Secure degrees of freedom of the Gaussian wiretap channel with helpers

Abstract

Abstract-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.

MISO broadcast channels with confidential messages and alternating CSIT

“…With the widespread adoption of multiple-input multiple-output (MIMO) systems, there has been a significant recent interest in information theoretic physical layer security, the main premise of which is to exploit the difference in the wireless channels of different users. Information theoretic security has been investigated for a variety of channel models ranging from fading channels [1], [2], MIMO wiretap channels [3]- [6], multiple access channels [7]- [9], multi-receiver wiretap channels [10], broadcast channels with confidential messages [11]- [13], wiretap channels with helpers [14], etc.…”

Multiuser Diversity for Secrecy Communications Using Opportunistic Jammer Selection: Secure DoF and Jammer Scaling Law

“…There have been many studies on utilizing jammers for increasing secure DoF [23], [24], [26]. In [23], cooperative jamming with structured jamming signals based on lattice coding was proposed for a Gaussian wiretap channel.…”

“…In ESA, the concept of ergodic IA [25] was extended to secrecy communications. In [26], cooperative jammers were exploited to increase secure DoF in a Gaussian wiretap channel, where transmitter and cooperative jammers send jointly designed signals according to channel conditions. Contrary to the previous works, in our proposed OJS schemes, the selected jammers adopt i.i.d Gaussian signals oblivious to CSI.…”

Secure degrees of freedom of the Gaussian multiple access wiretap channel

“…Therefore, our achievable scheme combines: channel prefixing, structured signalling, structured cooperative jamming, and interference alignment. Our converse is a generalization of our converse in [14]. We first show that the sum secrecy rate is upper bounded by the sum of differential entropies of all channel inputs except the one eliminated by the eavesdropper's observation.…”

“…For the K-user Gaussian MAC wiretap channel, the best known achievable sum secure d.o.f is [11], [14], [15] strike a better balance between these two end-effects, i.e., by hurting the eavesdropper sufficiently, and not hurting the legitimate receiver as much. In addition, [12] achieved positive sum secure d.o.f.…”