Federated learning (FL) has emerged as a distributed machine learning (ML) technique that can protect local data privacy for participating clients and improve system efficiency. Instead of sharing raw data, FL exchanges intermediate learning parameters, such as gradients, among clients. This article presents an efficient wireless communication approach tailored for FL parameter transmission, especially for Internet of Things (IoT) devices, to facilitate model aggregation. Our study considers practical wireless channels that can lead to random bit errors, which can substantially affect FL performance. Motivated by empirical gradient value distribution, we introduce a novel received bit masking method that confines received gradient values within prescribed limits. Moreover, given the intrinsic error resilience of ML gradients, our approach enables the delivery of approximate gradient values with errors without resorting to extensive error correction coding or retransmission. This strategy reduces computational overhead at both the transmitter and the receiver and minimizes communication latency. Consequently, our scheme is particularly well-suited for resource-constrained IoT devices. Additionally, we explore the inherent protection of the most significant bits (MSBs) through gray coding in high-order modulation. Our simulations demonstrate that our proposed scheme can effectively mitigate random bit errors in FL performance, achieving similar learning objectives, but with the 50% air time required by existing methods involving error correction and retransmission.