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An airfoil shape parameterization that can generate a compact design space is highly desirable in practice. In this paper, a compact airfoil parameterization is proposed by incorporating deep learning into the PAERO parameterization method based on the thin-airfoil theory. Following the PAERO parameterization, the mean camber line is represented by a number of aerodynamic performance parameters, which can be used to narrow down the design space according to the thin-airfoil theory. In order to further reduce the design space, the airfoil thickness distribution is represented by data-driven generative models, which are trained by the thickness distributions of existing airfoils. The trained models can automatically filter out the physically unreasonable airfoil shapes, resulting in a highly compact design space. The test results show that the proposed method is significantly more efficient and more robust than the widely used CST parameterization method for airfoil optimization.