In this paper, the problem of joint communication and computation design for probability graph-based semantic communication over wireless networks is investigated. In the considered model, the base station (BS) extracts the compressed small-sized semantic data by removing redundant information based on the shared knowledge base between the transceivers. In particular, the knowledge base is represented as a probability graph, which summarizes the statistic relations of massive knowledge graphs. On the user side, the compressed information is accurately inferred on the basis of the same probability graph as the BS. Although this approach brings additional computation resource consumption for semantic information extraction, it effectively reduces communication resource consumption through the transmission of small-sized data. Both the communication and computation cost models are derived based on the inference process of the probability graph. Based on the formulated models, the problem of joint communication and computation resource allocation is proposed to minimize the total energy consumption of the network considering both latency and power limitations. To solve this problem, the closed-form solution of the transmission power is obtained with fixed semantic compression ratio. Then, an effective linear search-based algorithm is proposed to obtain the optimal solution of the considered problem with low complexity. Simulation results demonstrate the effectiveness of the proposed system compared with the conventional non-semantic schemes.
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