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In this paper we derive the optimal detector for multilevel cell (MLC) flash memory channels with intercell interference (ICI). We start with the MLC channel model proposed by Dong et al. and just slightly alter the model to guarantee mathematical tractability of the optimal detectors (maximum likelihood and maximum a-posteriori sequence and symbol detectors). The optimal detector is obtained by computing branch metrics using Fourier transforms of analytically computable characteristic functions (corresponding to likelihood functions). We derive the detectors for both simple one-dimensional (1D) channel models and more realistic page-orientated two-dimensional (2D) channel models. Simulation results show that the hard-output bit error rate (BER) performance matches some previously known detectors, but that the soft-output detector outperforms previously known detectors by 0.35 dB.