  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.
