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Federated Learning (FL) is a distributed machine learning technique designed to utilize the distributed datasets collected by our mobile and internet-of-things devices. As such, it is natural to consider wireless communication for FL. In wireless networks, Over-the-Air Computation (AirComp) can accelerate FL training by harnessing the interference of uplink gradient transmissions. However, since AirComp utilizes analog transmissions, it introduces an inevitable estimation error due to channel fading and noise. In this paper, we propose retransmissions as a method to reduce such estimation errors and thereby improve the FL classification accuracy. First, we derive the optimal power control scheme with retransmissions. Then we investigate the performance of FL with retransmissions analytically and find an upper bound on the FL loss function. The analysis indicates that our proposed retransmission scheme …