This paper presents an approximate wireless communication scheme for federated learning (FL) model aggregation in the uplink transmission. We consider a realistic channel that reveals bit errors during FL model exchange in wireless networks. Our study demonstrates that random bit errors during model transmission can significantly affect FL performance. To overcome this challenge, we propose an approximate communication scheme based on the mathematical and statistical proof that machine learning (ML) model gradients are bounded under certain constraints. This bound enables us to introduce a novel encoding scheme for float-to-binary representation of gradient values and their QAM constellation mapping. Besides, since FL gradients are error-resilient, the proposed scheme simply delivers gradients with errors when the channel quality is satisfactory, eliminating extensive error-correcting codes and/or retransmission. The direct benefits include less overhead and lower latency. The proposed scheme is well-suited for resource-constrained devices in wireless networks. Through simulations, we show that the proposed scheme is effective in reducing the impact of bit errors on FL performance and saves at least half the time than transmission with error correction and retransmission to achieve the same learning performance. In addition, we investigated the effectiveness of bit protection mechanisms in high-order modulation when gray coding is employed and found that this approach considerably enhances learning performance.

翻译：本文提出了一种用于联邦学习（FL）模型聚合上行传输的近似无线通信方案。我们考虑了一个真实的信道模型，该模型揭示了无线网络中FL模型交换过程中的比特错误现象。研究表明，模型传输过程中的随机比特错误会显著影响联邦学习性能。为应对这一挑战，我们基于机器学习（ML）模型梯度在特定约束下存在有界性的数学与统计学证明，提出了一种近似通信方案。该有界性使我们能够引入一种新颖的编码方案，用于梯度值的浮点数-二进制表示及其QAM星座映射。此外，由于FL梯度具有容错性，所提方案在信道质量满足要求时直接传输带错误的梯度值，从而避免了大量纠错编码和/或重传操作。其直接优势包括更低的通信开销与延迟。该方案特别适用于无线网络中资源受限的设备。仿真结果表明，该方案能有效降低比特错误对联邦学习性能的影响，并在实现相同学习性能时，将传输时间减少至传统纠错重传方案的一半以下。此外，我们还研究了采用格雷编码时高阶调制中比特保护机制的有效性，发现该方法能显著提升学习性能。