Belief propagation (BP) and the concave convex procedure (CCCP) are bothmethods that utilize the Bethe free energy as a cost function and solveinformation processing tasks. We have developed a new algorithm that also usesthe Bethe free energy, but changes the roles of the master variables and theslave variables. This is called the Bowman-Levin (BL) approximation in thedomain of statistical physics. When we applied the BL algorithm to decode theGallager ensemble of short-length regular low-density parity check codes(LDPCC) over an additive white Gaussian noise (AWGN) channel, its averageperformance was somewhat better than that of either BP or CCCP. This impliesthat the BL algorithm can also be successfully applied to other problems towhich BP or CCCP has already been applied.
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