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The effect of the phase noise on the performance of bandwidth-efficient coded modulation is studied. To this end, the average mutual information (AMI) for specific constellations such as 8-phase-shift keying and 16-quadrature amplitude modulation is calculated in the presence of carrier phase error caused by imperfect carrier tracking over an additive white Gaussian noise channel. The AMI not only quantifies the effect of the phase noise from an information-theoretic viewpoint, but also serves as an estimate for a permissible amount of the phase noise for a given signal-to-noise ratio. The bit-error rate (BER) performance of a near-optimal turbo trellis-coded modulation scheme is then investigated over such a channel. For this purpose, an optimal branch metric which best fits the channel characteristics is derived. Furthermore, simple branch metrics (referred to as suboptimal, simplified, and Gaussian metrics) are derived, which may offer the tradeoff between BER performance and computational complexity. Numerical analysis shows that a near-optimal coded-modulation scheme renders a transmission system more robust against phase noise than is the case with a conventional trellis-coded modulation scheme.