Mohamed S. Nafea

Wiretap channel II with a noisy main channel

In this paper, a wiretap channel where the transmitter and receiver communicate through a discrete memoryless channel, and the eavesdropper (Eve) has perfect access to a fixed fraction of transmitted symbols (of its choosing) is considered. An outer bound for the rate-equivocation region of the channel, for all such fractions, is derived. An achievable scheme, which provides an inner bound for the rate-equivocation region, is proposed. The achievability is established by defining a class of good codebooks for which there exists a good partition that achieves the required level of equivocation no matter what subset of symbols Eve chooses. It is shown that, for a uniform input distribution, the probability of this class of good codes approaches 1 as the block length increases. This generalizes the wiretap II model to one with a noisy main channel.

Secure degrees of freedom for the MIMO wiretap channel with a multiantenna cooperative jammer.

A multiple antenna Gaussian wiretap channel with a multiantenna cooperative jammer (CJ) is considered and the secure degrees of freedom (s.d.o.f.), with N antennas at the sender, receiver, and eavesdropper, is derived for all possible values of the number of antennas at the cooperative jammer, K. In particular, the upper and lower bounds for the s.d.o.f. are provided for different ranges of K and shown to coincide. Gaussian signaling both for transmission and jamming is shown to be sufficient to achieve the s.d.o.f. of the channel, when the s.d.o.f. is integer-valued. By contrast, when the channel has a non-integer s.d.o.f., structured signaling and joint signal space and signal scale alignment are employed to achieve the s.d.o.f.

Secure degrees of freedom of N ×N ×M wiretap channel with a K-antenna cooperative jammer

The secure degrees of freedom (s.d.o.f.) of a multiantenna Gaussian wiretap channel with N antennas at the transmitter and receiver and an arbitrary number of antennas, M, at the wiretapper is characterized when a multiantenna cooperative jammer (CJ) is available as a helper. This generalizes our previous result that assumed the same number of antennas at the eavesdropper as the legitimate parties. In particular, for arbitrary values of N andM, the s.d.o.f. is derived for all possible values of the number of antenna at the CJ, K. The achievability is based on a variety of signalling, beamforming, and alignment techniques which vary according to the value of K, whether M is larger than, smaller than, or equal to N, and whether the s.d.o.f. is integer valued or not an integer. The converse is based on combining an upper bound for the s.d.o.f. which allows for cooperation between the transmitter and CJ and holds for some values of K, with another upper bound which exploits the secrecy and reliability constraints and holds for other values of K.

How many antennas does a cooperative jammer need for achieving the degrees of freedom of multiple antenna Gaussian channels in the presence of an eavesdropper

In this work, multiple antenna Gaussian wiretap channels with a multiantenna cooperative jammer are considered. In particular, the focus is on identifying the spatial resources needed at the cooperative jammer in order to achieve a secure degrees of freedom (s.d.o.f.) for the channel in question equal to the degrees of freedom (d.o.f.). In order to accomplish this goal, the cooperative jammer sets out to send correlated jamming signals. Simultaneously, the legitimate transmitter chooses a precoder that perfectly aligns its information signals over the jamming ones at the eavesdropper. Both terminals use structured signaling, i.e., discrete constellations. The proposed approach is shown to achieve full d.o.f. for the channel at hand as long as the cooperative jammer has twice the antennas of the eavesdropper. It is also shown that within 1/2 of the d.o.f. is achievable with one less antenna at the cooperative jammer.

On the diversity gain region of the Z-interference channels

In this work, we analyze the diversity gain region (DGR) of the single-antenna Rayleigh fading Z-Interference channel (ZIC). More specifically, we characterize the achievable DGR of the fixed-power split Han-Kobayashi (HK) approach under these assumptions. Our characterization comes in a closed form and demonstrates that the HK scheme with only a common message is a singular case, which achieves the best DGR among all HK schemes for certain multiplexing gains. Finally, we show that generalized time sharing, with variable rate and power assignments for the common and private messages, does not improve the achievable DGR.

Multi-terminal networks with an untrusted relay

This paper investigates the impact of cooperation with an untrusted relay in multi-source multi-destination networks. The set up considered is one where the relay is the only means of communications due to the absence of direct links between the sources and the destinations. Since the relay is untrusted, all messages from the sources need to be kept secret from the relay. Furthermore, the destinations are assumed to have different levels of security clearance, i.e., some private messages should only be decoded by their intended receiver and should be kept secret from other destinations. An achievable secure rate region is found by using random binning at the sources, cooperative jamming from the destinations, and compress-and-forward at the relay. Additionally, a genie aided outer bound on the secure rate region is derived. Comparison of inner and outer bounds are provided.

Degrees of freedom of the single antenna gaussian wiretap channel with a helper irrespective of the number of antennas at the eavesdropper

A Gaussian wiretap channel with a helper, i.e., a cooperative jammer, is considered and its secure degrees of freedom (s.d.o.f.) is computed. Previous work showed that the s.d.o.f. is upper bounded by 1 over 2 in this model when all parties are equipped with one antenna each. In this paper, the more challenging scenario where the eavesdropper has multiple antennas is tackled. Relying on structured signaling and cooperative jamming, specifically, by real interference alignment, it is shown that s.d.o.f. of 1 over 2 is achievable irrespective of the number of antennas the eavesdropper may have as long as the cooperative jammer has the same number of antennas as the eavesdropper. The design insight revealed is that the price to pay for the increase in the number of antennas at the eavesdropper is an equivalent increase in the number of antennas at the cooperative jammer in order to maintain the same s.d.o.f.

A new wiretap channel model and its strong secrecy capacity

In this paper, a new wiretap channel (WTC) model with a discrete memoryless (DM) main channel and a wiretapper who noiselessly observes a fixed portion, of her choice, of the transmitted symbols, while observing the remaining transmitted symbols through another DM channel (DMC), is considered. The strong secrecy capacity of the model is identified. The achievability is established using the output statistics of random binning framework which exploits the duality between source and channel coding problems. The converse is derived by upper bounding the secrecy capacity of an equivalent model with the secrecy capacity of a DM-WTC. This result generalizes both the classical DM-WTC and the WTC-II with a DM main channel.

Optimal strategies for targeted influence in signed networks

Online social communities often exhibit complex relationship structures, ranging from close friends to political rivals. As a result, persons are influenced by their friends and foes differently. Network applications can benefit from accompanying these structural differences in propagation schemes. In this paper, we study the optimal influence propagation policies for networks with positive and negative relationship types. We tackle the problem of minimizing the end-to-end propagation cost of influencing a target person in favor of an idea by utilizing the relationship types in the underlying social graph. The propagation cost is incurred by social and physical network dynamics such as frequency of interaction, the strength of friendship and foe ties, propagation delay or the impact factor of the propagating idea. We extend this problem by incorporating the impact of message deterioration and ignorance. We demonstrate our results in both a controlled environment and the Epinions dataset. Our results show that judicious propagation schemes lead to a significant reduction in the average cost and complexity of influence propagation compared to naïve myopic algorithms.

Secure Degrees of Freedom for the MIMO Wire-Tap Channel With a Multi-Antenna Cooperative Jammer

In this paper, a multiple antenna wire-tap channel in the presence of a multi-antenna cooperative jammer is studied. In particular, the secure degrees of freedom (s.d.o.f.) of this channel is established, with