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.

翻译：本文研究了在短码长体制下，针对莱斯衰落信道的可重构智能表面（RIS）通信系统，给定信噪比和码率时最优码的译码错误概率下界。短码长是超可靠低延迟通信（URLLC）满足服务质量（QoS）严格要求的核心特征。采用球堆积技术推导主要结果，利用Wald序贯t检验引理和高斯-切比雪夫求积法得到下界的闭式表达式。数值结果验证了所提方法的有效性，并表明与Polyanskiy-Poor-Verdu（PPV）界相比，本文结果具有紧致性。