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We present a joint phase estimation and decoding method for convolutional turbo codes in the presence of strong phase noise. In order to overcome the problem of phase ambiguity and cycle slips, a combined state-space model for the time varying phase and the component convolutional codes is introduced. The proposed algorithm uses a Gaussian sum approach to approximate the multimodal a posteriori probability density function (pdf) of the phase in a blind context. We compare our method to the well known alternative consisting in discretizing the phase.Monte-Carlo simulations for the turbo code used in the DVB-RCS standard show that the performances of the proposed scheme are close to decoding with perfect knowledge of the phase.