This paper investigates the ultra reliable and low latency communication (URLLC) performance of the IRS-aided MIMO system. The upper and lower bounds of the optimal average error probability (OAEP) for the coding rate 1/sqrt(Mn) of the capacity are derived, where n and M represent the blocklength and the number of transmit antennas, respectively. To achieve this goal, a new central limit theorem (CLT) for the mutual information density over the IRS-aided MIMO system is derived in the asymptotic regime where the block-length, the IRS size, and number of the antennas go to infinity with the same pace. The CLT is then utilized to derive the closed form upper and lower bounds for the OAEP. Based on the analysis result, a gradient-based algorithm is proposed to minimize the lower bound of the OAEP by optimizing the phase shift of the IRS. Simulation results validate the fitness of the CLT and the effectiveness of the proposed algorithm in optimizing the theoretical bound, as well as the performance of practical LDPC code.

翻译：本文研究了IRS辅助MIMO系统的超可靠低延迟通信（URLLC）性能。推导了容量编码速率1/sqrt(Mn)对应的最优平均差错概率（OAEP）的上下界，其中n和M分别表示码长和发射天线数量。为实现此目标，在码长、IRS尺寸及天线数量以相同速度趋于无穷的渐近区域中，推导了IRS辅助MIMO系统互信息密度的新中心极限定理（CLT）。进而利用该CLT导出OAEP的闭式上下界。基于分析结果，提出一种梯度下降算法，通过优化IRS的相移来最小化OAEP下界。仿真结果验证了CLT的拟合度、所提算法优化理论界的有效性，以及实际LDPC码的性能表现。