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The upper bound on bit error rate (BER) of a multiple-input multiple-output (MIMO) system with the serial concatenated bit-interleaved coded modulation (BICM) and linear dispersion code (LDC) is derived in this paper. This bound is evaluated based on the expurgated bound of BICM and the approach of moment generation function (MGF). Compared with simulated performance of the 16QAM Alamouti code (AC) and optimal QPSK LDC, this bound is tight in the range of medium to high signal-to-noise ratio (SNR). By utilizing the bound, we obtain the optimal choice of code rate and modulation size for fixed transmission rates in BICM-LDC MIMO system.