I. Introduction
The proliferation of 5G MEC has led to a rapid surge in the number of IoT devices accessing wireless networks. To address the capacity shortage caused by this growth, massive machine-type communication (mMTC) has become a hot research scenario for increasing network capacity in both industry and academia [1], [2]. The mMTC scenario, as seen in applications like smart cities [3], intelligent transportation systems [4], and environmental monitoring [5], involves a significant number of manufacturing devices and production applications that generate and transmit tasks concurrently [6], [7]. The combination of 5G MEC and mMTC provides a solid foundation for future intelligent IoT applications, driving digital transformation and innovative development across various industries. MEC, combined with mMTC, enables more intelligent applications that rely on real-time data analysis and processing, thereby promoting the widespread adoption of edge computing [8]. The large number of terminals accessing the network in the mMTC scenario leads to challenges like increased interference, congestion, and limited radio resources. What's more, stringent constraints, including high task transmission reliability and low task computing delay, are required in the mMTC scenario [9]. However, as the number of connected devices increases in mMTC scenario, network resources may become strained, leading to packet loss and increased latency, thereby affecting the reliability of transmission. When service reliability is compromised, important data may be lost, affecting the system's decision-making capability, particularly in real-time applications such as industrial control and autonomous driving. Additionally, unreliable transmission may require data retransmission, leading to increased system latency and negatively impacting user experience and system efficiency [10]. Meanwhile, the interdependence between resources in different facilities makes it more challenging to meet the requirements for delay and reliability. Furthermore, limited wireless network resources and the rapid increase in IoT-generated tasks can cause resource shortages, leading to queue congestion and transmission errors, which negatively impact service reliability. To improve service reliability and reduce task latency in the MEC support scenario, a task replication mechanism is introduced and has been extensively explored in previous works [11], [12]. By assigning the same task to multiple computing nodes, the task replication mechanism can fully utilize redundant resources. Once a computing node completes one task, the task processing finishes. In the 5G mMTC scenario, MEC utilizes the 5G core network to manage the access of mMTC devices. Application services are deployed on edge nodes to process data from mMTC devices. Task replication is implemented to enhance reliability and ensure seamless service continuity. Communication between devices and edge services occurs via the MQTT protocol, ensuring low-latency data transmission. Additionally, Kubernetes is used for the automated management of edge services, ensuring high availability and rapid recovery of services [13]. To further improve task reliability, the Finite Block Length (FBL) theory has been introduced to reduce the error rate from the network transmission layer. FBL theory considers the limited length of data packets transmitted, which leads to non-negligible error probabilities in transmission and is closer to the real transmission scenario, in contrast to the assumptions of traditional Shannon theory [14], [15].