Lifeng Lai

On the Secrecy Capacity of Fading Channels

We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyners wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We analyze the full channel state information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and eavesdropper, and the main channel CSI scenario, where only the legitimate receiver channel gain is known at the transmitter. In each scenario, the secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average SNR goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Remarkably, our results reveal the positive impact of fading on the secrecy capacity and establish the critical role of rate adaptation, based on the main channel CSI, in facilitating secure communications over slow fading channels.

The Relay–Eavesdropper Channel: Cooperation for Secrecy

This paper establishes the utility of user cooperation in facilitating secure wireless communications. In particular, the four-terminal relay-eavesdropper channel is introduced and an outer-bound on the optimal rate-equivocation region is derived. Several cooperation strategies are then devised and the corresponding achievable rate-equivocation region are characterized. Of particular interest is the novel noise-forwarding (NF) strategy, where the relay node sends codewords independent of the source message to confuse the eavesdropper. This strategy is used to illustrate the deaf helper phenomenon, where the relay is able to facilitate secure communications while being totally ignorant of the transmitted messages. Furthermore, NF is shown to increase the secrecy capacity in the reversely degraded scenario, where the relay node fails to offer performance gains in the classical setting. The gain offered by the proposed cooperation strategies is then proved theoretically and validated numerically in the additive white Gaussian noise (AWGN) channel.

Optimal selection of channel sensing order in cognitive radio

This paper investigates the optimal sensing order problem in multi-channel cognitive medium access control with opportunistic transmissions. The scenario in which the availability probability of each channel is known is considered first. In this case, when the potential channels are identical (except for the availability probabilities) and independent, it is shown that, although the intuitive sensing order (i.e., descending order of the channel availability probabilities) is optimal when adaptive modulation is not used, it does not lead to optimality in general with adaptive modulation. Thus, a dynamic programming approach to the search for an optimal sensing order with adaptive modulation is presented. For some special cases, it is proved that a simple optimal sensing order does exist. More complex scenarios are then considered, e.g., in which the availability probability of each channel is unknown. Optimal strategies are developed to address the challenges created by this additional uncertainty. Finally, a scheme is developed to address the issue of sensing errors.

Cognitive Medium Access: Exploration, Exploitation, and Competition

This paper considers the design of efficient strategies that allow cognitive users to choose frequency bands to sense and access among multiple bands with unknown parameters. First, the scenario in which a single cognitive user wishes to opportunistically exploit the availability of frequency bands is considered. By adopting tools from the classical bandit problem, optimal as well as low complexity asymptotically optimal solutions are developed. Next, the multiple cognitive user scenario is considered. The situation in which the availability probability of each channel is known is first considered. An optimal symmetric strategy that maximizes the total throughput of the cognitive users is developed. To avoid the possible selfish behavior of the cognitive users, a game-theoretic model is then developed. The performance of both models is characterized analytically. Then, the situation in which the availability probability of each channel is unknown a priori is considered. Low-complexity medium access protocols, which strike an optimal balance between exploration and exploitation in such competitive environments, are developed. The operating points of these low-complexity protocols are shown to converge to those of the scenario in which the availability probabilities are known. Finally, numerical results are provided to illustrate the impact of sensing errors and other practical considerations.

The Wiretap Channel With Feedback: Encryption Over the Channel

In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feed-forward and feedback signals share the same noisy channel in the present model. Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting. More specifically, the discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that the judicious use of feedback increases the secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. In the half-duplex scheme, a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source. Finally, this scheme is extended to the continuous real valued modulo-Lambda channel where it is shown that the secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper.

Interference Alignment for Secrecy

This paper studies the frequency/time selective K-user Gaussian interference channel with secrecy constraints. Two distinct models, namely the interference channel with confidential messages and the interference channel with an external eavesdropper, are analyzed. The key difference between the two models is the lack of channel state information (CSI) of the external eavesdropper. Using interference alignment along with secrecy precoding, it is shown that each user can achieve non-zero secure degrees of freedom (DoF) for both cases. More precisely, the proposed coding scheme achieves [(K-2)/(2K-2)] secure DoF with probability one per user in the confidential messages model. For the external eavesdropper scenario, on the other hand, it is shown that each user can achieve [(K-2)/(2K)] secure DoF in the ergodic setting. Remarkably, these results establish the positive impact of interference on the secrecy capacity region of wireless networks.

The Water-Filling Game in Fading Multiple-Access Channels

A game-theoretic framework is developed to design and analyze the resource allocation algorithms in fading multiple-access channels (MACs), where the users are assumed to be selfish, rational, and limited by average power constraints. The maximum sum-rate point on the boundary of the MAC capacity region is shown to be the unique Nash equilibrium of the corresponding water-filling game. This result sheds a new light on the opportunistic communication principle. The base station is then introduced as a player interested in maximizing a weighted sum of the individual rates. A Stackelberg formulation is proposed in which the base station is the designated game leader. In this setup, the base station announces first its strategy defined as the decoding order of the different users, in the successive cancellation receiver, as a function of the channel state. In the second stage, the users compete conditioned on this particular decoding strategy. This formulation is shown to be able to achieve all the corner points of the capacity region, in addition to the maximum sum-rate point. On the negative side, it is shown that there does not exist a base station strategy in this formulation that achieves the rest of the boundary points. To overcome this limitation, a repeated game approach, which achieves the capacity region of the fading MAC, is presented. Finally, the study is extended to vector channels highlighting interesting differences between this scenario and the scalar channel case.

The three-node wireless network: achievable rates and Cooperation strategies

We consider a wireless network composed of three nodes and limited by the half-duplex and total power constraints. This formulation encompasses many of the special cases studied in the literature and allows for capturing the common features shared by them. Here, we focus on three special cases, namely, 1) relay channel, 2) multicast channel, and 3) three-way channel. These special cases are judicially chosen to reflect varying degrees of complexity while highlighting the common ground shared by the different variants of the three-node wireless network. For the relay channel, we propose a new cooperation scheme that exploits the wireless feedback gain. This scheme combines the benefits of the decode-and-forward (DF) and compress-and-forward (CF) strategies and avoids the noiseless feedback assumption adopted in earlier works. Our analysis of the achievable rate of this scheme reveals the diminishing feedback gain in both the low and high signal-to-noise ratio (SNR) regimes. Inspired by the proposed feedback strategy, we identify a greedy cooperation framework applicable to both the multicast and three-way channels. Our performance analysis reveals the asymptotic optimality of the proposed greedy approach and the central role of list source-channel decoding in exploiting the receiver side information in the wireless network setting.

Multicast Routing for Decentralized Control of Cyber Physical Systems with an Application in Smart Grid

In cyber physical systems, communication is needed for conveying sensor observations to controllers; thus, the design of the communication sub-system is of key importance for the stabilization of system dynamics. In this paper, multicast routing is studied for networking of decentralized sensors and controllers. The challenges of uncertain destinations and multiple routing modes, which are significantly different from traditional data networks, are addressed by employing the theories of hybrid systems and linear matrix inequalities, thus forming a novel framework for studying the communication sub-system in cyber physical systems. Both cases of neglible delay and non-negligible delay are discussed. The proposed framework is then applied in the context of voltage control in smart grid. Numerical simulations using a 4-bus power grid model show that the proposed framework and algorithm can effectively stabilize cyber physical systems.

A Unified Framework for Key Agreement Over Wireless Fading Channels

The problem of key generation over wireless fading channels is investigated. First, a joint source-channel approach that combines existing source and channel models for key agreement over wireless fading channels is developed. It is shown that, in general, to fully exploit the resources provided by time-varying channel gains, one needs to combine both the channel model, in which Alice sends a key to Bob over a wireless channel, and the source model, in which Alice and Bob generate a key by exploiting the correlated observations obtained from the wireless fading channel. Asymptotic analyses suggest that in the long coherence time regime, the channel model is asymptotically optimal. On the other hand, in the high power regime, the source model is asymptotically optimal. Second, the framework is extended to the scenario with an active attacker. Assuming that the goal of the attacker is to minimize the key rate that can be generated using the proposed protocol and the attacker will employ such an attack strategy, the attackers optimal attack strategy is identified and the key rate under this attack model is characterized.