Short-packet communications are applied to various scenarios where transmission covertness and reliability are crucial due to the open wireless medium and finite blocklength. Although intelligent reflection surface (IRS) has been widely utilized to enhance transmission covertness and reliability, the question of how many reflection elements at IRS are required remains unanswered, which is vital to system design and practical deployment. The inherent strong coupling exists between the transmission covertness and reliability by IRS, leading to the question of intractability. To address this issue, the detection error probability at the warder and its approximation are derived first to reveal the relation between covertness performance and the number of reflection elements. Besides, to evaluate the reliability performance of the system, the decoding error probability at the receiver is also derived. Subsequently, the asymptotic reliability performance in high covertness regimes is investigated, which provides theoretical predictions about the number of reflection elements at IRS required to achieve a decoding error probability close to 0 with given covertness requirements. Furthermore, Monte-Carlo simulations verify the accuracy of the derived results for detection (decoding) error probabilities and the validity of the theoretical predictions for reflection elements. Moreover, results show that more reflection elements are required to achieve high reliability with tighter covertness requirements, longer blocklength and higher transmission rates.

翻译：短包通信广泛应用于无线介质开放且块长有限的场景中，其中传输的隐蔽性和可靠性至关重要。尽管智能反射面已被广泛用于增强传输隐蔽性和可靠性，但IRS所需反射单元数量这一问题仍未得到解答，而这对于系统设计和实际部署至关重要。IRS对传输隐蔽性和可靠性的内在强耦合特性导致该问题难以处理。为解决此问题，首先推导了监测者的检测错误概率及其近似式，以揭示隐蔽性能与反射单元数量之间的关系。此外，为评估系统的可靠性性能，还推导了接收端的解码错误概率。随后，研究了高隐蔽性条件下的渐近可靠性性能，提供了在给定隐蔽性要求下，使解码错误概率趋近于0所需的IRS反射单元数量的理论预测。进一步，蒙特卡洛仿真验证了所推导的检测（解码）错误概率的准确性以及反射单元理论预测的有效性。结果表明，更严格的隐蔽性要求、更长的块长和更高的传输速率需要更多反射单元来实现高可靠性。