We consider a two-user multiple-input multiple-output multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of N and K. We subdivide our problem into several regimes based on the values of N and K, and provide achievable schemes based on vector space alignment and real alignment techniques for fixed and fading channel gains. To prove the optimality of the achievable schemes, we provide matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel.We consider a two-user multiple-input multiple-output multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of N and K. We subdivide our problem into several regimes based on the values of N and K, and provide achievable schemes based on vector space alignment and real alignment techniques for fixed and fading channel gains. To prove the optimality of the achievable schemes, we provide matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel.

arXiv:1604.03541IEEE Transactions on Information TheoryJan 15, 201819 citations

Secure degrees of freedom of the MIMO multiple access wiretap channel

Pritam Mukherjee, Şennur Ulukuş

We consider a two-user multiple-input multiple- output (MIMO) multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of N and K. We subdivide our problem into several regimes based on the values of N and K, and provide alignment based achievable schemes and matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel.We consider a two-user multiple-input multiple- output (MIMO) multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of N and K. We subdivide our problem into several regimes based on the values of N and K, and provide alignment based achievable schemes and matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel.

Asilomar Conference on Signals, Systems and Computers (ACSSC)Nov 1, 20158 citations

Secure Degrees of Freedom of User Rank-Deficient Multiple Access Wiretap Channel

Hongtao Luo, Qiang Wang, Jingyi Chen

In this study, we investigate a two-user multiple-input multiple-output (MIMO) multiple access wiretap channel, in which the channel matrices of users exhibit rank deficiency. In this model, the legitimate transmitters and receiver are equipped with $M$ and $N$ antennas, respectively, while the eavesdropper has $K$ antennas. The channel matrices of legitimate users are rank-deficient, whereas those between transmitters and the eavesdropper are full-rank, representing a worst-case scenario. We derive the optimal secure degrees of freedom (SDoF) for this model by combining two separate outer bounds. Considering the variations in the number of antennas at each node and the rank of user channels, we categorize our analysis into several regimes. We then present achievable schemes for each regime, grounded in spatial interference alignment, symbol extension and zero-forcing techniques.In this study, we investigate a two-user multiple-input multiple-output (MIMO) multiple access wiretap channel, in which the channel matrices of users exhibit rank deficiency. In this model, the legitimate transmitters and receiver are equipped with$M$and$N$antennas, respectively, while the eavesdropper has$K$antennas. The channel matrices of legitimate users are rank-deficient, whereas those between transmitters and the eavesdropper are full-rank, representing a worst-case scenario. We derive the optimal secure degrees of freedom (SDoF) for this model by combining two separate outer bounds. Considering the variations in the number of antennas at each node and the rank of user channels, we categorize our analysis into several regimes. We then present achievable schemes for each regime, grounded in spatial interference alignment, symbol extension and zero-forcing techniques.

IEEE Wireless Communications and Networking ConferenceMar 24, 20251 citation

Real interference alignment for the K-user Gaussian interference compound wiretap channel

Jianwei Xie, Şennur Ulukuş

We study the K-user Gaussian interference wiretap channel with N external eavesdroppers. All the transmitters, receivers and eavesdroppers have a single antenna each. We propose an achievable scheme to lower bound the secure degrees of freedom (d.o.f.) for each transmitter-receiver pair. Our approach is based on the (real) interference alignment technique. Our achievable scheme not only aligns the interference at each receiver to prevent the d.o.f. from vanishing, but also aligns the signals observed by the eavesdroppers to reduce the secrecy penalty. The achievable secure d.o.f. of each transmitter-receiver pair is shown to be equations for almost all channel gains.We study the K-user Gaussian interference wiretap channel with N external eavesdroppers. All the transmitters, receivers and eavesdroppers have a single antenna each. We propose an achievable scheme to lower bound the secure degrees of freedom (d.o.f.) for each transmitter-receiver pair. Our approach is based on the (real) interference alignment technique. Our achievable scheme not only aligns the interference at each receiver to prevent the d.o.f. from vanishing, but also aligns the signals observed by the eavesdroppers to reduce the secrecy penalty. The achievable secure d.o.f. of each transmitter-receiver pair is shown to be equations for almost all channel gains.

Allerton Conference on Communication, Control, and ComputingSep 1, 201014 citations

Secure degrees of freedom of the Gaussian MIMO interference channel

Karim Banawan, Şennur Ulukuş

We consider the two-user multiple-input multiple- output (MIMO) interference channel with confidential messages (ICCM). We determine the exact sum secure degrees of freedom (s.d.o.f.) for the symmetric case of M antennas at both transmitters and N antennas at both receivers. We develop the converse by combining the broadcast channel with confidential messages (BCCM) cooperative upper bound, decodability upper bound for the IC with no secrecy constraints, and extensions of the secrecy penalty and role of a helper lemmas. We propose a novel achievable scheme for the 2 × 2 ICCM, which combines asymptotic real interference alignment with spatial interference alignment. Using this scheme, we provide achievable schemes for any M and N by proper vector space operations.We consider the two-user multiple-input multiple- output (MIMO) interference channel with confidential messages (ICCM). We determine the exact sum secure degrees of freedom (s.d.o.f.) for the symmetric case of M antennas at both transmitters and N antennas at both receivers. We develop the converse by combining the broadcast channel with confidential messages (BCCM) cooperative upper bound, decodability upper bound for the IC with no secrecy constraints, and extensions of the secrecy penalty and role of a helper lemmas. We propose a novel achievable scheme for the 2 × 2 ICCM, which combines asymptotic real interference alignment with spatial interference alignment. Using this scheme, we provide achievable schemes for any M and N by proper vector space operations.

Asilomar Conference on Signals, Systems and Computers (ACSSC)Nov 1, 201510 citations

MIMO Multiple Access Channel With an Arbitrarily Varying Eavesdropper: Secrecy Degrees of Freedom

Xiang He, Ashish J. Khisti, Aylin Yener

A two-transmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated. The channel matrices of the legitimate users are fixed and revealed to all the terminals, whereas the channel matrices of the eavesdropper are arbitrarily varying and only known to the eavesdropper. The secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint is characterized. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver, and uses a single-user wiretap code for each user, is shown to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weighted-sum-rate expression. This is accomplished by using induction, where at each step one combines the secrecy and multiple-access constraints associated with an adversary eavesdropping a carefully selected group of sub-channels.A two-transmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated. The channel matrices of the legitimate users are fixed and revealed to all the terminals, whereas the channel matrices of the eavesdropper are arbitrarily varying and only known to the eavesdropper. The secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint is characterized. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver, and uses a single-user wiretap code for each user, is shown to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weighted-sum-rate expression. This is accomplished by using induction, where at each step one combines the secrecy and multiple-access constraints associated with an adversary eavesdropping a carefully selected group of sub-channels.

IEEE Transactions on Information TheoryJun 20, 201367 citations

M

and

N

antennas, respectively, while the eavesdropper has

K

antennas. The channel matrices of legitimate users are rank-deficient, whereas those between transmitters and the eavesdropper are full-rank, representing a worst-case scenario. We derive the optimal secure degrees of freedom (SDoF) for this model by combining two separate outer bounds. Considering the variations in the number of antennas at each node and the rank of user channels, we categorize our analysis into several regimes. We then present achievable schemes for each regime, grounded in spatial interference alignment, symbol extension and zero-forcing techniques.