Short-Packet Transmission in Irregular Repetition Slotted ALOHA System Over the Rayleigh Fading Channel

Random access systems are potential for Internet of Things in the future wireless communication network for its operational simplicity. Irregular repetition slotted ALOHA (IRSA) system is one of the high-efficiency random access systems. In this paper, performance analysis of the irregular repetition slotted ALOHA systems with short-packet, i.e. finite-blocklength, transmission for the quasi-static Rayleigh fading channel is given. A cumulative distribution function of signal-to-interference power ratio (SIR) is derived and thus a closed-form expression of an average packet error probability (PEP) at the SIR with short packets for the Rayleigh fading channel is given. The closed-form expression makes it possible to optimize the degree distributions at a specific blocklength in the sense that the systems give the maximum system load.