An LDPCC decoding algorithm based on Bowman-Levin approximation

Belief propagation (BP) and the concave convex procedure (CCCP) are methods that can be used successfully to minimize the Bethe free energy of graphical models. The mechanisms of these methods, however, have not been well elucidated. We propose a method based on the Bowman-Levin (BL) approximation, which is another equation of the extrema of the Bethe free energy, so that we can compare the mechanisms of these methods and develop potentially better algorithms. We validated the BL algorithm through the decoding problem of low density parity check codes (LDPCC), and found that BL empirically ascends the Bethe free energy by means of simple iterated substitutions; BP and CCCP, on the other hand, descend the Bethe free energy. We also found that the gradient method causes BL to successfully converge.