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Application of multi-level coded modulation (MLCM) for 16-ary constellations in coherent systems is studied. An MLCM system with Reed-Solomon component codes and multi-stage decoder is considered. A systematic numerical method for finding set-partitioning and optimal code rates is presented. The method only requires the probability density function of received samples and can be applied to any constellation regardless of irregularity or lack of symmetry. Performance of the designed MLCM system is verified in presence of nonlinear phase noise and normal phase noise. For nonlinear phase noise limited system, it is shown that the block error rate (BLER) of the system can be improved using our approach for set-partitioning. For phase noise limited system, both BLER and bit error rate (BER) are studied for a phase noise optimized and square 16-quadrature amplitude modulation (16QAM). Post forward-error correction (FEC) BER performance of the optimized constellation over square 16QAM is studied for different levels of phase noise. It is shown that the optimized constellation along with MLCM system decreases the required signal-to-noise ratio by several dB at high phase noise regime and low post FEC BER.