We present a novel codec of depth-image-based representations for free-viewpoint 3D-TV. The proposed codec relies on a shape-adaptive wavelet transform and an explicit representation of the locations of major depth edges. Unlike classical wavelet transforms, the shape-adaptive transform generates small wavelet coefficients along depth edges, which greatly reduces the data entropy. The codec also shares the edge information between the depth map and the image to reduce their correlation. The wavelet transform is implemented by shape-adaptive lifting, which enables fast computations and perfect reconstruction. Experimental results on real data confirm the superiority of the proposed codec, with PSNR gains of up to 5.46dB on the depth map and up to 0.19dB on the image compared to standard wavelet codecs.