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This paper considers coded modulation systems based on low-density parity-check (LDPC) codes of finite lengths. The union bounds are derived for the bit error probabilities of the maximum likelihood decoding over both additive white Gaussian noise (AWGN) and flat fading channels. The bounds are useful to compare LDPC coded modulation schemes employing different LDPC code ensembles, constellations and mappings. The bounds and simulation results demonstrate that there is a significant performance gap between the maximum likelihood decoding and the iterative sum-product decoding for short-length codes. For moderate-length codes, the performance of iterative systems with Gray mapping is closer to the bound at the interested bit error rate (BER) levels for data communications.