In this paper, we propose De-RPOTA, a novel algorithm designed for decentralized learning, equipped with mechanisms for resource adaptation and privacy protection through over-the-air computation. We theoretically analyze the combined effects of limited resources and lossy communication on decentralized learning, showing it converges towards a contraction region defined by a scaled errors version. Remarkably, De-RPOTA achieves a convergence rate of $\mathcal {O}\left ({{\frac {1}{\sqrt {nT}}}}\right)$ in scenarios devoid of errors, matching the state-of-the-arts. Additionally, we tackle a power control challenge, breaking it down into transmitter and receiver sub-problems to hasten the De-RPOTA algorithm’s convergence. We also offer a quantifiable privacy assurance for our over-the-air computation methodology. Intriguingly, our findings suggest that network noise can actually strengthen the privacy of aggregated information, with over-the-air computation providing extra security for individual updates. Comprehensive experimental validation confirms De-RPOTA’s efficacy in communication resources limited environments. Specifically, the results on the CIFAR-10 dataset reveal nearly 30% reduction in communication costs compared to the state-of-the-arts, all while maintaining similar levels of learning accuracy, even under resource restrictions.