Gaussian Belief Propagation Solver for Systems of Linear Equations

TL;DR

This paper introduces a Gaussian belief propagation method for solving linear systems that avoids matrix inversion, enabling distributed computation and demonstrating faster convergence in applications like CDMA.

Contribution

It presents a novel GaBP-based solver for linear equations that is distributed, convergent, and faster than traditional iterative methods.

Findings

Faster convergence in CDMA decorrelation tasks

Distributed message-passing implementation

Theoretical analysis of convergence and exactness

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 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.