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28
Gaussian belief propagation solver for systems of linear equations
 in IEEE Int. Symp. on Inform. Theory (ISIT
, 2008
"... Abstract — The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation (GaBP) that does not involve direct matrix inversio ..."
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Cited by 20 (9 self)
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Abstract — The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation (GaBP) that does not involve direct matrix inversion. The iterative nature of our approach allows for a distributed messagepassing implementation of the solution algorithm. We also address some properties of the GaBP solver, including convergence, exactness, its maxproduct version and relation to classical solution methods. The application example of decorrelation in CDMA is used to demonstrate the faster convergence rate of the proposed solver in comparison to conventional linearalgebraic iterative solution methods. Solving a system of linear equations Ax = b is one of
Gaussian belief propagation based multiuser detection
 in IEEE Int. Symp. Inform. Theory (ISIT
, 2008
"... Abstract — In this work, we present a novel construction for solving the linear multiuser detection problem using the Gaussian Belief Propagation algorithm. Our algorithm yields an efficient, iterative and distributed implementation of the MMSE detector. Compared to our previous formulation, the new ..."
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Cited by 20 (14 self)
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Abstract — In this work, we present a novel construction for solving the linear multiuser detection problem using the Gaussian Belief Propagation algorithm. Our algorithm yields an efficient, iterative and distributed implementation of the MMSE detector. Compared to our previous formulation, the new algorithm offers a reduction in memory requirements, the number of computational steps, and the number of messages passed. We prove that a detection method recently proposed by Montanari et al. is an instance of ours, and we provide new convergence results applicable to both. I.
Linear Detection via Belief Propagation
 In the 45th Annual Allerton Conference on Communication, Control, and Computing, Allerton
"... Abstract — In this paper, the paradigm of linear detection is reformulated as a Gaussian belief propagation (GaBP) scheme, without resorting to direct matrix inversion. The derived iterative framework allows for a distributive messagepassing implementation of this important class of suboptimal tra ..."
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Cited by 16 (12 self)
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Abstract — In this paper, the paradigm of linear detection is reformulated as a Gaussian belief propagation (GaBP) scheme, without resorting to direct matrix inversion. The derived iterative framework allows for a distributive messagepassing implementation of this important class of suboptimal tractable estimators. The properties of GaBPbased linear detection are addressed, while its faster convergence, in comparison with conventional iterative solution methods, is demonstrated experimentally. I.
Large system analysis of linear multistage parallel interference cancellation
 IEEE Trans. Commun
, 2002
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Speed and accuracy comparison of techniques for multiuser detection in synchronous CDMA
 COMMUNICATIONS WITH THE IEEE VEHICULAR TECHNOLOGY SOCIETY. LEE FREITAG (M’88) RECEIVED THE B.S. AND M.S. DEGREES IN ELECTRICAL ENGINEERING FROM THE UNIVERSITY OF ALASKA, FAIRBANKS, IN 1986 AND
, 2004
"... In this letter, we compare the complexity and efficiency of several methods used for multiuser detection in a synchronous codedivision multipleaccess system. Various methods are discussed, including decisionfeedback (DF) detection, group decisionfeedback (GDF) detection, coordinate descent, qua ..."
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Cited by 11 (1 self)
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In this letter, we compare the complexity and efficiency of several methods used for multiuser detection in a synchronous codedivision multipleaccess system. Various methods are discussed, including decisionfeedback (DF) detection, group decisionfeedback (GDF) detection, coordinate descent, quadratic programming with constraints, spacealternating generalized EM (SAGE) detection, Tabu search, a Boltzmann machine detector, semidefinite relaxation, probabilistic data association (PDA), branch and bound (BBD), and the sphere decoding (SD) method. The efficiencies of the algorithms, defined as the probability of group detection error divided by the number of floating point computations, are compared under various situations. Of particular interest is the appearance of an “efficient frontier ” of algorithms, primarily composed of DF detector, GDF detector, PDA detector, the BBD optimal algorithm, and the SD method. The efficient frontier is the convex hull of algorithms as plotted on probability of error versus computational demands axes: algorithms not on this efficient frontier can be considered dominated by those that are.
Hidden convexity based near maximumlikelihood CDMA detection
 IN PROC. 39TH ANNU. CONF. INFORMATION SCIENCES SYSTEMS (CISS
, 2005
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Application of Computational Geometry to Multiuser Detection in CDMA
 IEEE Trans. Commun
, 2006
"... Abstract—The maximumlikelihood multiuser detection problem in codedivision multipleaccess is known to be an optimization problem with an objective function that is required to be optimized over a combinatorial decision region. Conventional suboptimal detectors relax the combinatorial decision reg ..."
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Cited by 5 (0 self)
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Abstract—The maximumlikelihood multiuser detection problem in codedivision multipleaccess is known to be an optimization problem with an objective function that is required to be optimized over a combinatorial decision region. Conventional suboptimal detectors relax the combinatorial decision region by a convex region, without altering the objective function to be optimized. We take an approach wherein the objective function is reduced to a form appropriate for the application of a polynomial complexity algorithm in computational geometry, while keeping the decision region combinatorial. The resulting detector allows a tradeoff between performance and computational complexity. The biterror rate performance of the detector has been found to be better than the decorrelator and the linear minimum meansquare error detectors, for the same level of complexity. Index Terms—Complexity, computational geometry (CG), multiuser detection (MUD), optimization methods. I.
Inference with Multivariate HeavyTails in Linear Models
"... Heavytailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closedform in graphical models which involve such heavytailed distributions. In this work, we propose a novel simple linear graphical model for independent lat ..."
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Cited by 4 (0 self)
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Heavytailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closedform in graphical models which involve such heavytailed distributions. In this work, we propose a novel simple linear graphical model for independent latent random variables, called linear characteristic model (LCM), defined in the characteristic function domain. Using stable distributions, a heavytailed family of distributions which is a generalization of Cauchy, Lévy and Gaussian distributions, we show for the first time, how to compute both exact and approximate inference in such a linear multivariate graphical model. LCMs are not limited to stable distributions, in fact LCMs are always defined for any random variables (discrete, continuous or a mixture of both). We provide a realistic problem from the field of computer networks to demonstrate the applicability of our construction. Other potential application is iterative decoding of linear channels with nonGaussian noise. 1
Multiuser detection using the Taguchi method for the DSCDMA systems
 IEEE Trans. Wireless Commun
"... Abstract—We study multiuser detection for directsequence codedivision multipleaccess systems in a multipath environment. Systems with unknown channel information are considered and the wellknown result for maximum likelihood multiuser detector is directly used in our work. Due to the high comput ..."
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Cited by 4 (2 self)
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Abstract—We study multiuser detection for directsequence codedivision multipleaccess systems in a multipath environment. Systems with unknown channel information are considered and the wellknown result for maximum likelihood multiuser detector is directly used in our work. Due to the high computational cost of the maximum likelihood detector, most existing works have investigated simplified, linearized, and/or suboptimal solutions that have less computational requirements. In our approach, we use the Taguchi method that involves the use of orthogonal arrays in estimating the gradient of the likelihood function. The Taguchi method has been widely used in experimental designs for problems with multiple parameters where the optimization of a cost function is required. In this work, we choose the likelihood function as the cost function in the Taguchi method. The use of the Taguchi method for multiuser detection is a novel idea, and it leads to efficient algorithms that can find a satisfactory solution by maximizing the likelihood function in a small number of iterations. One of the advantages of the present Taguchi method is that it is blind since no channel estimation is required to detect the transmitted data, which is not the case in many existing methods. Simulation results show that the Taguchi multiuser detector significantly outperforms the conventional receivers, is insensitive to initial values of parameters, and has performance close to that of minimum mean square error detectors and decorrelating detectors. In addition, our algorithm is suitable for parallel implementations. Index Terms—Directsequence codedivision multipleaccess (DSCDMA), maximum likelihood, multiuser detection, orthogonal
Generalized Feedback Detection for Spatial Multiplexing MultiAntenna Systems
"... Abstract — We present a unified detection framework for spatial multiplexing multipleinput multipleoutput (MIMO) systems by generalizing Heller’s classical feedback decoding algorithm for convolutional codes. The resulting generalized feedback detector (GFD) is characterized by three parameters: w ..."
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Cited by 3 (2 self)
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Abstract — We present a unified detection framework for spatial multiplexing multipleinput multipleoutput (MIMO) systems by generalizing Heller’s classical feedback decoding algorithm for convolutional codes. The resulting generalized feedback detector (GFD) is characterized by three parameters: window size, step size and branch factor. Many existing MIMO detectors are turned out to be special cases of the GFD. Moreover, different parameter choices can provide various performancecomplexity tradeoffs. The connection between MIMO detectors and tree search algorithms is also established. To reduce redundant computations in the GFD, a shared computation technique is proposed by using a tree data structure. Using a union bound based analysis of the symbol error rates, the diversity order and signaltonoise ratio (SNR) gain are derived analytically as functions of the three parameters; for example, the diversity order of the GFD varies between 1 and N. The complexity of the GFD varies between those of the maximumlikelihood (ML) detector and the zeroforcing decision feedback detector (ZFDFD). Extensive computer simulation results are also provided. Index Terms — MIMO, feedback decoding, decision feedback detector.