Factor Graph Framework for Serially Concatenated Coded CPM with Limiter Phase Discriminator Receiver

The paper addresses the system with the serially concatenated coded CPM (SCCCPM) and the nonlinear limiter phase discriminator receiver. We develop the FG framework allowing the use of the SPA factor node marginalization rules involving canonical distributions with finite number of parameters. We show that the straightforward application of the traditional constellation space approach is intractable. We also show that the sampled signal space does not allow an application of the parametrized canonical distributions for the variable nodes densities. The solutions we suggest in the paper stands on using the sampled parametric (phase) space of the CPM for all SPA processing. We use the idea of the component modulo mean approximation for the canonical signal phase distributions. The modulo operations are applied only on component mean values. This keeps the update rules simple by avoiding the circular distortion of the Gaussian component densities while still capturing the circular nature of the modulo operations on the signal phase.