Space-air-ground integrated networks (SAGINs) are emerging as a pivotal element in the evolution of future wireless networks. Despite their potential, the joint design of communication and computation within SAGINs remains a formidable challenge. In this paper, the problem of energy efficiency in SAGIN-enabled probabilistic semantic communication (PSC) system is investigated. In the considered model, a satellite needs to transmit data to multiple ground terminals (GTs) via an unmanned aerial vehicle (UAV) acting as a relay. During transmission, the satellite and the UAV can use PSC technique to compress the transmitting data, while the GTs can automatically recover the missing information. The PSC is underpinned by shared probability graphs that serve as a common knowledge base among the transceivers, allowing for resource-saving communication at the expense of increased computation resource. Through analysis, the computation overhead function in PSC is a piecewise function with respect to the semantic compression ratio. Therefore, it is important to make a balance between communication and computation to achieve optimal energy efficiency. The joint communication and computation problem is formulated as an optimization problem aiming to minimize the total communication and computation energy consumption of the network under latency, power, computation capacity, bandwidth, semantic compression ratio, and UAV location constraints. To solve this non-convex non-smooth problem, we propose an iterative algorithm where the closed-form solutions for computation capacity allocation and UAV altitude are obtained at each iteration. Numerical results show the effectiveness of the proposed algorithm.

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