Gaussian belief propagation solver for systems of linear equations

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 iter...

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Bibliographic Details
Published in2008 IEEE International Symposium on Information Theory pp. 1863 - 1867
Main Authors Shental, O., Siegel, P.H., Wolf, J.K., Bickson, D., Dolev, D.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.07.2008
Subjects
Equations
Iterative methods
Linear systems
Mathematical model
Probabilistic logic
Symmetric matrices
Vectors
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Summary: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 message-passing implementation of the solution algorithm. We also address some properties of the GaBP solver, including convergence, exactness, its max-product 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 linear-algebraic iterative solution methods.
ISBN:9781424422562
1424422566
ISSN:2157-8095
2157-8117
DOI:10.1109/ISIT.2008.4595311