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In this paper, blind deconvolution is analysed in the context of high-order statistics, supposing that the transmitted signal is iid. A new statistical criterium defining the optimal deconvolution is proposed. This result is used to define the structure of the optimal equalizer for some specific communication systems, wherein predistortion is used in the transmitter. Comparative simulations point out that the criterium leads to new insights and more efficient techniques for coping with channel nonlinearities.