Coded distributed machine learning mitigates straggler effects and provides privacy protection by introducing redundancy through coded computing. However, the system remains vulnerable to privacy breaches when the number of honest-but-curious nodes surpasses the designed threshold, or when outsider adversaries eavesdrop on sensitive data. To address these limitations, we propose a privacy-preserving and straggler-resilient distributed learning framework, namely, differential privacy-based Lagrange coded computing (DP-LCC). First, we design a three-layer protection strategy against privacy threats and stragglers by retaining labels at the master, obfuscating features via Lagrange interpolation, and injecting calibrated noise into local computations. Second, we theoretically prove that the aggregated gradient is an unbiased estimator with bounded variance, and derive convergence bounds under both Gaussian and Laplace mechanisms, revealing the trade-off between privacy budgets and model utility. Third, we provide a comprehensive analysis of the system's computational complexity, privacy composition, and heterogeneity to verify the framework's efficiency and adaptability in realistic distributed environments. Extensive experiments on four benchmark datasets validate the theoretical results, demonstrating the robustness of DP-LCC against varying system parameters and heterogeneous environments.

Differentially private distributed machine learning protects privacy by injecting artificial noise to the computing results. To further improve energy efficiency, the natural noise in the wireless environment can be used to protect privacy. In this paper, we study the problem of coded distributed machine learning over Gaussian multiple-access wireless channels to achieve differential privacy by exploiting the natural noise. Firstly, we propose an aggregation scheme using differentially private Lagrange encoding in a wireless environment, where the local computing results are uploaded to the master through orthogonal channels. Then, we develop an achievable privacy protection level to illustrate the impact of transmit power and power allocation on privacy. Additionally, we establish a theoretical convergence upper bound of the proposed scheme, providing a clear understanding of the potential limitations and capabilities of the system. Finally, we demonstrate a trade-off between system resource settings, convergence, and privacy protection levels through experiments. Specifically, increasing the signal-to-noise ratio (SNR) and power allocated for gradient computation leads to a decrease in the privacy protection level of the system and an increase in training accuracy. Moreover, reducing the dataset partitions results in better training accuracy.