Probability of Error for Optimal Codes in a Reconfigurable Intelligent Surface Aided URLLC System

The lower bound on the decoding error probability for the optimal code given a signal-to-noise ratio and a code rate are investigated in this letter for the reconfigurable intelligent surface (RIS) communication system over a Rician fading channel at the short blocklength regime, which is the key characteristic of ultra-reliable low-latency communications (URLLC) to meet the need for strict adherence to quality of service (QoS) requirements. Sphere packing technique is used to derive our main results. The Wald sequential t-test lemma and the Gaussian-Chebyshev quadrature are the main tools to obtain the closed-form expression for the lower bound. Numerical results are provided to validate our results and demonstrate the tightness of our results compared to the Polyanskiy-Poor-Verdu (PPV) bound.