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In this paper, we study joint iterative data detection and channel decoding under imperfect channel state information (CSI). We apply the Markov Chain Monte Carlo technique to generate a list of channel estimates (LCE) that maximizes the a posteriori probabilities of the transmitted data, given the received signal and the soft feedback from the channel decoder. The LCE is refined over each iteration of data detection and decoding to facilitate improved channel estimation and thus yields superior detection performance. It is shown that, even with a small list size, the proposed MCMC-LCE detector outperforms the coherent detector in which data detection is performed based on a single channel estimate (SCE). As opposed to the noncoherent detectors which impose stringent constraints on the fading distribution, the MCMC-LCE detector is applicable to general fading distributions. It also offers a low complexity that is linear in the coherent length of the channel and the list size.