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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,doi:10.1109/isit.2008.4595311 dblp:conf/isit/ShentalSWBD08 fatcat:wzsru2pwtbbmba5thfezb2pmry