Merging Belief Propagation and the Mean Field Approximation: A Free\n Energy Approach

We present a joint message passing approach that combines belief propagation\nand the mean field approximation. Our analysis is based on the region-based\nfree energy approximation method proposed by Yedidia et al. We show that the\nmessage passing fixed-point equations obtained with this combination correspond\nto stationary points of a constrained region-based free energy approximation.\nMoreover, we present a convergent implementation of these message passing\nfixedpoint equations provided that the underlying factor graph fulfills certain\ntechnical conditions. In addition, we show how to include hard constraints in\nthe part of the factor graph corresponding to belief propagation. Finally, we\ndemonstrate an application of our method to iterative channel estimation and\ndecoding in an orthogonal frequency division multiplexing (OFDM) system.\n