## 1 Introduction  
Mobile Edge Computing (MEC) has been recognized as a key enabling technology supporting ultra-reliable and latency-sensitive applications in the future Sixth-Generation Mobile Networks (6G) [1, 2], such as autonomous driving [3], simultaneous localization and mapping [4], intelligent manufacturing [5], and unmanned aerial vehicle [6]. For instance, in autonomous driving, vehicles need to promptly transmit and process real-time data from various sources, including sensors on vehicles and other roadside servers, to achieve comprehensive awareness of the road environment and make reliable decisions for the following actions. Since vehicles may travel at high speeds, the process needs to be completed within tens of milliseconds and with high reliability. Considering the limited performance and resources of User Equipment (UE), and dynamic wireless channels, Ultra-Reliable Low-Latency Communications (URLLC) in MEC networks is challenging. In the MEC network, an edge server typically serves multiple UEs. Given the finite communication and computation resources, there is often competition among UEs. Therefore, offloading decisions and resource allocation impact system performance and should be taken into account during system design [7, 8, 9, 10, 11, 12]. In [7, 8], the authors optimize latency in the MEC network by controlling the offloading strategy and power allocation. In addition to making an offloading decision, the authors in [9] allocate the CPU frequency of the MEC server and assign wireless bandwidth for the transmission. The work in [10] provides an optimal design to minimize the overall error probability by server selection and time allocation. The authors of [11] introduce a fast futures-enabled resource trading mechanism to determine optimal transmission power and further propose a hybrid market approach that integrates futures and spot trading to facilitate resource trading in [12]. However, all of these studies are based on the assumption of infinite blocklength, which means the transmission of data packets is considered arbitrarily reliable at Shannon's capacity. To meet low latency requirements, data packets wirelessly uploading/offloading in MEC networks are more likely to operate via short block codes, so-called communications in the Finite Blocklength (FBL) regime [13]. In the FBL regime, transmission error possibly occurs even when the coding rate is set to be lower than the Shannon capacity. When transmitting data packets with shorter blocklength to reduce transmission delay, the probability of transmission error increases correspondingly. Therefore, minimizing latency with a reliability guarantee under the FBL regime should be carefully investigated. In the past few years, a set of works have taken the FBL impacts into consideration in the performance analysis and system design for MEC networks [14; 15; 16; 17]. The study in [14] introduces an energy-efficient algorithm for dynamic computation offloading in a multi-access edge computing scenario, focusing on delay-critical applications by incorporating URLLC through FBL and reliability constraints to manage radio and computational resources jointly. The authors of [15] propose an efficient algorithm for an unmanned aerial vehicle-enabled MEC system with URLLC-based offloading to minimize the maximum computation latency, considering the FBL transmission and its impact on the data rate. Moreover, the work in [16] proposes an MEC-aided integrated sensing and communication scheme that leverages short-packet transmissions to efficiently offload radar-sensing data to an edge-server, ensuring low latency and high reliability for radar data analysis while minimizing system energy consumption. In [17], the authors investigate the effects of short-packet transmission on the radio resource allocation and minimize the energy cost for mission-critical Internet-of-Things (IoT) in an MEC system.