We say that a network coding scheme is strongly 1-secure if a source node s can multicast n field elements {m1, · · · ,mn} to a set of sink nodes {t1, · · · , tq} in such a way that any single edge leaks no information on any S ⊂ {m1, · · · ,mn} with |S| = n − 1, where n = mintimax-flow(s, ti) is the maximum transmission capacity. We also say that a strongly h-secure network coding scheme is strongly (h + 1)secure if any h + 1 edges leak no information on any S ⊂ {m1, · · · ,mn} with |S| = n − (h + 1). In this paper, we show the first explicit algorithm which can construct strongly k-secure network coding schemes. In particular, it runs in polynomial time for fixed k.

Information Theoretic Security

The year 2015 marks the 30th birthday of DC (Difference of Convex functions) programming and DCA (DC Algorithms) which constitute the backbone of nonconvex programming and global optimization. In this article we offer a short survey on thirty years of developments of these theoretical and algorithmic tools. The survey is comprised of three parts. In the first part we present a brief history of the field, while in the second we summarize the state-of-the-art results and recent advances. We focus on main theoretical results and DCA solvers for important classes of difficult nonconvex optimization problems, and then give an overview of real-world applications whose solution methods are based on DCA. The third part is devoted to new trends and important open issues, as well as suggestions for future developments.

DC programming and DCA: thirty years of developments

Physical layer security (PLS) has been extensively explored as an alternative to conventional cryptographic schemes for securing wireless links. Many studies have shown that the cooperation between the legitimate nodes of a network can significantly enhance their secret communications performance, relative to the noncooperative case. Motivated by the importance of this class of PLS systems, this paper provides a comprehensive survey of the recent works on cooperative relaying and jamming techniques for securing wireless transmissions against eavesdropping nodes, which attempt to intercept the transmissions. First, it provides a in-depth overview of various secure relaying strategies and schemes. Next, a review of recently proposed solutions for cooperative jamming techniques is provided with an emphasis on power allocation and beamforming techniques. Then, the latest developments in hybrid techniques, which use both cooperative relaying and jamming, are elaborated. Finally, several key challenges in the domain of cooperative security are presented along with an extensive discussion on the applications of cooperative security in key enablers for 5G communications, such as nonorthogonal multiple access, device-to-device communications, and massive multiple-input multiple-output systems.

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A Comprehensive Survey on Cooperative Relaying and Jamming Strategies for Physical Layer Security

Precoding has been conventionally considered as an effective means of mitigating or exploiting the interference in the multiantenna downlink channel, where multiple users are simultaneously served with independent information over the same channel resources. The early works in this area were focused on transmitting an individual information stream to each user by constructing weighted linear combinations of symbol blocks (codewords). However, more recent works have moved beyond this traditional view by: 1) transmitting distinct data streams to groups of users and 2) applying precoding on a symbol-per-symbol basis. In this context, the current survey presents a unified view and classification of precoding techniques with respect to two main axes: 1) the switching rate of the precoding weights, leading to the classes of block-level and symbol-level precoding and 2) the number of users that each stream is addressed to, hence unicast, multicast, and broadcast precoding. Furthermore, the classified techniques are compared through representative numerical results to demonstrate their relative performance and uncover fundamental insights. Finally, a list of open theoretical problems and practical challenges are presented to inspire further research in this area 1 . 1 The concepts of precoding and beamforming are used interchangeably throughout this paper.

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Symbol-Level and Multicast Precoding for Multiuser Multiantenna Downlink: A State-of-the-Art, Classification, and Challenges

The broadcast nature of the wireless medium allows unintended users to eavesdrop on confidential information transmission. In this regard, we investigate the problem of secure communication between a source and a destination via a wireless energy harvesting untrusted node that acts as a helper to relay the information; however, the source and destination nodes wish to keep the information confidential from the relay node. To realize the positive secrecy rate, we use destination-assisted jamming. Being an energy-starved node, the untrusted relay harvests energy from the received radio-frequency (RF) signals, which include the source's information signal and the destination's jamming signal. Thus, we utilize the jamming signal efficiently by leveraging it as a useful energy source. At the relay, to enable energy harvesting and information processing, we adopt power splitting (PS) and time switching (TS) policies. To evaluate the secrecy performance of this proposed scenario, we derive analytical expressions for two important metrics, viz., the secrecy outage probability and the ergodic secrecy rate. The numerical analysis reveals design insights into the effects of different system parameters such as PS ratio, energy harvesting time, target secrecy rate, transmit signal-to-noise ratio (SNR), relay location, and energy conversion efficiency factor, on secrecy performance. Specifically, the PS policy achieves better optimal secrecy outage probability and optimal ergodic secrecy rate than that of the TS policy at higher target secrecy rate and transmit SNR, respectively.

Secure Communication via a Wireless Energy Harvesting Untrusted Relay

We apply the concept of artificial and controlled interference in a two-hop relay network with an untrusted relay, aiming at enhancing the wireless communication secrecy between the source and the destination node. In order to shield the square quadrature amplitude-modulated (QAM) signals transmitted from the source node to the relay, the destination node designs and transmits artificial noise (AN) symbols to jam the relay reception. The objective of our considered AN design is to degrade the error probability performance at the untrusted relay, for different types of channel state information (CSI) at the destination. By considering perfect knowledge of the instantaneous CSI of the source-to-relay and relay-to-destination links, we first present an analytical expression for the symbol error rate (SER) performance at the relay. Based on the assumption of an average power constraint at the destination node, we then derive the optimal phase and power distribution of the AN that maximizes the SER at the relay. Furthermore, we obtain the optimal AN design for the case where only statistical CSI is available at the destination node. For both cases, our study reveals that the Gaussian distribution is generally not optimal to generate AN symbols. The presented AN design takes into account practical parameters for the communication links, such as QAM signaling and maximum likelihood decoding.

Securing Relay Networks with Artificial Noise: An Error Performance-Based Approach

We apply the concept of artificial noise (AN) transmission in an untrusted relay network to enhance secure communication between the source and destination. Specifically, in addition to square quadrature amplitude modulated (QAM) signals broadcasted by the source, the relay simultaneously receives AN symbols designed and transmitted by the destination. For the relay, based on the assumption of additive white Gaussian noise, we derive the analytical symbol error rate (SER) expression, which is maximized for the optimal AN design. Under an average power constraint, we find the optimal phase and power distribution of the AN. Interestingly, our study shows that the Gaussian distribution is generally not optimal to generate AN and the results in this paper can be used as benchmarks for future analyses of AN-based techniques. More importantly, rather than conducting analysis from an information-theoretic perspective, our SER-based approach takes practical communication issues into account, such as QAM signalling.

Enhancing physical layer security in untrusted relay networks with artificial noise: A symbol error rate based approach

In this paper, we propose a novel single-group multicast beamforming technique using non-orthogonal space-time block coding (STBC). In the system, a multi-antenna base station broadcasts its information to a large group of single-antenna users. We introduce a modified max-min fair beamforming optimization problem, which maximizes the worst user's modified Euclidean distance instead of the conventional worst user's signal-to-noise ratio. Our beamforming formulation extends the traditional max-min fair problem, by taking the pairwise error probability of the employed STBC into consideration, which in turns improves the overall system performance. For the resulting non-convex quadratically constrained quadratic program, an iterative inner convex approximation method is devised, in which the non-convex part of the problem is linearized and a sequence of inner convex optimization problems is solved. Simulation results demonstrate considerable improvement for networks with a large number of users.

Full-rate general rank beamforming in single-group multicasting networks using non-orthogonal STBC

In this work we present a novel scheme for load management in microgrids based on stochastic scheduling of loads under risk-limiting constraints. When trying to enforce adequate power supply in a microgrid, the volatility of renewable resources such as wind energy has to be considered. In the risk of inadequate power supply, loads have to be scheduled, which can be achieved by directly controlling individual loads or by setting pricing incentives to encourage beneficial behavior of the customers. A common drawback of conventional methods lies in the need of sophisticated control strategies and a significant amount of real-time signaling exchange between the microgrid and the central control unit. To address these issues, we propose a scheme that does not require a direct control of individual loads. Our method relies on sorting the appliances in the network into groups, and allowing these groups to schedule themselves stochastically according to broadcasted scheduling probabilities. In this paper, we propose an optimization problem to determine these group scheduling probabilities, as well as for choosing the best utilization of conventional generators, in a day-ahead planning scenario of an isolated microgrid. Using an outage-risk limiting constraint, we control the risk of inadequate power supply causing network outages. The proposed scheme can be easily implemented with unidirectional communication from a central control unit via simple broadcast messages.

Stochastic load scheduling for risk-limiting economic dispatch in smart microgrids

Recent information theoretic results have shown that interference can be exploited in wireless relay-assisted networks to secure the information communicated between two legitimate network nodes from the potentially untrusted nodes. In this paper, we consider a two-hop multi-relay network with untrusted relays, where the destination node, aiming at securing the source node's information signal, designs and broadcasts artificial noise (AN) symbols to jam the reception by the multiple relays. By focusing on the case where long-term channel state information is available at the destination, the objective of the considered AN design is to increase the decoding error probability at all the relays. Given an average power constraint at the destination, we propose a unified AN scheme to optimally generate the phase and the power of the AN symbols to maximize the minimum average symbol error rate (ASER) at the relays. The proposed AN generation scheme accounts for practical modulations, such as square quadrature amplitude modulation and M-ary phase-shift-keying. In addition, it is not restricted to specific channel fading model. Numerical and simulation results clearly show that the proposed scheme achieves considerably higher ASER performance than various AN generations, including the frequently used Gaussian distribution.

Ying Liu

Papers

Securing Relay Networks with Artificial Noise: An Error Performance-Based Approach

Enhancing physical layer security in untrusted relay networks with artificial noise: A symbol error rate based approach

Full-rate general rank beamforming in single-group multicasting networks using non-orthogonal STBC

Stochastic load scheduling for risk-limiting economic dispatch in smart microgrids

Artificial noise design for secure multi-relay networks over generalized fading channels