<p>This paper proposes a novel communication-efficient framework based on nonuniform-quantized federated learning (Non-QuanFL) for federated learning (FL), which leverages optimized nonuniform quantization to reduce the communication overhead while preserving model accuracy. In this framework, the model transmission phase employs a data-oriented nonuniform quantization technique that dynamically adapts to the statistical gradient distribution. Unlike conventional methods, which apply uniform quantization or fixed-level distributions, Non-QuanFL allocates more quantization levels to frequently occurring gradient values and minimizes distortion by preserving critical gradient information. This framework consists of three key phases of preprocessing, nonuniform quantization, and gradient reconstruction, ensuring that communication costs are significantly reduced without sacrificing convergence speed. Experimental results demonstrate that Non-QuanFL achieves up to a 29.4% reduction in the communication cost compared to SLMQ while maintaining comparable model performance, which is helpful to implement an energy-efficient distributed learning network oriented on carbon reduction (CR). In particular, on the FeMNIST dataset, Non-QuanFL reduces the communication cost from 12.43Gb (SLMQ) to 7.15Gb, and on CIFAR10, Non-QuanFL with adaptive quantization achieves an 18.2% cost reduction compared to the conventional methods. Moreover, the proposed scheme maintains a fast convergence rate and high test accuracy across multiple datasets, making it highly suitable for large-scale, resource-constrained FL deployments.</p>