiretap channel where a transmitter with no channel state information wishes to send a confidential message to its legitimate receiver in the presence of an eavesdropper. It has been known that the secrecy capacity of such a channel does not scale with signal-to-noise ratio under general conditions. Taking into account the different temporal fading structures at the legitimate receiver and the eavesdropper, we characterize lower and upper bounds on the secrecy degrees of freedom (s.d.o.f.) of the channel at hand. Our results show that a positive s.d.o.f. can be ensured whenever two receivers experience the asynchronous variation. Remarkably, simple linear precoding schemes provide the optimal s.d.o.f. in most cases of interest by aligning either the confidential signal at the eavesdropper or the artificial noise at the legitimate receiver.
We study the secure degrees of freedom (d.o.f.) of one-hop wireless networks by considering four fundamental wireless network structures: 1) Gaussian wiretap channel; 2) Gaussian broadcast channel with confidential messages; 3) Gaussian interference channel with confidential messages; and 4) Gaussian multiple access wiretap channel. The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the secure d.o.f. of the Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper, which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap channel with a helper is 1/2. Our achievable scheme is based on real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact secure d.o.f. in this case is M/M+1.We then generalize this approach to more general network structures with multiple messages. We show that the sum secure d.o.f. of the Gaussian broadcast channel with confidential messages and M helpers is 1, the sum secure d.o.f. of the twouser interference channel with confidential messages is 2/3, the sum secure d.o.f. of the two-user interference channel with confidential messages and M helpers is 1, and the sum secure d.o.f. of the K-user multiple access wiretap channel is K(K-1)/K(K-1)+1.