An Application of Tree-Structured Expectation Propagation for Channel Decoding

Pablo M. Olmos, Luis Salamanca, Juan José Murillo-Fuentes, Fernando Pérez-Cruz

Abstract: We show an application of a tree structure for approximate inference in graphical models using the expectation propagation algorithm. These approximations are typically used over graphs with short-range cycles. We demonstrate that these approximations also help in sparse graphs with long-range loops, as the ones used in coding theory to approach channel capacity. For asymptotically large sparse graph, the expectation propagation algorithm together with the tree structure yields a completely disconnected approximation to the graphical model but, for for finite-length practical sparse graphs, the tree structure approximation to the code graph provides accurate estimates for the marginal of each variable. Furthermore, we propose a new method for constructing the tree structure on the fly that might be more amenable for sparse graphs with general factors.