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We propose the multilevel maximum a posteriori probability (MAP) detector suitable for use in polarization-multiplexed optical communications using multilevel modulation and coherent detection. The proposed multilevel MAP detection scheme considers two symbols transmitted over two orthogonal polarization states as a two-component symbol. We demonstrate experimentally that the proposed MAP scheme is effective in eliminating the bit-error-ratio (BER) floor phenomenon introduced by the conventional MAP equalizer, which considers the symbols transmitted over both polarizations independently. To improve further tolerance to optical fiber polarization-mode dispersion, we iterate extrinsic soft information between the MAP detector and soft-iterative decoder, in a turbo equalization fashion. Penalty of less than 1.5 dB at 20 Gb/s (and BER of 10-6 ) for differential group delay of 100 ps is reported.