Networked Slepian-Wolf: theory, algorithms, and scaling laws

Consider a set of correlated sources located at the nodes of a network, and a set of sinks that are the destinations for some of the sources. The minimization of cost functions which are the product of a function of the rate and a function of the path weight is considered, for both the data-gathering scenario, which is relevant in sensor networks, and general traffic matrices, relevant for general networks. The minimization is achieved by jointly optimizing a) the transmission structure, which is shown to consist in general of a superposition of trees, and b) the rate allocation across the source nodes, which is done by Slepian-Wolf coding. The overall minimization can be achieved in two concatenated steps. First, the optimal transmission structure is found, which in general amounts to finding a Steiner tree, and second, the optimal rate allocation is obtained by solving an optimization problem with cost weights determined by the given optimal transmission structure, and with linear constraints given by the Slepian-Wolf rate region. For the case of data gathering, the optimal transmission structure is fully characterized and a closed-form solution for the optimal rate allocation is provided. For the general case of an arbitrary traffic matrix, the problem of finding the optimal transmission structure is NP-complete. For large networks, in some simplified scenarios, the total costs associated with Slepian-Wolf coding and explicit communication (conditional encoding based on explicitly communicated side information) are compared. Finally, the design of decentralized algorithms for the optimal rate allocation is analyzed

Data driven wireless network design : a multi-level modeling approach

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Information-theoretic limits of dense underwater networks

Information-theoretic throughput scaling laws are analyzed in an underwater acoustic network with n regularly located nodes on a unit square, in which both bandwidth and received signal power can be severely limited. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of n. We first characterize an attenuation parameter that depends on the frequency scaling as well as the transmission distance. In the dense network having unit area, a cut-set upper bound on the capacity scaling is then derived. We show that there exists either a bandwidth or a power limitation, or both, according to the path-loss attenuation regimes, thus yielding the upper bound that has three fundamentally different operating regimes. In the dense network, we also describe an achievable scheme based on the simple nearest-neighbor multi-hop transmission. The operating regimes that guarantee the order optimality are identified, where frequency scaling is instrumental towards achieving the order optimality in the regimes

Convergence Speed of the Consensus Algorithm with Interference and Sparse Long-Range Connectivity

We analyze the effect of interference on the convergence rate of average consensus algorithms, which iteratively compute the measurement average by message passing among nodes. It is usually assumed that these algorithms converge faster with a greater exchange of information (i.e., by increased network connectivity) in every iteration. However, when interference is taken into account, it is no longer clear if the rate of convergence increases with network connectivity. We study this problem for randomly-placed consensus-seeking nodes connected through an interference-limited network. We investigate the following questions: (a) How does the rate of convergence vary with increasing communication range of each node? and (b) How does this result change when each node is allowed to communicate with a few selected far-off nodes? When nodes schedule their transmissions to avoid interference, we show that the convergence speed scales with $r^{2-d}$, where $r$ is the communication range and $d$ is the number of dimensions. This scaling is the result of two competing effects when increasing $r$: Increased schedule length for interference-free transmission vs. the speed gain due to improved connectivity. Hence, although one-dimensional networks can converge faster from a greater communication range despite increased interference, the two effects exactly offset one another in two-dimensions. In higher dimensions, increasing the communication range can actually degrade the rate of convergence. Our results thus underline the importance of factoring in the effect of interference in the design of distributed estimation algorithms.Comment: 27 pages, 4 figure

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