Submodularity and Optimality of Fusion Rules in Balanced Binary Relay Trees

We study the distributed detection problem in a balanced binary relay tree, where the leaves of the tree are sensors generating binary messages. The root of the tree is a fusion center that makes the overall decision. Every other node in the tree is a fusion node that fuses two binary messages from its child nodes into a new binary message and sends it to the parent node at the next level. We assume that the fusion nodes at the same level use the same fusion rule. We call a string of fusion rules used at different levels a fusion strategy. We consider the problem of finding a fusion strategy that maximizes the reduction in the total error probability between the sensors and the fusion center. We formulate this problem as a deterministic dynamic program and express the solution in terms of Bellman's equations. We introduce the notion of stringsubmodularity and show that the reduction in the total error probability is a stringsubmodular function. Consequentially, we show that the greedy strategy, which only maximizes the level-wise reduction in the total error probability, is within a factor of the optimal strategy in terms of reduction in the total error probability

Detection Performance in Balanced Binary Relay Trees with Node and Link Failures

We study the distributed detection problem in the context of a balanced binary relay tree, where the leaves of the tree correspond to $N$ identical and independent sensors generating binary messages. The root of the tree is a fusion center making an overall decision. Every other node is a relay node that aggregates the messages received from its child nodes into a new message and sends it up toward the fusion center. We derive upper and lower bounds for the total error probability $P_N$ as explicit functions of $N$ in the case where nodes and links fail with certain probabilities. These characterize the asymptotic decay rate of the total error probability as $N$ goes to infinity. Naturally, this decay rate is not larger than that in the non-failure case, which is $\sqrt N$. However, we derive an explicit necessary and sufficient condition on the decay rate of the local failure probabilities $p_k$ (combination of node and link failure probabilities at each level) such that the decay rate of the total error probability in the failure case is the same as that of the non-failure case. More precisely, we show that $\log P_N^{-1}=\Theta(\sqrt N)$ if and only if $\log p_k^{-1}=\Omega(2^{k/2})$

Cooperative Detection and Network Coding in Wireless Networks

In cooperative communication systems, multiple terminals in wireless networks share their antennas and resources for information exchange and processing. Recently, cooperative communications have been shown to achieve significant performance improvements in terms of transmission reliability, coverage area extension, and network throughput, with respect to existing classical communication systems. This dissertation is focused on two important applications of cooperative communications, namely: (i) cooperative distributed detection in wireless sensor networks, and (ii) many-to-many communications via cooperative space-time network coding. The first application of cooperative communications presented in this dissertation is concerned with the analysis and modeling of the deployment of cooperative relay nodes in wireless sensor networks. Particularly, in dense wireless sensor networks, sensor nodes continuously observe and collect measurements of a physical phenomenon. Such observations can be highly correlated, depending on the spatial separation between the sensor nodes as well as how the physical properties of the phenomenon are evolving over time. This unique characteristic of wireless sensor networks can be effectively exploited with cooperative communications and relays deployment such that the distributed detection performance is significantly improved as well as the energy efficiency. In particular, this dissertation studies the Amplify-and-Forward (AF) relays deployment as a function of the correlation of the observations and analyzes the achievable spatial diversity gains as compared with the classical wireless sensor networks. Moreover, it is demonstrated that the gains of cooperation can be further leveraged to alleviate bandwidth utilization inefficiencies in current sensor networks. Specifically, the deployment of cognitive AF cooperative relays to exploit empty/under-utilized time-slots and the resulting energy savings are studied, quantified and compared. The multiple terminal communication and information exchange form the second application of cooperative communications in this dissertation. Specifically, the novel concept of Space-Time-Network Coding (STNC) that is concerned with formulation of the many-to-many cooperative communications over Decode-and-Forward (DF) nodes is studied and analyzed. Moreover, the exact theoretical analysis as well as upper-bounds on the network symbol error rate performance are derived. In addition, the tradeoff between the number of communicating nodes and the timing synchronization errors is analyzed and provided as a network design guideline. With STNC, it is illustrated that cooperative diversity gains are fully exploited per node and significant performance improvements are achieved. It is concluded that the STNC scheme serves as a potential many-to-many cooperative communications scheme and that its scope goes much further beyond the generic source-relay-destination communications

Distributed Detection and Estimation in Wireless Sensor Networks

In this article we consider the problems of distributed detection and estimation in wireless sensor networks. In the first part, we provide a general framework aimed to show how an efficient design of a sensor network requires a joint organization of in-network processing and communication. Then, we recall the basic features of consensus algorithm, which is a basic tool to reach globally optimal decisions through a distributed approach. The main part of the paper starts addressing the distributed estimation problem. We show first an entirely decentralized approach, where observations and estimations are performed without the intervention of a fusion center. Then, we consider the case where the estimation is performed at a fusion center, showing how to allocate quantization bits and transmit powers in the links between the nodes and the fusion center, in order to accommodate the requirement on the maximum estimation variance, under a constraint on the global transmit power. We extend the approach to the detection problem. Also in this case, we consider the distributed approach, where every node can achieve a globally optimal decision, and the case where the decision is taken at a central node. In the latter case, we show how to allocate coding bits and transmit power in order to maximize the detection probability, under constraints on the false alarm rate and the global transmit power. Then, we generalize consensus algorithms illustrating a distributed procedure that converges to the projection of the observation vector onto a signal subspace. We then address the issue of energy consumption in sensor networks, thus showing how to optimize the network topology in order to minimize the energy necessary to achieve a global consensus. Finally, we address the problem of matching the topology of the network to the graph describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Secrecy Constrained Distributed Inference in Wireless Sensor Networks

Comprised of a large number of low-cost, low-power, mobile and miniature sensors, wireless sensor networks are widely employed in many applications, such as environmental monitoring, health-care, and diagnostics of complex systems. In wireless sensor networks, the sensor outputs are transmitted across a wireless communication network to legitimate users such as fusion centers for final decision-making. Because of the wireless links across the network, the data are vulnerable to security breaches. For many applications, the data collected by local sensors are extremely sensitive, and care must be taken to prevent that information from being leaked to any malicious third parties, e.g., eavesdroppers. Eavesdropping is one of the most significant threats to wireless sensor networks, where local sensors are tapped by an eavesdropper in order to intercept information. I considered distributed inference in the presence of a global, greedy and informed eavesdropper who has access to all local node outputs rather than access. My goal is to develop secured distributed systems against eavesdropping attacks using a physical-layer security approach instead of cryptography techniques because of the stringent constraints on sensor networks energy and computational capability. The physical-layer security approach utilizes the characteristics of the physical layer, including transmission channels noises, and the information of the source. Additionally, physical-layer security for distributed inference is scalable due to the low computational complexity. I first investigate secrecy constrained distributed detection under both Neyman-Pearson and Bayesian frameworks. I analyze the asymptotic detection performance and proposed a novel way of analyzing the maximum performance trade-off using Kullback-Leibler divergence ratio between the fusion center and eavesdropper. Under the Neyman-Pearson framework, I show that the eavesdropper\u27s detection performance can be limited such that her decision-making is no better than random guessing; meanwhile, the detection performance at the fusion center is guaranteed at the prespecified level. Similar analyses and proofs are provided under the Bayesian framework, where it was shown that an eavesdropper can be constrained to an error probability level equal to her prior information. Additionally, I derive the asymptotic error exponent and show that asymptotic perfect secrecy and asymptotic perfect detection are possible by increasing the number of sensors under both frameworks if the fusion center has noiseless channels to the sensors. For secrecy constrained distributed estimation, I conducted similar analysis under both a classical setting and Bayesian setting. I derived the maximum achievable secrecy performance and show that under the condition that the eavesdropper has noisy channels and the fusion center has noiseless channels, both asymptotic perfect secrecy and asymptotic perfect estimation can be achieved under a classical setting. Similarly, under a Bayesian setting, I derived the performance trade-off using Fisher information ratio and show that the fusion center outperforms the eavesdropper significantly in the simulation section. Secrecy constrained in distributed inference with Rayleigh fading binary symmetric channel is considered as well. Similarly, I derive the maximum achievable secrecy performance ratio for both detection and estimation. The maximum achievable trade-off turns out to be almost the same in distributed estimation as in distributed detection. This suggests that a universal framework for generally structured inference problems are feasible. Further investigations are needed to justify this conjecture for more general applications

Adaptive remote visualization system with optimized network performance for large scale scientific data

This dissertation discusses algorithmic and implementation aspects of an automatically configurable remote visualization system, which optimally decomposes and adaptively maps the visualization pipeline to a wide-area network. The first node typically serves as a data server that generates or stores raw data sets and a remote client resides on the last node equipped with a display device ranging from a personal desktop to a powerwall. Intermediate nodes can be located anywhere on the network and often include workstations, clusters, or custom rendering engines. We employ a regression model-based network daemon to estimate the effective bandwidth and minimal delay of a transport path using active traffic measurement. Data processing time is predicted for various visualization algorithms using block partition and statistical technique. Based on the link measurements, node characteristics, and module properties, we strategically organize visualization pipeline modules such as filtering, geometry generation, rendering, and display into groups, and dynamically assign them to appropriate network nodes to achieve minimal total delay for post-processing or maximal frame rate for streaming applications. We propose polynomial-time algorithms using the dynamic programming method to compute the optimal solutions for the problems of pipeline decomposition and network mapping under different constraints. A parallel based remote visualization system, which comprises a logical group of autonomous nodes that cooperate to enable sharing, selection, and aggregation of various types of resources distributed over a network, is implemented and deployed at geographically distributed nodes for experimental testing. Our system is capable of handling a complete spectrum of remote visualization tasks expertly including post processing, computational steering and wireless sensor network monitoring. Visualization functionalities such as isosurface, ray casting, streamline, linear integral convolution (LIC) are supported in our system. The proposed decomposition and mapping scheme is generic and can be applied to other network-oriented computation applications whose computing components form a linear arrangement