Finite Blocklength Error Probability Distribution for Designing Ultra Reliable Low Latency Systems

Future wireless systems are envisioned to support completely new use cases with extremely stringent requirements on both latency and reliability, e.g., Ultra-Reliable Low-Latency Communication. However, guaranteeing truly reliable services is quite challenging, much more under strict latency constraints. Notice that when it comes to reliability, the traditional approaches relying on average performance figures do not provide sufficient reliability guarantees. Instead, analyses/designs based on risk measures are more useful since they offer a more fine-grained probabilistic information of the system reliability. In this paper, we depart from novel information theory results on finite-blocklength (FB) coding, which characterize the error-latency trade-off under strict delay constraints, to highlight that the FB error probability is in fact a random variable in fading scenarios. Then, we provide accurate analytical approximations for the FB error probability distribution. This allows us to evaluate some well-known risk measures and, based on them, quantify the system reliability under strict latency constraints from different standpoints. We validate our results via simulation and provide numerical examples that illustrate, for instance, that two systems performing similar in terms of average reliability, may offer services with different risk perceptions.