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This paper proposes two new types of maximum a posteriori probability (MAP) receivers for multiple-input-multiple-output and orthogonal frequency-division multiplexing mobile communications with a channel coding such as the low-density parity-check code. One proposed receiver employs the expectation-maximization algorithm so as to improve performance of approximated MAP detection. Differently from a conventional receiver employing the minimum mean-square estimation (MMSE) algorithm, it applies the recursive least squares (RLS) algorithm to the channel estimation in order to track a fast fading channel. For the purpose of further improvement, the other proposed receiver applies a new adaptive algorithm that can be derived from the message passing on factor graphs. The algorithm exploits all detected signals but one of targeted time, and can gain a considerable advantage over the MMSE and RLS. Computer simulations show that the first proposed receiver is superior in channel-tracking ability to the conventional receiver employing the MMSE. Furthermore, it is demonstrated that the second proposed receiver remarkably outperforms both the conventional and the first proposed ones.