Short Frame Length Approximation for IRSA

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.