In this paper, we propose a decentralized learning framework that incorporates both power control and privacy guarantees. Specifically, we enable a set of clients in a wireless multicast network to jointly train a common model while maintaining a prescribed per-iteration maximum privacy leakage level. The communication network is represented by a rowstochastic adjacency matrix, allowing us to capture asymmetric channel gains as well as heterogeneous maximum transmit power levels. Differential privacy is enforced through an explicit powersplitting strategy that allocates each node's limited maximum transmit power between model coefficients and injected Gaussian noise, thereby jointly controlling learning performance and privacy leakage. We further prove that the proposed algorithm achieves a cumulative regret bound of O(logT), whereTdenotes the time horizon. To evaluate the practical performance of our approach, we perform comprehensive experiments on the CIFAR-10 dataset under both IID and non-IID data distributions, considering different privacy levels, diverse numbers of clients, and various graph topologies. The results demonstrate strong performance across the considered settings and improved performance over existing methods, highlighting the effectiveness of the proposed algorithm under realistic wireless communication constraints.

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