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The iterative demodulation and decoding algorithm introduced in 2005 by Colavolpe, Barbieri, and Caire to cope with channels affected by phase noise needs pilot symbols to bootstrap. However, pilot symbols reduce the spectral efficiency of the system and, consequently, system's throughput. The aim of this paper is to show that trellis-based demodulation can be used to bootstrap the iterative process without the need of pilot symbols. Also, the complexity issue of trellis-based demodulation is addressed in this paper. The result is that the performance of iterative demodulation and decoding after the iterations is virtually unaffected by complexity reduction, provided that the reduced-complexity demodulator guarantees cycle-slip-free operation. From the numerical results presented in this paper, we show that cycle-slip-free operation can be achieved with substantial complexity reduction also for phase noise …