  In federated learning, particularly in cross-device scenarios, secure
aggregation has recently gained popularity as it effectively defends against
inference attacks by malicious aggregators. However, secure aggregation often
requires additional communication overhead and can impede the convergence rate
of the global model, which is particularly challenging in wireless network
environments with extremely limited bandwidth. Therefore, achieving efficient
communication compression under the premise of secure aggregation presents a
highly challenging and valuable problem. In this work, we propose a novel
uplink communication compression method for federated learning, named FedMPQ,
which is based on multi shared codebook product quantization.Specifically, we
utilize updates from the previous round to generate sufficiently robust
codebooks. Secure aggregation is then achieved through trusted execution
environments (TEE) or a trusted third party (TTP).In contrast to previous
works, our approach exhibits greater robustness in scenarios where data is not
independently and identically distributed (non-IID) and there is a lack of
sufficient public data. The experiments conducted on the LEAF dataset
demonstrate that our proposed method achieves 99% of the baseline's final
accuracy, while reducing uplink communications by 90-95%
