We propose a unified signal compression framework that uses a generative adversarial network (GAN) to compress heterogeneous signals. The compressed signal is represented as a latent vector and fed into a generator network that is trained to produce high quality realistic signals that minimize a target objective function. To efficiently quantize the compressed signal, non-uniformly quantized optimal latent vectors are identified by iterative back-propagation with alternating direction method of multipliers (ADMM) optimization performed for each iteration. The performance of the proposed signal compression method is assessed using multiple metrics including PSNR and MS-SSIM for image compression and also PESR, Kaldi, LSTM, and MLP performance for speech compression. Test results show that the proposed work outperforms recent state-of-the-art hand-crafted and deep learning-based signal compression methods.