  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.
