Toward Communication-Efficient Over-the-Air Federated Learning: Synergistic Compression for Uplink and Downlink Transmission

The rapid proliferation of Internet of Things (IoT) is generating an unprecedented volume of distributed data, necessitating efficient decentralized learning paradigms. Federated learning (FL) has emerged as a compelling distributed collaborative intelligence framework, renowned for its privacy protection benefits. However, the communication overhead associated with intermediate model exchanges remains a critical bottleneck in FL. Aiming at reducing the communication cost of FL equipped with promising over-the-air computation (AirComp) technique, this work designs specialized model compression schemes for both uplink and downlink communications. For uplink transmission with AirComp, we analyze its unique constraints and propose a hybrid global sparsification scheme that combines the benefits of conventional Top-k and Rand-k algorithms. We further develop an algorithm to strategically allocate transmission budgets between the two concatenated sparsification operations, accounting for both model temporal correlation and the cost of index synchronization. For downlink transmission, we introduce a group-based mixed-precision quantization (MPQ) scheme and integrates the broadcast of grouping information with uplink sparsification pattern to further mitigate communication burden. Moreover, we conduct theoretical analysis under realistic channel conditions and typical FL settings to validate the advantages and establish convergence guarantees of our approaches. Experimental results demonstrate that, compared to existing schemes, the proposed methods significantly improve communication efficiency and ensure client scalability, and concurrently verify the benefits of the uplink-downlink synergistic design.