在去中心化场景下，用相关噪声协作生成隐私保护的合成数据。

In this work, we explore differentially private synthetic data generation in a decentralized-data setting by building on the recently proposed Differentially Private Class-Centric Data Aggregation (DP-CDA). DP-CDA synthesizes data in a centralized setting by mixing multiple randomly-selected samples from the same class and injecting carefully calibrated Gaussian noise, ensuring (ε, δ)-differential privacy. When deployed in a decentralized or federated setting, where each client holds only a small partition of the data, DP-CDA faces new challenges. The limited sample size per client increases the sensitivity of local computations, requiring higher noise injection to maintain the differential privacy guarantee. This, in turn, leads to a noticeable degradation in the utility compared to the centralized setting. To mitigate this issue, we integrate the Correlation-Assisted Private Estimation (CAPE) protocol into the federated DP-CDA framework and propose CAPE Assisted Federated DP-CDA algorithm. CAPE enables limited collaboration among the clients by allowing them to generate jointly distributed (anti-correlated) noise that cancels out in aggregate, while preserving privacy at the individual level. This technique significantly improves the privacy-utility trade-off in the federated setting. Extensive experiments on MNIST and FashionMNIST datasets demonstrate that the proposed CAPE Assisted Federated DP-CDA approach can achieve utility comparable to its centralized counterpart under some parameter regime, while maintaining rigorous differential privacy guarantees.