Abstract: Channel prediction can be leveraged to mitigate the performance loss caused by the outdated channels of mobile users, or improve resource usage efficiency and user experience by predictive resource allocation for wireless systems. Despite that the time consumed for training a machine learning model is usually long, the computational complexity of online inference with a well-trained model is low. Hence, machine learning is expected to be applicable for real-time wireless tasks such as channel prediction. Federated learning can take the advantage of the gathered data and computing resources at mobile devices, meanwhile protecting privacy-sensitive user data. In many privacy-insensitive wireless communication problems, the main motivation for using federated learning is to reduce communication overhead with respect to centralized learning, which needs to upload dataset for training. In this paper, we compare the total amount of data required by federated learning and centralized learning for uploading compressed model parameters or training data to the central processor when predicting average channel gain, instantaneous channel gain and the next cell to associate. Our results show that the amount of uplink data required for federated learning is not always smaller than centralized learning, even after several thousand folds of compression. This suggests that the communication efficient of federated learning still needs to be reduced significantly.