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4,976
Iterative (turbo) soft interference cancellation and decoding for coded CDMA
 IEEE Trans. Commun
, 1999
"... Abstract — The presence of both multipleaccess interference (MAI) and intersymbol interference (ISI) constitutes a major impediment to reliable communications in multipath codedivision multipleaccess (CDMA) channels. In this paper, an iterative receiver structure is proposed for decoding multiuse ..."
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Cited by 295 (15 self)
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Abstract — The presence of both multipleaccess interference (MAI) and intersymbol interference (ISI) constitutes a major impediment to reliable communications in multipath codedivision multipleaccess (CDMA) channels. In this paper, an iterative receiver structure is proposed for decoding multiuser information data in a convolutionally coded asynchronous multipath DSCDMA system. The receiver performs two successive softoutput decisions, achieved by a softinput softoutput (SISO) multiuser detector and a bank of singleuser SISO channel decoders, through an iterative process. At each iteration, extrinsic information is extracted from detection and decoding stages and is then used as a priori information in the next iteration, just as in Turbo decoding. Given the multipath CDMA channel model, a direct implementation of a slidingwindow SISO multiuser detector has a prohibitive computational complexity. A lowcomplexity SISO multiuser detector is developed based on a novel nonlinear interference suppression technique, which makes use of both soft interference cancellation and instantaneous linear minimum meansquare error filtering. The properties of such a nonlinear interference suppressor are examined, and an efficient recursive implementation is derived. Simulation results demonstrate that the proposed lowcomplexity iterative receiver structure for interference suppression and decoding offers significant performance gain over the traditional noniterative receiver structure. Moreover, at high signaltonoise ratio, the detrimental effects of MAI and ISI in the channel can almost be completely overcome by iterative processing, and singleuser performance can be approached. Index Terms — Coded CDMA, instantaneous MMSE filtering, multiuser detection, soft interference cancellation, Turbo processing.
Fading relay channels: Performance limits and spacetime signal design
 IEEE J. SELECT. AREAS COMMUN
, 2004
"... Cooperative diversity is a transmission technique where multiple terminals pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay ch ..."
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Cited by 269 (4 self)
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Cooperative diversity is a transmission technique where multiple terminals pool their resources to form a virtual antenna array that realizes spatial diversity gain in a distributed fashion. In this paper, we examine the basic building block of cooperative diversity systems, a simple fading relay channel where the source, destination and relay terminals are each equipped with single antenna transceivers. We consider three different TDMAbased cooperative protocols that vary the degree of broadcasting and receive collision. The relay terminal operates in either the amplifyandforward (AF) or decodeandforward (DF) modes. For each protocol, we study the ergodic and outage capacity behavior (assuming Gaussian code books) under the AF and DF modes of relaying. We analyze the spatial diversity performance of the various protocols and find that full spatial diversity (secondorder in this case) is achieved by certain protocols provided that appropriate power control is employed. Our analysis unifies previous results reported in the literature and establishes the superiority (both from a capacity as well as a diversity pointofview) of a new protocol proposed in this paper. The second part of the paper is devoted to (distributed) spacetime code design for fading relay channels operating in the AF mode. We show that the corresponding code design criteria consist of the traditional rank and determinant criteria for the case of colocated antennas as well as appropriate power control rules. Consequently spacetime codes designed for the case of colocated multiantenna channels can be used to realize cooperative diversity provided that appropriate power control is employed.
Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifolds
 Journal of Machine Learning Research
, 2003
"... The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation. ..."
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Cited by 260 (9 self)
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The problem of dimensionality reduction arises in many fields of information processing, including machine learning, data compression, scientific visualization, pattern recognition, and neural computation.
Nineteen Dubious Ways to Compute the Exponential of a Matrix
 SIAM Review
, 1978
"... Abstract. In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and efficienc ..."
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Cited by 240 (0 self)
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Abstract. In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and efficiency indicates that some of the methods are preferable to others but that none are completely satisfactory. Most of this paper was originally published in 1978. An update, with a separate bibliography, describes a few recent developments.
Shape fluctuations and random matrices
, 1999
"... We study a certain random growth model in two dimensions closely related to the onedimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the TracyWidom largest eigenvalue distribution for the Gaussian Uni ..."
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Cited by 235 (10 self)
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We study a certain random growth model in two dimensions closely related to the onedimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the TracyWidom largest eigenvalue distribution for the Gaussian Unitary Ensemble (GUE).
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative ..."
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Cited by 224 (14 self)
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The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NPhard, because it contains vector cardinality minimization as a special case. In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability, provided the codimension of the subspace is sufficiently large. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this preexisting concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization. We also discuss several algorithmic approaches to solving the norm minimization relaxations, and illustrate our results with numerical examples.
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 215 (31 self)
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A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combinatorial in nature, are there efficient methods for finding the sparsest solution? These questions have been answered positively and constructively in recent years, exposing a wide variety of surprising phenomena; in particular, the existence of easilyverifiable conditions under which optimallysparse solutions can be found by concrete, effective computational methods. Such theoretical results inspire a bold perspective on some important practical problems in signal and image processing. Several wellknown signal and image processing problems can be cast as demanding solutions of undetermined systems of equations. Such problems have previously seemed, to many, intractable. There is considerable evidence that these problems often have sparse solutions. Hence, advances in finding sparse solutions to underdetermined systems energizes research on such signal and image processing problems – to striking effect. In this paper we review the theoretical results on sparse solutions of linear systems, empirical
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join a ..."
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Cited by 214 (5 self)
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Motivated by applications to sensor, peertopeer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join and old nodes leave the network. Algorithms for such networks need to be robust against changes in topology. Additionally, nodes in sensor networks operate under limited computational, communication, and energy resources. These constraints have motivated the design of “gossip ” algorithms: schemes which distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm. Designing the fastest gossip algorithm corresponds to minimizing this eigenvalue, which is a semidefinite program (SDP). In general, SDPs cannot be solved in a distributed fashion; however, exploiting problem structure, we propose a distributed subgradient method that solves the optimization problem over the network. The relation of averaging time to the second largest eigenvalue naturally relates it to the mixing time of a random walk with transition probabilities derived from the gossip algorithm. We use this connection to study the performance and scaling of gossip algorithms on two popular networks: Wireless Sensor Networks, which are modeled as Geometric Random Graphs, and the Internet graph under the socalled Preferential Connectivity (PC) model.