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We propose a maximum a posteriori probability (MAP) turbo equalizer based on the sliding-window multilevel Bahl-Cocke-Jelinek-Raviv algorithm. This scheme is suitable for simultaneous nonlinear and linear impairment mitigation in multilevel coded-modulation schemes with coherent detection. The proposed scheme employs large-girth quasicyclic LDPC codes as channel codes. We demonstrate the efficiency of this method in dealing with fiber nonlinearities by performing Monte Carlo simulations. In addition, we provide the experimental results that demonstrate the efficiency of this method in dealing with polarization mode dispersion. We also study the ultimate channel capacity limits, assuming an independent identically distributed source.