Conference Paper

# On the secure degrees of freedom of wireless X networks

Electr. Eng. & Comput. Sci., Univ. of California, Irvine, CA

DOI: 10.1109/ALLERTON.2008.4797643 Conference: Communication, Control, and Computing, 2008 46th Annual Allerton Conference on Source: IEEE Xplore

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**ABSTRACT:**The sum secure degrees of freedom (s.d.o.f.) of two fundamental multi-user network structures, the K-user Gaussian multiple access (MAC) wiretap channel and the K-user interference channel (IC) with secrecy constraints, have been determined recently as K(K-1)/(K(K-1)+1) [1,2] and K(K-1)/(2K-1) [3,4], respectively. In this paper, we determine the entire s.d.o.f. regions of these two channel models. The converse for the MAC follows from a middle step in the converse of [1,2]. The converse for the IC includes constraints both due to secrecy as well as due to interference. Although the portion of the region close to the optimum sum s.d.o.f. point is governed by the upper bounds due to secrecy constraints, the other portions of the region are governed by the upper bounds due to interference constraints. Different from the existing literature, in order to fully understand the characterization of the s.d.o.f. region of the IC, one has to study the 4-user case, i.e., the 2 or 3-user cases do not illustrate the generality of the problem. In order to prove the achievability, we use the polytope structure of the converse region. In both MAC and IC cases, we develop explicit schemes that achieve the extreme points of the polytope region given by the converse. Specifically, the extreme points of the MAC region are achieved by an m-user MAC wiretap channel with (K-m) helpers, i.e., by setting (K-m) users' secure rates to zero and utilizing them as pure (structured) cooperative jammers. The extreme points of the IC region are achieved by a (K-m)-user IC with confidential messages, m helpers, and N external eavesdroppers, for m>=1 and a finite N. A byproduct of our results in this paper is that the sum s.d.o.f. is achieved only at one extreme point of the s.d.o.f. region, which is the symmetric-rate extreme point, for both MAC and IC channel models.04/2014; -
##### Conference Paper: Secure degrees of freedom of the Gaussian wiretap channel with helpers

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**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 M/M+1.Communication, Control, and Computing (Allerton), 2012 50th Annual Allerton Conference on; 01/2012 -
##### Conference Paper: Opportunistic jammer selection for secure degrees of freedom

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**ABSTRACT:**In this paper, we propose two opportunistic jammer selection schemes for secure communications aided by jammers using the concept of interference alignment. Because jamming signals are interference to both a legitimate receiver and a eavesdropper, the legitimate receiver selects two jammers whose jamming signals are the most aligned in a small dimensional subspace. The alignment is measured by either interference-to-noise ratio (INR) or chordal distance for the opportunistic jammer selection. We find the achievable secure degrees of freedom (DoF) by the proposed jammer selection schemes when the number of jammers goes to infinity and find the computational complexity of each scheme.Global Communications Conference (GLOBECOM), 2012 IEEE; 01/2012

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