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Secure degrees of freedom region of the Gaussian multiple access wiretap channel
 In Asilomar Conference
, 2013
"... Abstract — [1] showed that the sum secure degrees of freedom (s.d.o.f.) of the Kuser Gaussian multiple access (MAC) wiretap channel is K(K−1) K(K−1)+1. In this paper, we determine the entire s.d.o.f. region of the Kuser Gaussian MAC wiretap channel. The converse follows from a middle step in the c ..."
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Abstract — [1] showed that the sum secure degrees of freedom (s.d.o.f.) of the Kuser Gaussian multiple access (MAC) wiretap channel is K(K−1) K(K−1)+1. In this paper, we determine the entire s.d.o.f. region of the Kuser Gaussian MAC wiretap channel. The converse follows from a middle step in the converse of [1]. The achievability follows from exploring the polytope structure of the converse region, determining its extreme points, and then showing that each extreme point can be achieved by an muser 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. A byproduct of our result is that the sum s.d.o.f. is achieved only at one corner point of the s.d.o.f. region. I.
Secure Degrees of Freedom Regions of Multiple Access and Interference Channels: The Polytope Structure∗
, 2014
"... The sum secure degrees of freedom (s.d.o.f.) of two fundamental multiuser network structures, the Kuser Gaussian multiple access (MAC) wiretap channel and the Kuser 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], res ..."
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The sum secure degrees of freedom (s.d.o.f.) of two fundamental multiuser network structures, the Kuser Gaussian multiple access (MAC) wiretap channel and the Kuser 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 4user case, i.e., the 2 or 3user 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 muser 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 symmetricrate extreme point, for both MAC and IC channel models.
Secure Degrees of Freedom of Onehop Wireless Networks with No Eavesdropper CSIT∗
, 2015
"... We consider three channel models: the wiretap channel withM helpers, the Kuser multiple access wiretap channel, and the Kuser interference channel with an external eavesdropper, when no eavesdropper's channel state information (CSI) is available at the transmitters. In each case, we establish ..."
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We consider three channel models: the wiretap channel withM helpers, the Kuser multiple access wiretap channel, and the Kuser interference channel with an external eavesdropper, when no eavesdropper's channel state information (CSI) is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSIT does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper's CSIT, the Kuser multiple access wiretap channel reduces to a wiretap channel with (K − 1) helpers from a sum s.d.o.f. perspective, and the optimal sum s.d.o.f. reduces from K(K−1)K(K−1)+1 to K−1 K. For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from K(K−1)2K−1 to K−1 2 in the absence of the eavesdropper's CSIT. Our results show that the lack of eavesdropper's CSIT does not have a signicant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large. This implies that physical layer security can be made robust to the unavailability of eavesdropper CSIT at high signal to noise ratio (SNR) regimes by careful modication of the achievable schemes as demonstrated in this paper. 1
Secure degrees of freedom of the interference channel with no eavesdropper CSI
 in IEEE Inf. Theory Workshop
, 2015
"... Abstract—We consider the Kuser interference channel with an external eavesdropper, with no eavesdropper’s channel state information at the transmitters (CSIT). We determine the exact sum secure degrees of freedom (s.d.o.f.) for this channel by providing a new alignment based achievable scheme and ..."
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Abstract—We consider the Kuser interference channel with an external eavesdropper, with no eavesdropper’s channel state information at the transmitters (CSIT). We determine the exact sum secure degrees of freedom (s.d.o.f.) for this channel by providing a new alignment based achievable scheme and a matching converse. Our results show that the lack of eavesdropper’s CSIT does not have a significant impact on the optimal s.d.o.f. of the interference channel with an external eavesdropper, especially when the number of users is large. I.
Secure Degrees of Freedom of Multiuser Networks: OneTimePads in the Air via Alignment
, 2015
"... Interference alignment techniques are powerful methods that best exploit available degrees of freedom in multiterminal settings. Extensions involving secure degrees of freedom are reviewed in an expository manner, focusing on the secrecy penalty and role of a helper in the design of secure systems u ..."
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Interference alignment techniques are powerful methods that best exploit available degrees of freedom in multiterminal settings. Extensions involving secure degrees of freedom are reviewed in an expository manner, focusing on the secrecy penalty and role of a helper in the design of secure systems using real interference alignment, cooperative jamming, and structured signaling. By Jianwei Xie and Sennur Ulukus, Member IEEE ABSTRACT  We revisit the recent secure degrees of freedom (s.d.o.f.) results for onehop multiuser wireless networks by considering three fundamental wireless network structures: Gaussian wiretap channel with helpers, Gaussian multiple access wiretap channel, and Gaussian interference channel with secrecy constraints. We present main enabling tools and resulting communication schemes in an expository manner, along with key insights and design principles emerging from them. The main achievable schemes are based on real interference alignment, channel prefixing via cooperative jamming, and structured signalling. Real interference alignment enables aligning the cooperative jamming signals together with the message carrying signals at the eavesdroppers to protect them akin to onetimepad protecting messages in wired systems. Real interference alignment also enables decodability at the legitimate receivers by rendering message carrying and cooperative jamming signals separable, and simultaneously aligning the cooperative jamming signals in the smallest possible subspace. The main converse techniques are based on two key lemmas which quantify 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; and the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. These two lemmas when applied according to the unique structure of individual networks provide tight converses. Finally, we present a blind cooperative jamming scheme for the helper network with no eavesdropper channel state information at the transmitters that achieves the same optimal s.d.o.f. as in the case of full eavesdropper channel state information.