  In this work, a new low complexity iterative algorithm for decoding data
transmitted over strong phase noise channels is presented. The algorithm is
based on the Sum & Product Algorithm (SPA) with phase noise messages modeled as
Tikhonov mixtures. Since mixture based Bayesian inference such as SPA, creates
an exponential increase in mixture order for consecutive messages, mixture
reduction is necessary. We propose a low complexity mixture reduction algorithm
which finds a reduced order mixture whose dissimilarity metric is
mathematically proven to be upper bounded by a given threshold. As part of the
mixture reduction, a new method for optimal clustering provides the closest
circular distribution, in Kullback Leibler sense, to any circular mixture. We
further show a method for limiting the number of tracked components and further
complexity reduction approaches. We show simulation results and complexity
analysis for the proposed algorithm and show better performance than other
state of the art low complexity algorithms. We show that the Tikhonov mixture
approximation of SPA messages is equivalent to the tracking of multiple phase
trajectories, or also can be looked as smart multiple phase locked loops (PLL).
When the number of components is limited to one the result is similar to a
smart PLL.
