This work proposes LDVS, a learnable binary local descriptor devised for matching natural images within the MPEG CDVS framework. LDVS descriptors are learned so that they can be sign-quantized and compared using the Hamming distance. The underlying convolutional architecture enjoys a moderate parameters count for operations on mobile devices. Our experiments show that LDVS descriptors perform favorably over comparable learned binary descriptors at patch matching on two different datasets. A complete pair-wise image matching pipeline is then designed around LDVS descriptors, integrating them in the reference CDVS evaluation framework. Experiments show that LDVS descriptors outperform the compressed CDVS SIFT-like descriptors at pair-wise image matching over the challenging CDVS image dataset.