In this letter, we study a wireless federated learning (FL) system where network pruning is applied to local users with limited resources. Although pruning is beneficial to reduce FL latency, it also deteriorates learning performance due to the information loss. Thus, a trade-off problem between communication and learning is raised. To address this challenge, we quantify the effects of network pruning and packet error on the learning performance by deriving the convergence rate of FL with a non-convex loss function. Then, closed-form solutions for pruning control and bandwidth allocation are proposed to minimize the weighted sum of FL latency and FL performance. Finally, numerical results demonstrate that 1) our proposed solution can outperform benchmarks in terms of cost reduction and accuracy guarantee, and 2) a higher pruning rate would bring less communication overhead but also worsen FL accuracy, which is consistent with our theoretical analysis.
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