  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.
