  Many satellite communication systems operating today employ low cost
upconverters or downconverters which create phase noise. This noise can
severely limit the information rate of the system and pose a serious challenge
for the detection systems. Moreover, simple solutions for phase noise tracking
such as PLL either require low phase noise or otherwise require many pilot
symbols which reduce the effective data rate. In the last decade we have
witnessed a significant amount of research done on joint estimation and
decoding of phase noise and coded information. These algorithms are based on
the factor graph representation of the joint posterior distribution. The
framework proposed in [5], allows the design of efficient message passing
algorithms which incorporate both the code graph and the channel graph. The use
of LDPC or Turbo decoders, as part of iterative message passing schemes, allows
the receiver to operate in low SNR regions while requiring less pilot symbols.
In this paper we propose a multiple hypotheses algorithm for joint detection
and estimation of coded information in a strong phase noise channel. We also
present a low complexity mixture reduction procedure which maintains very good
accuracy for the belief propagation messages.
