Pseudo Prior Belief Propagation for densely connected discrete graphs

This paper proposes a new algorithm for the linear least squares problem where the unknown variables are constrained to be in a finite set. The factor graph that corresponds to this problem is very loopy; in fact, it is a complete bipartite graph. Hence, applying the Belief Propagation (BP) algorithm yields very poor results. The Pseudo Prior Belief Propagation (PPBP) algorithm is a variant of the BP algorithm that can achieve near maximum likelihood (ML) performance with low computational complexity. First, we use the minimum mean square error (MMSE) detection to yield a pseudo prior information on each variable. Next we integrate this information into a loopy Belief Propagation (BP) algorithm as a pseudo prior. We show that, unlike current paradigms, the Belief Propagation (BP) algorithm can be advantageous even for dense graphs with many short loops. The performance of the proposed algorithm is demonstrated on the MIMO detection problem based on simulation results.