  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.
