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Abstract A new demapper is presented for communication channels that can be modeled with data-dependent noise on the received symbols. This includes optical and satellite channels with various types of distortion. The demapper incorporates the covariance information of the received symbol clusters to capture noise variation across the constellation and any dependency between the in-phase and quadrature components. Two communication scenarios are considered, and it is shown that the demapper is advantageous when a system is dominated by distortion as opposed to thermal noise. Channel coding considerations are presented, and reductions up to 4 dB in the required SNR are achieved.