Analog Digital Belief Propagation: From theory to practice

We introduce a novel message passing (BP) algorithm, named Analog-Digital Belief Propagation (ADBP). The algorithm works with factor graph over linear models and uses messages in a particular class of parameterized Gaussian-like distributions by tracking their parameters. With respect to the regular Gaussian BP, this algorithm adds two operations to the factor graph, namely the wrapping and the discretization of variables. This addition allows to use ADBP to construct iterative decoders for mod-M ring encoders that have a complexity independent from the size of the alphabets, thus opening the possibility to construct efficient decoders for systems with unbounded spectral efficiencies. In this paper we derive the updating rules of ADBP and show some possible simplifications of them that make ADBP suitable for implementation in practical systems.