In this paper, the problem of minimum rate maximization for probabilistic semantic communication (PSCom) in industrial Internet of Things (IIoT) is investigated. In the considered model, users employ semantic information extraction techniques to compress the original data before sending it to the base station (BS). During this semantic compression process, knowledge graphs are employed to represent the semantic information, and the probability graph sharing between users and the BS is utilized to further compress the knowledge graph. The semantic compression process can significantly reduce the transmitted data size, but it inevitably introduces additional computation overhead. Considering the limited power budget of the user, we formulate a joint communication and computation optimization problem is formulated aiming to maximize the minimum equivalent rate among all users while meeting total power and semantic compression ratio constraints. To address this problem, two algorithms with different computational complexities are proposed to obtain suboptimal solutions. One algorithm is based on a prorate distribution of transmission power, while the other traverses the combinations of semantic compression ratios among all users. In both algorithms, bisection is employed in order to achieve the greatest minimum equivalent rate. The simulation results validate the effectiveness of the proposed algorithms.

翻译：本文研究了工业物联网（IIoT）中概率语义通信（PSCom）的最小速率最大化问题。在所考虑的模型中，用户采用语义信息提取技术在将原始数据发送到基站（BS）之前对其进行压缩。在此语义压缩过程中，知识图谱被用来表示语义信息，并利用用户与基站之间的概率图谱共享来进一步压缩知识图谱。语义压缩过程能显著减小传输数据量，但不可避免地会引入额外的计算开销。考虑到用户有限的功率预算，我们构建了一个联合通信与计算优化问题，其目标是在满足总功率和语义压缩比约束的同时，最大化所有用户中的最小等效速率。为解决该问题，本文提出了两种具有不同计算复杂度的算法来获得次优解。一种算法基于传输功率的按比例分配，另一种则遍历所有用户的语义压缩比组合。在两种算法中，均采用二分法以实现最大的最小等效速率。仿真结果验证了所提算法的有效性。