Analytical Optimal Blocklength Allocation in Multiuser URLLC Networks with Individual Latency Constraints

In this paper, we focus on an ultra-reliable low latency communication (URLLC) scenario and investigate the multi-access services with individual latency constraints. More specifically, the wireless communications between the access point and multiple users are requested to be accomplished while satisfying different maximum allowed delays. Taking the finite blocklength (FBL) impacts into account, we model the individual latency constraints as diverse blocklength consumption limits for users and concentrate on a blocklength allocation problem minimizing the overall decoding error probability. Aiming at achieving the optimal blocklength design in an extremely efficient manner, we start with characterizing the optimal solution features and find out that the error probability derivatives in the optimal solution follow a stepwisely increasing manner. As a result, we are enabled to alternatively determine the derivative step levels for optimally solving the problem. Subsequently, an efficient algorithm is proposed for the optimal step level design and for recovering the optimal blocklength solution. The solution optimality is then verified via both theoretical discussions and numerical evaluations. In addition, our proposed analytical solution based on step level design has also been numerically confirmed with an extremely lower complexity, in comparison with the conventional convex optimization approach.