We present a novel deep neural network (DNN) architecture for compressing an image when a correlated image is available as side information only at the decoder. This problem is known as distributed source coding (DSC) in information theory. In particular, we consider a pair of stereo images, which generally have high correlation with each other due to overlapping fields of view, and assume that one image of the pair is to be compressed and transmitted, while the other image is available only at the decoder. In the proposed architecture, the encoder maps the input image to a latent space, quantizes the latent representation, and compresses it using entropy coding. The decoder is trained to extract the Wyner's common information between the input image and the correlated image from the latter. The received latent representation and the locally generated common information are passed through a decoder network to obtain an enhanced reconstruction of the input image. The common information provides a succinct representation of the relevant information at the receiver. We train and demonstrate the effectiveness of the proposed approach on the KITTI dataset of stereo image pairs. Our results show that the proposed architecture is capable of exploiting the decoder-only side information, and outperforms previous work on stereo image compression with decoder side information.