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Based on Monte-Carlo integral, an efficient method of the discrete channel capacity estimation is proposed. Through the proposed method, the channel capacities with PSK and QAM input are obtained. Numerical results show that the proposed method can accurately estimate the constrained capacity with less computation, and that the PSK and QAM input-constrained capacities with the same modulation orders are approximately equal. The constrained capacity with uniform distribution input can be considered as the lower bound of channel capacity with QAM input.