  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 address the properties of the GaBP solver,
including convergence, exactness, computational complexity, message-passing
efficiency and its relation to classical solution methods. We use numerical
examples and applications, like linear detection, to illustrate these
properties through the use of computer simulations. This empirical study
demonstrates the attractiveness (e.g., faster convergence rate) of the proposed
GaBP solver in comparison to conventional linear-algebraic iterative solution
methods.
