The joint detection uses Kalman filtering (KF) to estimate the prior probability of control outputs to assist channel decoding. In this paper, we regard the joint detection as maximum a posteriori (MAP) decoding and derive the lower and upper bounds based on the pairwise error probability considering system interference, quantization interval, and weight distribution. We first derive the limiting bounds as the signal-to-noise ratio (SNR) goes to infinity and the system interference goes to zero. Then, we construct an infinite-state Markov chain to describe the consecutive packet losses of the control systems to derive the MAP bounds. Finally, the MAP bounds are approximated as the bounds of the transition probability from the state with no packet loss to the state with consecutive single packet loss. The simulation results show that the MAP performance of $\left(64,16\right)$ polar code and 16-bit CRC coincides with the limiting upper bound as the SNR increases and has $3.0$dB performance gain compared with the normal approximation of the finite block rate at block error rate $10^{-3}$.

Solving multiphase flow problem remains challenging, particularly under data-scarce, long-timestep, and large-scale conditions. Traditional data-driven models suffer from low accuracy and poor generalization in complex multiphase flow scenarios due to limited labeled data. In this study, we propose a multiphase phase physics-informed neural network framework that integrates spatiotemporal information with static geological features and dynamic well control variables. A hybrid loss function combines observational errors with residuals from multiphase flow governing equations, enabling accurate prediction of pressure and saturation while maintaining physical consistency. Experimental results show that the proposed method significantly outperforms baseline models including ANN, Transformer, and Informer, achieving higher accuracy in terms of R2, relative L2error, and RMSE. Ablation experiments further highlight the performance by incorporating physical parameters as input features.

Meeting the deterministic demands of industrial tasks can be quite challenging due to the diversity of devices and the unclear relationship between tasks and platforms in industrial edge computing scenarios. To tackle this issue, this study introduces an entropy-weighted scheduling method grounded in resource quantification. First, we scrutinized the affinity challenge when tasks operate across different platforms and broadened the scope of scheduling evaluation criteria within existing real-time systems. This expansion was accomplished by examining the alignment between various task attributes and platform characteristics through resource quantification. Subsequently, we employed the entropy weight method to handle the information entropy of all scheduling evaluation criteria and calculated the weighted sums to allocate the optimal scheduling device for each task. Ultimately, the entropy-weighted scheduling algorithm, which relies on resource quantification, was formulated to assess the algorithm’s scheduling performance under various parameter configurations. The experimental analysis indicated that the scheduling method based on resource quantification could effectively optimize the resource demand relationship between tasks and platforms, and the scheduling success rate of the proposed algorithm was 5.1%, 7.7%, and 34.5% higher than those of multitarget tracking sensor scheduling algorithm, D-Quantify, and RRA algorithms, respectively.

Minimum weight distribution (MWD) is an important metric to calculate the first term of union bound called minimum weight union bound (MWUB). In this paper, we first prove the maximum likelihood (ML) performance approaches MWUB as signal-to-noise ratio (SNR) goes to infinity and provide the deviation when MWD and SNR are given. Then, we propose a nested reliability sequence, namely MWD sequence, to construct polar codes independently of channel information. In the sequence, synthetic channels are sorted by partial MWD which is used to evaluate the influence of information bit on MWD and we prove the MWD sequence is the optimum sequence evaluated by MWUB for polar codes obeying partial order. Finally, we introduce an entropy constraint to establish a relationship between list size and MWUB and propose a heuristic construction method named entropy constraint bit-swapping (ECBS) algorithm, where we initialize information set by the MWD sequence and gradually swap information bit and frozen bit to satisfy the entropy constraint. The simulation results show the MWD sequence is more suitable for constructing polar codes with short code length than the polar sequence in 5G and the ECBS algorithm can improve MWD to show better performance as list size increases.

In 6G-enabled vehicle-to-edge networks, through deploying computing power resources closer to mobile vehicles for providing low latency and highly reliable services, Mobile Edge Computing (MEC) as an emerging paradigm has promoting mobile vehicles with limited capacities to come with diversified artificial intelligence (AI) applications. Nevertheless, the computing power of MEC server is still finite, seeking the optimal resource pricing and allocation strategies for MEC servers, and determining the optimal computation offloading for intelligent vehicle applications, still remain challenging issues that are necessary to be reasonably solved to improve the service experience. To address this issue, a scenario that multiple intelligent vehicle applications cooperatively initiate computation offloading requests in 6G-enabled multi-server multi-access vehicle-to-edge computing systems is considered in this paper, and with the defined reasonable utilities for MEC servers and intelligent vehicle applications, a solution of bidding-enabled dynamic resource pricing for computation offloading is proposed. Concretely, through considering the relationship of resource supply and demand, and the bidding among MEC servers, a dynamic resource pricing scheme is designed for MEC servers, meanwhile, with the complete consideration of dynamic resource pricing and time-varying wireless channel interference in multi-cell networks, a Q-learning based offloading decision algorithm is proposed for intelligent vehicle applications. Simulation experiments finally are conducted to demonstrate the efficiency in achieving the win-win situation with guaranteed utilities for both MEC servers and intelligent vehicle applications.

Deterministic response is the core foundation for the safe operation of industrial production systems. However, with the increasing demand for intelligence, flexibility, and agility, ensuring the deterministic response of computing and control tasks while meeting new demands has become the primary issue that manufacturers urgently need to address. In response to this issue, this article focuses on AI-driven cyber–physical production systems (AI-CPPSs) and conducts research on the adaptive interaction mechanism of network, computing, and manufacturing resources with guaranteed performance. The efficient adaptive configuration of network, computing, and manufacturing resources is used to meet the response requirements of dynamic tasks. To achieve on-demand configuration of multidimensional resources for tasks, we first propose an AI-CPPS-oriented modeling method named the hourglass method, which redefines task models and multidimensional resources with resources as the core. Furthermore, through the proposed method of computing power quantification and a heterogeneous frame structure, we achieve the unified arrangement of network, computing, and manufacturing resources in the time dimension. Finally, to ensure the security and reliability of resource interaction, a multidimensional resource interaction mechanism is proposed for network computing control, namely, the quicksand mechanism. The experimental results indicate that the proposed quicksand mechanism can optimize resource utilization based on ensuring a deterministic task response.

Industrial Internet, motivated by the deep integration of new-generation information and communication technology (ICT) and advanced manufacturing technology, will open up the production chain, value chain, and industry chain by establishing complete interconnections between humans, machines, and things. This will also help establish novel manufacturing and service modes, where personalized and customized production for differentiated services is a typical paradigm of future intelligent manufacturing. Thus, there is an urgent requirement to break through the existing chimney-like service mode provided by the hierarchical heterogeneous network architecture and establish a transparent channel for manufacturing and services using a flat network architecture. Starting from the basic concepts of process manufacturing and discrete manufacturing, we first analyze the basic requirements of typical manufacturing tasks. Then, with an overview on the developing process of industrial Internet, we systematically compare the current networking technologies and further analyze the problems of the present industrial Internet. On this basis, we propose to establish a novel “thin waist” that integrates sensing, communication, computing, and control for the future industrial Internet. Furthermore, we perform a deep analysis and engage in a discussion on the key challenges and future research issues regarding the multi-dimensional collaborative sensing of task–resource, the end-to-end deterministic communication of heterogeneous networks, and virtual computing and operation control of industrial Internet.

Compared to industrial wired networks, 5G can improve device mobility and reduce the cost of networking. However, the real-time performance and reliability of 5G new radio (NR) still need to be improved to satisfy industrial applications’ requirements. In factories, the main factor that affects the performance of 5G NR is the unstable signal quality caused by high temperatures and metal. Although assigning dedicated resources to all transmissions and retransmissions is an effective method to improve the performance of 5G NR, the unstable signal quality causes the resources required for retransmissions to be uncertain. To address the problem, we introduce the mixed-criticality task model to 5G NR. When high-criticality packets cannot be transmitted, they are allowed to preempt the resources shared with low-criticality packets. The mixed-criticality scheduling problem of 5G NR is NP-hard. We formulate it as an optimization modulo theories (OMT) specification and propose a scheduling algorithm based on bin packing methods to make 5G NR satisfy industrial applications’ requirements. Finally, we conduct extensive evaluations based on an industrial 5G testbed and random test cases. The evaluation results indicate that our algorithm makes communication reliability greater than 99.9% on unlicensed spectrum, and for most test cases, our algorithm is close to optimal solutions.

Time synchronization is one of the key technologies in Industrial Wireless Sensor Networks (IWSNs). Considering the demand of low energy consumption, fast convergence and robustness for IWSNs, this paper presents a novel Cluster-based Maximum consensus Time Synchronization method. Based on the theory of distributed consensus, the method utilizes the maximum consensus approach to realize the intra-cluster time synchronization. In the inter-cluster time synchronization, adjacent clusters exchange the time messages via overlapping nodes to synchronize with each other. In addition, the clustering technique is incorporated in the method, which can effectively reduce the redundant data. And the hops can be controlled, which improves the energy efficiency and convergence rate very well. At last, the simulation results show that our method reduces the communication overhead and improves the convergence rate in comparison to existing works.