I. Introduction
In the 5th generation (5G) communication systems, there are diverse applications ranging from high data rate delay tolerant services to ultra-reliable and low-latency communications (URLLC) [1]. By achieving ultra-low end-to-end (E2E) delay and ultra-high reliability, URLLC lies the foundation for emerging latency-critical applications, such as factory automation, autonomous vehicles, and virtual/augmented reality [2]. Devices in these applications will generate some tasks that require to be processed within a short time. To reduce processing time at the local server of each device and to avoid delays in backhauls and core networks, mobile edge computing (MEC) is one promising solution [3]. However, when a task is packetized in a short packet and offloaded to a MEC server via a wireless link, the packet may be lost when the channel is in deep fading [4]. Besides, short blocklength channel codes will cause the none-zero decoding error rate, even for an arbitrarily high signal-to-noise ratio (SNR) [5], [6]. Thus, achieving ultra-high reliability and ultra-low latency is very challenging in MEC systems.