In this letter, we propose a short-frame (SF) approximation for the packet loss rate of Irregular Repetition Slotted ALOHA (IRSA) particularly suitable for very short frames, up to 50 slots. The reason for limiting the frame size is to allow low-latency communications, a typical requirement in Industrial Internet of Things (IIoT) applications. We extend the Error Floor approximation (EF) through a recursive evaluation of inter-related stopping sets (STs). The tighter approximation yields the user degree distribution that minimizes the packet loss rate (PLR). For a scenario with 10 slots and 5 users, the degree distribution optimized adopting the SF approximation results in a 20% lower PLR compared to the one optimized with the EF approximation.

中文翻译：

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IRSA 的短帧长近似

在这封信中，我们提出了不规则重复时隙 ALOHA (IRSA) 丢包率的短帧 (SF) 近似值，特别适用于非常短的帧，最多 50 个时隙。限制帧大小的原因是允许低延迟通信，这是工业物联网 (IIoT) 应用程序中的典型要求。我们通过对相互关联的停止集 (ST) 的递归评估来扩展误差层近似 (EF)。更严格的近似产生最小化丢包率 (PLR) 的用户度分布。对于具有 10 个时隙和 5 个用户的场景，与使用 EF 近似优化的度分布相比，采用 SF 近似优化的度分布导致 PLR 降低 20%。