Gaussian Belief Propagation Solver for Systems of Linear Equations

Details Gaussian Belief Propagation Solver for Systems of Linear Equations Gaussian Belief Propagation Solver for Systems of Linear Equations

2008-10-09

arxiv.org/abs/0810.1736v1

The 2008 IEEE International Symposium on Information Theory (ISIT 2008), Toronto, July 2008

Computer Science

Information Theory

5 pages, 2 figures, appeared in the 2008 IEEE International Symposium on Information Theory, Toronto, July 2008

Scientific paper

10.1109/ISIT.2008.4595311

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.

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