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77
Broadcast gossip algorithms for consensus
 IEEE TRANS. SIGNAL PROCESS
, 2009
"... Motivated by applications to wireless sensor, peertopeer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and computing in an arbitrarily connected network of nodes. Specifically, we study a broadcastingbased gossiping algorithm to compute the (possib ..."
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Cited by 93 (7 self)
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Motivated by applications to wireless sensor, peertopeer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and computing in an arbitrarily connected network of nodes. Specifically, we study a broadcastingbased gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcast gossip algorithm converges almost surely to a consensus. We prove that the random consensus value is, in expectation, the average of initial node measurements and that it can be made arbitrarily close to this value in mean squared error sense, under a balanced connectivity model and by trading off convergence speed with accuracy of the computation. We provide theoretical and numerical results on the mean square error performance, on the convergence rate and study the effect of the “mixing parameter ” on the convergence rate of the broadcast gossip algorithm. The results indicate that the mean squared error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithm to achieve a given distance to consensus through theoretical and numerical results.
Decentralized maximum likelihood estimation for sensor networks composed of nonlinearly coupled dynamical systems
 IEEE Trans. Signal Process
, 2007
"... Abstract—In this paper, we propose a decentralized sensor network scheme capable to reach a globally optimum maximumlikelihood (ML) estimate through selfsynchronization of nonlinearly coupled dynamical systems. Each node of the network is composed of a sensor and a firstorder dynamical system ini ..."
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Cited by 29 (2 self)
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Abstract—In this paper, we propose a decentralized sensor network scheme capable to reach a globally optimum maximumlikelihood (ML) estimate through selfsynchronization of nonlinearly coupled dynamical systems. Each node of the network is composed of a sensor and a firstorder dynamical system initialized with the local measurements. Nearby nodes interact with each other exchanging their state value, and the final estimate is associated to the state derivative of each dynamical system. We derive the conditions on the coupling mechanism guaranteeing that, if the network observes one common phenomenon, each node converges to the globally optimal ML estimate. We prove that the synchronized state is globally asymptotically stable if the coupling strength exceeds a given threshold. Acting on a single parameter, the coupling strength, we show how, in the case of nonlinear coupling, the network behavior can switch from a global consensus system to a spatial clustering system. Finally, we show the effect of the network topology on the scalability properties of the network, and we validate our theoretical findings with simulation results. Index Terms—Distributed consensus, distributed estimation, dynamical systems, sensor networks. I.
A Distributed Minimum Variance Estimator for Sensor Networks
"... Abstract—A distributed estimation algorithm for sensor networks is proposed. A noisy timevarying signal is jointly tracked by a network of sensor nodes, in which each node computes its estimate as a weighted sum of its own and its neighbors’ measurements and estimates. The weights are adaptively up ..."
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Cited by 25 (4 self)
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Abstract—A distributed estimation algorithm for sensor networks is proposed. A noisy timevarying signal is jointly tracked by a network of sensor nodes, in which each node computes its estimate as a weighted sum of its own and its neighbors’ measurements and estimates. The weights are adaptively updated to minimize the variance of the estimation error. Both estimation and the parameter optimization is distributed; no central coordination of the nodes is required. An upper bound of the error variance in each node is derived. This bound decreases with the number of neighboring nodes. The estimation properties of the algorithm are illustrated via computer simulations, which are intended to compare our estimator performance with distributed schemes that were proposed previously in the literature. The results of the paper allow to tradingoff communication constraints, computing efforts and estimation quality for a class of distributed filtering problems.
Average TimeSynch: a consensusbased protocol for clock synchronization in wireless sensor networks
, 2011
"... This paper describes a new consensusbased protocol, referred to as Average TimeSync (ATS), for synchronizing the clocks of a wireless sensor network. This algorithm is based on a cascade of two consensus algorithms, whose main task is to average local information. The proposed algorithm has the adv ..."
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Cited by 24 (1 self)
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This paper describes a new consensusbased protocol, referred to as Average TimeSync (ATS), for synchronizing the clocks of a wireless sensor network. This algorithm is based on a cascade of two consensus algorithms, whose main task is to average local information. The proposed algorithm has the advantage of being totally distributed, asynchronous, robust to packet drop and sensor node failure, and it is adaptive to timevarying clock drifts and changes of the communication topology. In particular, a rigorous proof of convergence to global synchronization is provided in the absence of process and measurement noise and of communication delay. Moreover, its effectiveness is shown through a number of experiments performed on a real wireless sensor network.
Zeroerror function computation in sensor networks
 In To appear in Proceedings of the 48th IEEE Conference on Decision and Control (CDC
, 2009
"... Abstract — We consider the problem of data harvesting in wireless sensor networks. A designated collector node seeks to compute a function of the sensor measurements. For a directed graph G = (V,E) on the sensor nodes, we wish to determine the optimal encoders on each edge which achieve zeroerror b ..."
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Cited by 22 (8 self)
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Abstract — We consider the problem of data harvesting in wireless sensor networks. A designated collector node seeks to compute a function of the sensor measurements. For a directed graph G = (V,E) on the sensor nodes, we wish to determine the optimal encoders on each edge which achieve zeroerror block computation of the function at the collector node. Our goal is to characterize the rate region in R E . We start with the two node problem, and determine a necessary and sufficient condition for the encoder that yields the optimal alphabet, from which we then calculate the minimum worst case and average case complexity. We then extend this result to trees and derive a necessary and sufficient condition for the encoder on each edge. The further extension of these results to directed acyclic graphs is not immediate. We provide an outer bound on the rate region by finding the disambiguation requirements for each cut, and describe examples where this outer bound is tight. Finally, we consider a collocated network of nodes with a specified order of transmission. We determine a necessary and sufficient condition for each encoder which is based on the transmissions received, and show that the average case complexity of computing a typethreshold function is Θ(1), in comparison to the worst case complexity of Θ(logn). I.
Cascade multiterminal source coding
 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY. AUTHORIZED LICENSED USE LIMITED TO: STANFORD UNIVERSITY. DOWNLOADED ON MARCH 02,2010 AT 16:56:04 EST FROM IEEE XPLORE. RESTRICTIONS APPLY
, 2009
"... We investigate distributed source coding of two correlated sources X and Y where messages are passed to a decoder in a cascade fashion. The encoder of X sends a message at rate R 1 to the encoder of Y. The encoder of Y then sends a message to the decoder at rate R 2 based both on Y and on the messa ..."
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Cited by 22 (6 self)
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We investigate distributed source coding of two correlated sources X and Y where messages are passed to a decoder in a cascade fashion. The encoder of X sends a message at rate R 1 to the encoder of Y. The encoder of Y then sends a message to the decoder at rate R 2 based both on Y and on the message it received about X. The decoder's task is to estimate a function of X and Y. For example, we consider the minimum mean squarederror distortion when encoding the sum of jointly Gaussian random variables under these constraints. We also characterize the rates needed to reconstruct a function of X and Y losslessly. Our general contribution toward understanding the limits of the cascade multiterminal source coding network is in the form of inner and outer bounds on the achievable rate region for satisfying a distortion constraint for an arbitrary distortion function d(x, y, z). The inner bound makes use of a balance between two encoding tacticsrelaying the information about X and recompressing the information about X jointly with Y. In the Gaussian case, a threshold is discovered for identifying which of the two extreme strategies optimizes the inner bound. Relaying outperforms recompressing the sum at the relay for some rate pairs if the variance of X is greater than the variance of Y.
Scaling bounds for function computation over large networks
 in Information Theory, IEEE Intl. Symposium on
, 2007
"... Abstract — We develop order bounds on the refresh rate of computing two classes of functions over large multihop sensor networks – namely, typethreshold (e.g. max) and typesensitive functions (e.g. average). The refresh rate quantifies how often the function can be recomputed with new data at se ..."
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Cited by 18 (2 self)
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Abstract — We develop order bounds on the refresh rate of computing two classes of functions over large multihop sensor networks – namely, typethreshold (e.g. max) and typesensitive functions (e.g. average). The refresh rate quantifies how often the function can be recomputed with new data at sensor nodes. We first show that for typethreshold functions optimal refresh rate of Θ(1) is possible over networks whose connectivity graphs have finite degree. Next, even for a simple representative typesensitive function, we show that the maximum refresh rate that can be achieved in a wide class of networks of n nodes with any multihop digital communication scheme is at most Θ(1 / log n), if the goal is to compute the function with deterministic guarantees. On the other hand, we show that relaxing the requirements to allow probabilistic guarantees enables a refresh rate of Θ(1) over any graph with bounded degree and a refresh rate of Θ(1/log log n) for random planar networks. Further, for such networks operating over an AWGN channel with signal power pathloss, we show that even refresh rate of Θ(1) can be achieved with vanishing distortion when the power pathloss exponent is strictly less than 4. Thus, relaxing deterministic computation guarantees to probabilistic requirements enables sizeable improvement in refresh rates. I.
RFIDbased networks  exploiting diversity and redundancy
 IN WINGS LAB TECHNICAL REPORT
, 2006
"... In this article, we outline a research agenda for developing protocols and algorithms for densely populated RFID based systems covering a wide geographic area. This will need multiple readers collaborating to read RFID tag data. We consider cases where the tag data is used for identification, or for ..."
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Cited by 14 (1 self)
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In this article, we outline a research agenda for developing protocols and algorithms for densely populated RFID based systems covering a wide geographic area. This will need multiple readers collaborating to read RFID tag data. We consider cases where the tag data is used for identification, or for sensing environmental parameters. We address performance issues related to accuracy and efficiency in such systems by exploiting diversity and redundancy. We discuss how tag multiplicity can be used to improve accuracy. In a similar fashion, we explore how reader diversity, achieved by using multiple readers with potentially partially overlapping coverage areas, can be exploited to improve accuracy and efficiency. Finally, we show how multiple antennas in a reader can be used to improve accuracy and access rates by utilizing antenna diversity. RFID tag/sensor data can be highly redundant for the purpose of answering a higher level query. For example, often the higher level query needs to compute a statistic or a function on the sensory data obtained by the RFID sensors, and does not need all the individual sensor readings. We outline the need for efficient tagtoreader communication, and readertoreader coordination effectively compute such functions at low overhead.
Resilient asymptotic consensus in robust networks
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2013
"... This paper addresses the problem of resilient innetwork consensus in the presence of misbehaving nodes. Secure and faulttolerant consensus algorithms typically assume knowledge of nonlocal information; however, this assumption is not suitable for largescale dynamic networks. To remedy this, we foc ..."
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Cited by 13 (6 self)
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This paper addresses the problem of resilient innetwork consensus in the presence of misbehaving nodes. Secure and faulttolerant consensus algorithms typically assume knowledge of nonlocal information; however, this assumption is not suitable for largescale dynamic networks. To remedy this, we focus on local strategies that provide resilience to faults and compromised nodes. We design a consensus protocol based on local information that is resilient to worstcase security breaches, assuming the compromised nodes have full knowledge of the network and the intentions of the other nodes. We provide necessary and sufficient conditions for the normal nodes to reach asymptotic consensus despite the influence of the misbehaving nodes under different threat assumptions. We show that traditional metrics such as connectivity are not adequate to characterize the behavior of such algorithms, and develop a novel graphtheoretic property referred to as network robustness. Network robustness formalizes the notion of redundancy of direct information exchange between subsets of nodes in the network, and is a fundamental property for analyzing the behavior of certain distributed algorithms that use only local information.
Broadcast gossip algorithms
 in Proc. IEEE Information Theory Workshop (ITW
"... Abstract—Motivated by applications to wireless sensor, peertopeer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and for computing in an arbitrarily connected network of nodes. Specifically, we propose a broadcastingbased gossiping algorithm to comput ..."
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Cited by 13 (2 self)
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Abstract—Motivated by applications to wireless sensor, peertopeer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and for computing in an arbitrarily connected network of nodes. Specifically, we propose a broadcastingbased gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcast gossip algorithms almost surely converge to a consensus. In addition, the random consensus value is, in expectation, equal to the desired value, i.e., the average of initial node measurements. However, the broadcast gossip algorithms do not converge to the initial average in absolute sense because of the fact that the sum is not preserved at every iteration. We provide theoretical results on the mean square error performance of the broadcast gossip algorithms. The results indicate that the mean square error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithms to achieve a given distance to consensus through numerical simulations. Index Terms—Distributed average consensus, broadcasting, sensor networks, gossip algorithms. I.