Random discrete measure of the phase posterior pdf in turbo synchronization

In this paper we consider the iterative decoding of channels with strong phase noise. We propose to use a random discrete measure to estimate the phase posterior pdf given the past observations (forward pdf) and another random discrete measure to estimate the phase posterior pdf given the future observations (backward pdf). The particle filter algorithm is used to recursively generate the supports in the relevant phase space area and recursively update the weights associated to these supports. An estimation of the phase posterior pdf given all the past and future observations is then derived from the forward and backward measures. The relevance of our proposal is finally illustrated through simulation of binary LDPC codes and QPSK modulation over a severe Wiener-Levy phase noise with a standard deviation of π_Δ = 6 degrees. Our algorithm is compared with a forward-backward message passing algorithm performed over a trellis resulting from the discretization of the phase. The proposed algorithm leads to a a slight performance degradation compared to the optimal treillis based method.