System and method for reproducing a carrier phase in optical communications

This embodiment of the invention provides a method to deal with cycle-slip for high-speed optical communications utilize any higher order multi-dimensional modulation formats, with respect to the angle skew and residual phase noise problem. Its embodiment, the slip process analyzer, the skew angle estimator, and using the phase noise variance estimator, carrier phase recovery for more accurate likelihood calculation on the basis of the high-order hidden Markov model (HMM) ( give a feed-forward soft-decision information of the CPE). Log likelihood calculation can be performed jointly in the dual polarization with a binding Markov state transition. Some embodiments use a kernel filter or particle filter for the log-likelihood calculations.