Problem

Wireless federated learning (FL) faces significant challenges due to the inherent limitations of wireless resources, leading to unreliable communication links at the network edge. Traditional FL approaches, often relying on centralized paradigms, incur high data transfer costs and pose privacy risks. While previous research has explored compensation methods for transmission errors or uniform resource allocation, these strategies often fail to address the root cause of unreliable communication or adequately prioritize the varying importance of data components within the learning task. Specifically, existing methods tend to overlook the heterogeneous importance of data at a finer granularity, such as within individual gradients, and often limit device participation, thereby compromising model generalizability in resource-constrained scenarios.

Method

The authors propose Sign-Prioritized FL (SP-FL), an importance-aware framework designed to enhance wireless FL performance by prioritizing the transmission of critical gradient information. The core idea involves a sign-modulus decoupled transmission strategy where gradient signs are sent in separate packets from their moduli. This allows for the reuse of correctly received sign packets, even if the corresponding modulus packets are lost, by employing a compensatory modulus vector at the parameter server (PS). To further optimize for importance, SP-FL formulates a hierarchical resource allocation problem. This problem simultaneously optimizes bandwidth allocation among multiple devices (device-level importance disparity, based on gradient norm) and power allocation between sign and modulus packets (packet-level importance disparity, prioritizing signs). To make the long-term optimization problem tractable, a one-step convergence analysis of SP-FL is conducted, explicitly characterizing data importance at both levels. The problem is then solved using an alternating optimization algorithm, employing the Newton-Raphson method for power allocation and successive convex approximation (SCA) for bandwidth allocation. A low-complexity alternative, using an interior-point penalty function method, is also provided for large-scale systems.

Results

Extensive simulations confirm the effectiveness and robustness of the proposed SP-FL framework. The theoretical one-step convergence bound closely aligns with the actual loss function, validating the analytical framework. SP-FL consistently outperforms existing baseline methods, demonstrating up to 9.96% higher testing accuracy on the CIFAR-10 dataset, particularly in resource-constrained scenarios with limited transmit power, stringent latency thresholds, and high device density, as well as in highly heterogeneous (non-IID) data distributions. The framework also achieves a superior convergence rate. The low-complexity method, while computationally less intensive, maintains strong performance, making it suitable for large-scale FL systems. Furthermore, using historical local gradients for compensation yielded improved performance compared to global gradients. The studies also highlighted the feasibility and benefits of incorporating a sign retransmission mechanism, which improved convergence and test accuracy under practical communication constraints. Optimal quantization bit levels were shown to be dynamic, depending on available wireless resources.

Implications

The SP-FL framework represents a significant advancement for federated learning in wireless environments, especially for future 6G networks and ubiquitous intelligent applications at the edge. By intelligently prioritizing the transmission of gradient signs and dynamically allocating resources based on data importance at both device and packet levels, SP-FL offers a robust solution to the pervasive challenge of unreliable communication. This shift from uniform reliability to importance-aware transmission enables more efficient and resilient collaborative AI training, ensuring high model accuracy and faster convergence even under severe wireless resource constraints. The proposed methodology has broad implications for designing next-generation distributed machine learning systems that can operate effectively in real-world, dynamic wireless settings.