This paper analyzes the performance of an intelligent reflecting surface (IRS)-aided short-packet communication system over Nakagami-m fading channels. In this system, the base station adopts non-orthogonal multiple access (NOMA) to transmit to a near user and a far user, and its transmission to the far user is aided by the IRS. Both continuous phase shifts (CPSs) and discrete phase shifts (DPSs) are considered for the IRS. By using order statistic and moment matching, we approximate the

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... end channel gain to follow the Gamma distribution and then derive the approximate closed-form expressions for the average block error rate (BLER) in the high signal-to-noise ratio (SNR) regime and then conduct a refifined analysis of the interplay among the minimum common blocklength, optimal power allocation, and the related parameters of IRS (e.g., the number of elements of the IRS) for achieving target BLERs at two users. Finally, numerical and simulation results demonstrate the accuracy of theoretical analysis. They also show that the IRS-aided short-packet NOMA system outperforms the system without IRS, and that DPSs with 3-bit quantization achieve a similar performance as the optimal CPSs.