In this paper, we delve into the challenge of optimizing joint communication and computation for semantic communication over wireless networks using a probability graph framework. In the considered model, the base station (BS) extracts the small-sized compressed semantic information through removing redundant messages based on the stored knowledge base. Specifically, the knowledge base is encapsulated in a probability graph that encapsulates statistical relations. At the user side, the compressed information is accurately deduced using the same probability graph employed by the BS. While this approach introduces an additional computational overhead for semantic information extraction, it significantly curtails communication resource consumption by transmitting concise data. We derive both communication and computation cost models based on the inference process of the probability graph. Building upon these models, we introduce a joint communication and computation resource allocation problem aimed at minimizing the overall energy consumption of the network, while accounting for latency, power, and semantic constraints. To address this problem, we obtain a closed-form solution for transmission power under a fixed semantic compression ratio. Subsequently, we propose an efficient linear search-based algorithm to attain the optimal solution for the considered problem with low computational complexity. Simulation results underscore the effectiveness of our proposed system, showcasing notable improvements compared to conventional non-semantic schemes.

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