Privacy-preserving communication compression and robust aggregation for hierarchical federated learning

Hierarchical federated learning (HFeL) improves the scalability of federated learning (FeL) by introducing edge-assisted aggregation, but privacy leakage, Byzantine contamination, and repeated communication overhead remain tightly coupled under heterogeneous data distributions. To address these challenges, we propose PCRHFeL, a cloud-edge-client framework that jointly delivers privacy, efficiency, and robustness. At the client layer, Top- K sparsification reduces the transmitted update size, after which Gaussian perturbation provides a Wasserstein differential privacy (WDP)-compatible release before the update becomes visible to the edge server. At the edge layer, median-scaled adaptive clipping first constrains abnormal update magnitudes, and norm-based trimming then removes residual extreme updates before edge aggregation. At the cloud layer, only filtered edge updates are fused through sample-size-aware weighting. This layered design forms a sparse-private-robust processing chain rather than a collection of independent modules. We derive cumulative WDP privacy accounting, edge- and cloud-level robustness bounds, and convergence guarantees for strongly convex and non-convex objectives, in which Top- K distortion, full-dimensional WDP perturbation, and residual Byzantine deviation appear explicitly. Experiments on MNIST, Fashion-MNIST, and CIFAR-10 under IID, Non-IID, and multiple Byzantine attacks show that PCRHFeL preserves competitive benign utility while improving adversarial robustness. Progressive ablation, parameter sensitivity, and measured communication-cost results further clarify the contribution and operating trade-offs of each component.