  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.
