On Error Probability Analysis of Short-Packet Communications in Massive Internet of Things

In this paper, we present a novel reliability analysis of massive Internet of Things (IoT) connectivity in cellular networks. In massive IoT networks, IoT devices sporadically and unpredictably send short data packets to nearby base stations (BSs), potentially interfering with other IoT devices with whom they share the uplink channel. Assuming slotted ALOHA random access policy, we investigate the probability that an IoT device transmitting a short data packet is not decoded at the nearest BS under Nakagami fading. We derive error probability expressions combining the tools of finite block-length (FBL) information theory and stochastic geometry. Derived FBL-based results are confirmed by Monte Carlo simulations and further compared with the asymptotic expressions available in the previous studies that are obtained under assumption that a device transmits asymptotically long data packets. Numerical results confirm the accuracy of the obtained expressions and their applicability to the massive IoT system design and performance evaluation under a wide range of system parameters. For example, the matching between the values obtained by numerical integration and approximation results of the FBL error probability is in the range between 97.6-99.4 % for different choices of the parameters.