On the Convexity of Energy-Efficient Packet Scheduling Problem with Finite Blocklength Codes

This paper considers an energy-efficient packet scheduling problem over green data networks, aiming at minimizing the transmission energy subject to the First-In-First-Out and strict delay constraints. Traditionally, such a problem is studied based on the classical Shannon capacity formula. However, Shannon capacity is valid only when the code blocklength approaches infinity and therefore is not practical for some applications in 5G system which allow short delays only. In this paper, we formulate the packet scheduling problem using the recently developed channel capacity formula for the finite blocklength code. It turns out that the newly formulated problem is much more challenging to solve than the traditional ones. Nevertheless, we analytically show that our scheduling problem can possess certain desirable monotonic and convex properties. Based on these properties, by applying a successive upper bound minimization (SUM) method, an iterative packet scheduling algorithm is proposed to efficiently solve the considered problem. Simulation results show that, compared with the proposed design using the finite blocklength channel capacity, the traditional design based on Shannon capacity will seriously underestimate the required transmission energy for reliable communications.