Summary: As many coded systems operate at very low signal-to-noise ratios, synchronization becomes a very difficult task. In many cases, conventional algorithms will either require long training sequences or result in large BER degradations. By exploiting code properties, these problems can be avoided. In this contribution, we present several iterative maximum-likelihood (ML) algorithms for joint carrier phase estimation and ambiguity resolution. These algorithms operate on coded signals by accepting soft information from the MAP decoder. Issues of convergence and initialization are addressed in detail. Simulation results are presented for turbo codes, and are compared to performance results of conventional algorithms. Performance comparisons are carried out in terms of BER performance and mean square estimation error (MSEE). We show that the proposed algorithm reduces the MSEE and, more importantly, the BER degradation. Additionally, phase ambiguity resolution can be performed without resorting to a pilot sequence, thus improving the spectral efficiency.