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

TL;DR

This paper derives a lower bound on decoding error probability for optimal codes in RIS-assisted URLLC systems over Rician channels at short blocklengths, using sphere packing and statistical tools.

Contribution

It provides a novel closed-form lower bound on error probability for RIS-URLLC systems, validated against existing bounds and tailored for short blocklength regimes.

Findings

The derived bound is tight and close to the PPV bound.

Numerical results confirm the accuracy of the theoretical lower bound.

The analysis highlights the impact of RIS and channel conditions on error probability.

Abstract

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.