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157
Computation over MultipleAccess Channels
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2007
"... The problem of reliably reconstructing a function of sources over a multipleaccess channel is considered. It is shown that there is no sourcechannel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure ..."
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Cited by 139 (24 self)
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The problem of reliably reconstructing a function of sources over a multipleaccess channel is considered. It is shown that there is no sourcechannel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure of the channel probability transition matrix and the function are appropriately matched. Even when the channel and function are mismatched, these computation codes often outperform separationbased strategies. Achievable distortions are given for the distributed refinement of the sum of Gaussian sources over a Gaussian multipleaccess channel with a joint sourcechannel lattice code. Finally, computation codes are used to determine the multicast capacity of finite field multipleaccess networks, thus linking them to network coding.
Complexity in geometric sinr
 In MobiHoc
, 2007
"... In this paper we study the problem of scheduling wireless links in the geometric SINR model, which explicitly uses the fact that nodes are distributed in the Euclidean plane. We present the first NPcompleteness proofs in such a model. In particular, we prove two problems to be NPcomplete: Scheduli ..."
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Cited by 77 (2 self)
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In this paper we study the problem of scheduling wireless links in the geometric SINR model, which explicitly uses the fact that nodes are distributed in the Euclidean plane. We present the first NPcompleteness proofs in such a model. In particular, we prove two problems to be NPcomplete: Scheduling and OneShot Scheduling. The first problem consists in finding a minimumlength schedule for a given set of links. The second problem receives a weighted set of links as input and consists in finding a maximumweight subset of links to be scheduled simultaneously in one shot. In addition to the complexity proofs, we devise an approximation algorithm for each problem.
Toward a theory of innetwork computation in wireless sensor networks
 IEEE Communications Magazine
, 2006
"... Abstract — Sensor networks are not just data networks with sensors being the sources of data. Rather, they are often developed and deployed for a specific application, and the entire network operation is accordingly geared towards satisfying this application. For overall system efficiency, it may be ..."
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Cited by 77 (1 self)
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Abstract — Sensor networks are not just data networks with sensors being the sources of data. Rather, they are often developed and deployed for a specific application, and the entire network operation is accordingly geared towards satisfying this application. For overall system efficiency, it may be necessary for nodes to perform computations on data, as opposed to simply originating or forwarding data. Thus, the entire network can be viewed as performing an application specific distributed computation. The topic of this paper is to survey some lines of research which may be useful in developing a theory of innetwork computation, that aims to elucidate how a wireless sensor network should efficiently perform such distributed computation. We review several existing approaches to computation problems in network settings, with a particular emphasis on the communication aspect of computation. We begin by studying the basic twoparty communication complexity model and how to optimally compute functions of distributed inputs in this setting. We proceed to larger multihop networks, and study how blockcomputation and function structure can be exploited to provide greater computational throughput. We then consider distributed computation problems in networks subject to noise. Finally, we review some randomized gossip based approaches to computing aggregate functions in networks. These are diverse approaches spanning many different research communities, but together may find a role in the development of a more substantial theoretical foundation for sensor networks. I.
Capacity of Arbitrary Wireless Networks
, 2009
"... In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclide ..."
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Cited by 73 (7 self)
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In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclidean space. We consider the problem separately from the routing problem and the power control problem, i.e., all requests are singlehop, and all nodes transmit at a fixed power level. The existing solutions to this problem have either concentrated on specialcase topologies, or presented optimality guarantees which become arbitrarily bad (linear in the number of nodes) depending on the network’s topology. We propose the first scheduling algorithm with approximation guarantee independent of the topology of the network. The algorithm has a constant approximation guarantee for the problem of maximizing the number of links scheduled in one timeslot. Furthermore, we obtain a O(log n) approximation for the problem of minimizing the number of time slots needed to schedule a given set of requests. Simulation results indicate that our algorithm does not only have an exponentially better approximation ratio in theory, but also achieves superior performance in various practical network scenarios. Furthermore, we prove that the analysis of the algorithm is extendable to higherdimensional Euclidean spaces, and to more realistic boundeddistortion spaces, induced by nonisotropic signal distortions. Finally, we show that it is NPhard to approximate the scheduling problem to within n 1−ε factor, for any constant ε> 0, in the nongeometric SINR model, in which pathloss is independent of the Euclidean coordinates of the nodes.
Distributed function calculation via linear iterations in the presence of malicious agents – part I: Attacking the network,” in
 Proc. of the American Control Conference,
, 2008
"... AbstractGiven a network of interconnected nodes, each with its own value (such as a measurement, position, vote, or other data), we develop a distributed strategy that enables some or all of the nodes to calculate any arbitrary function of the node values, despite the actions of malicious nodes in ..."
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Cited by 66 (5 self)
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AbstractGiven a network of interconnected nodes, each with its own value (such as a measurement, position, vote, or other data), we develop a distributed strategy that enables some or all of the nodes to calculate any arbitrary function of the node values, despite the actions of malicious nodes in the network. Our scheme assumes a broadcast model of communication (where all nodes transmit the same value to all of their neighbors) and utilizes a linear iteration where, at each timestep, each node updates its value to be a weighted average of its own previous value and those of its neighbors. We consider a node to be malicious or faulty if, instead of following the predefined linear strategy, it updates its value arbitrarily at each timestep (perhaps conspiring with other malicious nodes in the process). We show that the topology of the network completely characterizes the resilience of linear iterative strategies to this kind of malicious behavior. First, when the network contains 2f or fewer vertexdisjoint paths from some node xj to another node xi, we provide an explicit strategy for f malicious nodes to follow in order to prevent node xi from receiving any information about xj 's value. Next, if node xi has at least 2f + 1 vertexdisjoint paths from every other (nonneighboring) node, we show that xi is guaranteed to be able to calculate any arbitrary function of all node values when the number of malicious nodes is f or less. Furthermore, we show that this function can be calculated after running the linear iteration for a finite number of timesteps (upper bounded by the number of nodes in the network) with almost any set of weights (i.e., for all weights except for a set of measure zero).
Distributed detection in sensor networks with packet losses and finite capacity links
 IEEE Transactions on Signal Processing
, 2006
"... We consider a multiobject detection problem over a sensor network (SNET) with limited range multimodal sensors. Limited range sensing environment arises in a sensing field prone to signal attenuation and path losses. The general problem complements the widely considered decentralized detection pro ..."
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Cited by 64 (5 self)
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We consider a multiobject detection problem over a sensor network (SNET) with limited range multimodal sensors. Limited range sensing environment arises in a sensing field prone to signal attenuation and path losses. The general problem complements the widely considered decentralized detection problem where all sensors observe the same object. In this paper we develop a distributed detection approach based on recent development of the false discovery rate (FDR) and the associated BH test procedure. The BH procedure is based on rank ordering of scalar test statistics. We first develop scalar test statistics for multidimensional data to handle multimodal sensor observations and establish its optimality in terms of the BH procedure. We then propose a distributed algorithm in the ideal case of infinite attenuation for identification of sensors that are in the immediate vicinity of an object. We demonstrate communication message scalability to large SNETs by showing that the upper bound on the communication message complexity scales linearly with the number of sensors that are in the vicinity of objects and is independent of the total number of sensors in the SNET. This brings forth an important principle for evaluating the performance of an SNET, namely, the need for scalability of communications and performance with respect to the number of objects or events in an SNET irrespective of the network size. We then account for finite attenuation by modeling sensor observations as corrupted by uncertain interference arising from distant objects and developing robust extensions to our idealized distributed scheme. The robustness properties ensure that both the error performance and communication message complexity degrade gracefully with interference. 1
Information Dissemination in Powerconstrained Wireless Networks
, 2006
"... Dissemination of common information through broadcasting is an integral part of wireless network operations such as query of interested events, resource discovery and code update. In this paper, we characterize the behavior of information dissemination in powerconstrained wireless networks by defin ..."
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Cited by 51 (2 self)
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Dissemination of common information through broadcasting is an integral part of wireless network operations such as query of interested events, resource discovery and code update. In this paper, we characterize the behavior of information dissemination in powerconstrained wireless networks by defining two quantities, i.e., broadcast capacity and information diffusion rate and derive fundamental limits in both random extended and dense networks. We find that using multihop relay, the rate of broadcasting continuous stream is Θ(log(n) − α 2) in extended networks; while direct singlehop broadcast is efficient for dense networks. Furthermore, regardless of the density, information can diffuse at constant speed, i.e., Θ(1) in both extended and dense networks. The theoretical bounds obtained and proof techniques are instrumental to the modeling and design of efficient wireless network protocols.
Distributed Function Calculation and Consensus Using Linear Iterative Strategies
, 2007
"... Given an arbitrary network of interconnected nodes, we develop and analyze a distributed strategy that enables a subset of the nodes to calculate any given function of the node values. Our scheme utilizes a linear iteration where, at each timestep, each node updates its value to be a weighted avera ..."
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Cited by 47 (12 self)
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Given an arbitrary network of interconnected nodes, we develop and analyze a distributed strategy that enables a subset of the nodes to calculate any given function of the node values. Our scheme utilizes a linear iteration where, at each timestep, each node updates its value to be a weighted average of its own previous value and those of its neighbors. We show that this approach can be viewed as a linear dynamical system, with dynamics that are given by the weight matrix of the linear iteration, and with outputs for each node that are captured by the set of values that are available to that node at each timestep. In networks with timeinvariant topologies, we use observability theory to show that after running the linear iteration for a finite number of timesteps with almost any choice of weight matrix, each node obtains enough information to calculate any arbitrary function of the initial node values. The problem of distributed consensus via linear iterations, where all nodes in the network calculate the same function, is treated as a special case of our approach. In particular, our scheme allows nodes in networks with timeinvariant topologies to reach consensus on any arbitrary function of the initial node values in a finite number of steps for almost any choice of weight matrix.
A Unifying Perspective on the Capacity of Wireless Ad Hoc
"... Abstract—We present the first unified modeling framework for the computation of the throughput capacity of random wireless ad hoc networks in which information is disseminated by means of unicast routing, multicast routing, broadcasting, or different forms of anycasting. We introduce (n, m, k)casti ..."
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Cited by 44 (14 self)
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Abstract—We present the first unified modeling framework for the computation of the throughput capacity of random wireless ad hoc networks in which information is disseminated by means of unicast routing, multicast routing, broadcasting, or different forms of anycasting. We introduce (n, m, k)casting as a generalization of all forms of onetoone, onetomany and manytomany information dissemination in wireless networks. In this context, n, m, and k denote the total number of nodes in the network, the number of destinations for each communication group, and the actual number of communicationgroup members that receive information (i.e., k ≤ m), respectively. We compute upper and lower bounds for the (n, m, k)cast throughput capacity in random wireless networks. When m = k = Θ(1), the resulting capacity equals the wellknown capacity result for multipair unicasting by Gupta and Kumar. We demonstrate that Θ(1 / √ mn log n) bits per second constitutes a tight bound for the capacity of multicasting (i.e., m = k < n) when m ≤ Θ (n/(log n)). We show that the multicast capacity of a wireless network equals its capacity for multipair unicasting when the number of destinations per multicast source is not a function of n. We also show that the multicast capacity of a random wireless ad hoc network is Θ (1/n), which is the broadcast capacity of the network, when m ≥ Θ(n / log n). Furthermore, we show that Θ ( √ m/(k √ n log n)), Θ(1/(k log n)) and Θ(1/n) bits per second constitutes a tight bound for the throughput capacity of multicasting (i.e., k < m < n) when Θ(1) ≤ m ≤ Θ (n / log n), k ≤ Θ (n / log n) ≤ m ≤ n and Θ (n / log n) ≤ k ≤ m ≤ n respectively.
Decentralized Detection in Wireless Sensor Networks with Channel Fading Statistics
 EURASIP J. Wirel. Commun. Netw
, 2007
"... Abstract—Distributed detection strategies for wireless sensor networks are studied under the assumption of spatially and temporally independent and identically distributed (i.i.d.) observations at the sensor nodes. Both intelligent (with knowledge of observation statistics) and dumb (oblivious of ..."
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Cited by 31 (2 self)
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Abstract—Distributed detection strategies for wireless sensor networks are studied under the assumption of spatially and temporally independent and identically distributed (i.i.d.) observations at the sensor nodes. Both intelligent (with knowledge of observation statistics) and dumb (oblivious of observation statistics) sensors are considered. Two types of communication channels are studied: a parallel access channel (PAC) in which each sensor has a dedicated additive white Gaussian noise (AWGN) channel to a decision center, and a multipleaccess channel (MAC) in which the decision center receives a coherent superposition of the sensor transmissions. Our results show that the MAC yields significantly superior detection performance for any network power constraint. For intelligent sensors, uncoded (finite duration) communication of local loglikelihood ratios over the MAC achieves the optimal error exponent of the centralized (noisefree channel) benchmark as the number of nodes increases, even with sublinear network power scaling. Motivated by this result, we propose a distributed detection strategy for dumb sensors—histogram fusion—in which each node appropriately quantizes its temporal data and communicates its type or histogram to the decision center. It is shown that uncoded histogram fusion over the MAC is also asymptotically optimal under sublinear network power scaling with an additional advantage: knowledge of observation statistics is needed only at the decision center. Histogram fusion achieves exponential decay in error probability with the number of nodes even under a finite total network power. In principle, a vanishing error probability at a slower subexponential rate can be attained even with vanishing total network power in the limit. These remarkable power/energy savings with the number of nodes are due to the inherent beamforming gain in the MAC. Index Terms—Distributed beamforming, distributed detection, energy efficiency, error exponents, low latency, types. I.