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545
Cooperative diversity in wireless networks: efficient protocols and outage behavior
 IEEE Trans. Inform. Theory
, 2004
"... Abstract—We develop and analyze lowcomplexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals’ relaying signals for one another. We outline several str ..."
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Cited by 1604 (30 self)
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Abstract—We develop and analyze lowcomplexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals’ relaying signals for one another. We outline several strategies employed by the cooperating radios, including fixed relaying schemes such as amplifyandforward and decodeandforward, selection relaying schemes that adapt based upon channel measurements between the cooperating terminals, and incremental relaying schemes that adapt based upon limited feedback from the destination terminal. We develop performance characterizations in terms of outage events and associated outage probabilities, which measure robustness of the transmissions to fading, focusing on the high signaltonoise ratio (SNR) regime. Except for fixed decodeandforward, all of our cooperative diversity protocols are efficient in the sense that they achieve full diversity (i.e., secondorder diversity in the case of two terminals), and, moreover, are close to optimum (within 1.5 dB) in certain regimes. Thus, using distributed antennas, we can provide the powerful benefits of space diversity without need for physical arrays, though at a loss of spectral efficiency due to halfduplex operation and possibly at the cost of additional receive hardware. Applicable to any wireless setting, including cellular or ad hoc networks—wherever space constraints preclude the use of physical arrays—the performance characterizations reveal that large power or energy savings result from the use of these protocols. Index Terms—Diversity techniques, fading channels, outage probability, relay channel, user cooperation, wireless networks. I.
Optimization Flow Control, I: Basic Algorithm and Convergence
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1999
"... We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm. In thi ..."
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Cited by 652 (62 self)
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We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using gradient projection algorithm. In this system sources select transmission rates that maximize their own benefits, utility minus bandwidth cost, and network links adjust bandwidth prices to coordinate the sources' decisions. We allow feedback delays to be different, substantial and timevarying, and links and sources to update at different times and with different frequencies. We provide asynchronous distributed algorithms and prove their convergence in a static environment. We present measurements obtained from a preliminary prototype to illustrate the convergence of the algorithm in a slowly timevarying environment.
The price of anarchy is independent of the network topology
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 2002
"... We study the degradation in network performance caused by the selfish behavior of noncooperative network users. We consider a model of selfish routing in which the latency experienced by network traffic on an edge of the network is a function of the edge congestion, and network users are assumed to ..."
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Cited by 205 (17 self)
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We study the degradation in network performance caused by the selfish behavior of noncooperative network users. We consider a model of selfish routing in which the latency experienced by network traffic on an edge of the network is a function of the edge congestion, and network users are assumed to selfishly route traffic on minimumlatency paths. The quality of a routing of traffic is measured by the sum of travel times, also called the total latency. The outcome of selfish routing—a Nash equilibrium—does not in general minimize the total latency; hence, selfish behavior carries the cost of decreased network performance. We quantify this degradation in network performance via the price of anarchy, the worstpossible ratio between the total latency of a Nash equilibrium and of an optimal routing of the traffic. We show the price of anarchy is determined only by the simplest of networks. Specifically, we prove that under weak hypotheses on the class of allowable edge latency functions, the worstcase ratio between the total latency of a Nash equilibrium and of a minimumlatency routing for any multicommodity flow network is achieved by a singlecommodity
Toeplitz and Circulant Matrices: A review
, 2001
"... The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of "finite section" Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simp ..."
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Cited by 103 (0 self)
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The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of "finite section" Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hopes of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. Acknowledgements The author gratefully acknowledges the assistance of Ronald M. Aarts of the Philips Research Labs in correcting many typos and errors in the 1993 revision, Liu Mingyu in pointing out errors corrected in the 1998 revision, Paolo Tilli of the Scuola Normale Superiore of Pisa for pointing out an incorrect corollary and providing the correction, and to David Neuho# of the University of Michigan for pointing out several typographical errors and some confusing notation. For corrections, comments, and improvements to the 2001 revision thanks are due to William Trench, John Dattorro, and Young HanKim. In particular, Trench brought the WielandtHo#man theorem and its use to prove strengthened results to my attention. Section 2.4 largely follows his suggestions, although I take the blame for any introduced errors. Contents 1
WalkSums and Belief Propagation in Gaussian Graphical Models
 Journal of Machine Learning Research
, 2006
"... We present a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose the correlation between each pair of variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edg ..."
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Cited by 95 (15 self)
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We present a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose the correlation between each pair of variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edgewise partial correlation coefficients. This representation holds for a large class of Gaussian graphical models which we call walksummable. We give a precise characterization of this class of models, and relate it to other classes including diagonally dominant, attractive, nonfrustrated, and pairwisenormalizable. We provide a walksum interpretation of Gaussian belief propagation in trees and of the approximate method of loopy belief propagation in graphs with cycles. The walksum perspective leads to a better understanding of Gaussian belief propagation and to stronger results for its convergence in loopy graphs.
Stopping set distribution of LDPC code ensembles
 IEEE Trans. Inform. Theory
, 2005
"... Abstract—Stopping sets determine the performance of lowdensity paritycheck (LDPC) codes under iterative decoding over erasure channels. We derive several results on the asymptotic behavior of stopping sets in Tannergraph ensembles, including the following. An expression for the normalized average ..."
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Cited by 63 (1 self)
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Abstract—Stopping sets determine the performance of lowdensity paritycheck (LDPC) codes under iterative decoding over erasure channels. We derive several results on the asymptotic behavior of stopping sets in Tannergraph ensembles, including the following. An expression for the normalized average stopping set distribution, yielding, in particular, a critical fraction of the block length above which codes have exponentially many stopping sets of that size. A relation between the degree distribution and the likely size of the smallest nonempty stopping set, showing that for a I
Priority Service and MaxMin Fairness
, 2003
"... We study a priority service where users are free to choose the priority of their traffic, but are charged accordingly by the network. We assume that each user chooses priorities to maximize its own net benefit, and model the resulting interaction among users as a noncooperative game. We show that t ..."
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Cited by 60 (1 self)
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We study a priority service where users are free to choose the priority of their traffic, but are charged accordingly by the network. We assume that each user chooses priorities to maximize its own net benefit, and model the resulting interaction among users as a noncooperative game. We show that there exists an unique equilibrium for this game and that in equilibrium the bandwidth allocation is weighted maxmin fair.
Curve Matching and Stereo Calibration
 Image and Vision Computing
, 1991
"... The topological obstacles to the matching of smooth curves in stereo images are shown to occur at epipolar tangencies. Such points are good matching primitives, even when the image curves correspond to smooth surface profiles. An iterative scheme for improving camera calibration based on these resul ..."
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Cited by 53 (0 self)
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The topological obstacles to the matching of smooth curves in stereo images are shown to occur at epipolar tangencies. Such points are good matching primitives, even when the image curves correspond to smooth surface profiles. An iterative scheme for improving camera calibration based on these results is derived and performance demonstrated on real data.