Reliable and Timely Short-Packet Communications in Joint Communication and Over-the-Air Computation Offloading Systems: Analysis and Optimization

Abstract

This paper addressed the trade-off between timeliness and reliability in joint communication and over-the-air computation offloading (JCACO) system under short-packet communications (SPCs). The inevitable decoding errors introduced by SPC lead to errors in the data aggregation process of over-the-air computation (AirComp). Due to limited resources, pursuing high reliability may prevent the JCACO system from meeting delay requirements, resulting in a trade-off between reliability and timeliness. To address this issue, this paper investigates the timeliness and reliability of the JCACO system. Specifically, the moment generating function method is used to derive the delay outage probability (DOP) of the JCACO system, and the outage probability of AirComp is calculated based on the errors that occur during its data aggregation process. The paper established an asymptotic relationship between blocklength, DOP, and AirComp outage probability (AOP). To balance timeliness and reliability, an AOP minimization problem is formulated under constraints of delay, queue stability, and limited resources based on computation offloading strategies and beamformer design. To overcome the issues of slow convergence and susceptibility to local optima in traditional algorithms, this paper proposed a stochastic successive mean-field game (SS-MFG) algorithm. This algorithm utilizes stochastic continuous convex approximation methods to leverage Nash equilibria among different users, achieving faster convergence to the global optimal solution. Numerical results indicate that SS-MFG reduces AOP by up to 60%, offering up to a 20% improvement in optimization performance compared to other algorithms while also converging faster.