  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.
