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We consider the problem of carrier phase estimation in a wireless digital receiver. Starting from a generic message passing framework, we derive an iterative algorithm which combines the Belief Propagation (BP) and the Mean Field (MF) approach for statistical inference. In particular, the computation of a soft phase estimate is based on MF, while BP is used for the derivation of a modified demapper which takes the phase uncertainty into account. Besides proposing an efficient phase estimator, this paper also serves as a demonstration of the practical relevance of algorithms that are rooted in multiple inference frameworks.