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This note provides a detailed description and derivation of the domaindecomposition algorithm that appears in previous works by the author. Given alarge re-estimation problem, domain decomposition provides an iterative methodfor assembling Boltzmann distributions associated to small subproblems into anapproximation of the Bayesian posterior of the whole problem. The algorithm isamenable to using Boltzmann sampling to approximate these Boltzmanndistributions. In previous work, we have shown the capability of heuristicversions of this algorithm to solve LDPC decoding and circuit fault diagnosisproblems too large to fit on quantum annealing hardware used for sampling.Here, we rigorously prove soundness of the method.

A belief propagation algorithm based on domain decomposition