Semantic communication is a promising communication paradigm that utilizes Deep Neural Networks (DNNs) to extract the information relevant to downstream tasks, hence significantly reducing the amount of transmitted data. In current practice, the semantic communication transmitter for a specific task is typically pre-trained and shared by all users. However, due to user heterogeneity, it is desirable to use different transmitters according to the available computational and communication resources of users. In this paper, we first show that it is possible to dynamically adjust the computational and communication overhead of DNN-based transmitters, thereby achieving adaptive semantic communication. After that, we investigate the user association and resource allocation problem in a multi-cell network where users are equipped with adaptive semantic communication transmitters. To solve this problem, we decompose it into three subproblems involving the scheduling of each user, the resource allocation of each base station (BS), and the user association between users and BSs. Then we solve each problem progressively based on the solution of the previous subproblem. The final algorithm can obtain near-optimal solutions in polynomial time. Numerical results show that our algorithm outperforms benchmarks under various situations.

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