Semantic communications are expected to accomplish various semantic tasks with relatively less spectrum resource by exploiting the semantic feature of source data. To simultaneously serve both the data transmission and semantic tasks, joint data compression and semantic analysis has become pivotal issue in semantic communications. This paper proposes a deep separate source-channel coding (DSSCC) framework for the joint task and data oriented semantic communications (JTD-SC) and utilizes the variational autoencoder approach to solve the rate-distortion problem with semantic distortion. First, by analyzing the Bayesian model of the DSSCC framework, we derive a novel rate-distortion optimization problem via the Bayesian inference approach for general data distributions and semantic tasks. Next, for a typical application of joint image transmission and classification, we combine the variational autoencoder approach with a forward adaption scheme to effectively extract image features and adaptively learn the density information of the obtained features. Finally, an iterative training algorithm is proposed to tackle the overfitting issue of deep learning models. Simulation results reveal that the proposed scheme achieves better coding gain as well as data recovery and classification performance in most scenarios, compared to the classical compression schemes and the emerging deep joint source-channel schemes.
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