Analog Digital Belief Propagation

We introduce a message passing belief propagation (BP) algorithm for factor graph over linear models that uses messages in the form of Gaussian-like distributions. With respect to the regular Gaussian BP, the proposed algorithm adds two operations to the model, namely the wrapping and the discretization of variables. This addition requires the derivation of proper modifications of message representations and updating rules at the BP nodes. We named the new algorithm Analog-Digital-Belief-Propagation (ADBP). The ADBP allows to construct iterative decoders for mod-M ring encoders that have a complexity independent from the size M of the alphabets, thus yielding efficient decoders for very high spectral efficiencies.