Recent advances in Synthetic Aperture Radar (SAR) sensors have enabled the acquisition of very high-resolution images with wide swaths, large bandwidth and in multiple polarization channels. As a result of the significant increase of SAR data size, an effective compression of the acquired data is of paramount importance. However, conventional data compression methods demonstrate limited effectiveness when applied to SAR data. In order to tackle this problem, in this study, a Complex-Valued (CV) end-to-end deep learning-based architecture based on convolutional autoencoders is proposed to compress Single Look Complex (SLC) SAR data. By relying on dual polarization SAR data, one of the polarization channels of the data is used as the side information to assist the reconstruction of the compressed channel with lower data loss. The obtained results demonstrate the remarkable potential and capability of CV deep learning-based methods for SAR data compression.