Holoscopic imaging, also known as integral, light field, and plenoptic imaging, is an appealing technology for glassless 3D video systems, which has recently emerged as a prospective candidate for future image and video applications, such as 3D television. However, to successfully introduce 3D holoscopic video applications into the market, adequate coding tools that can efficiently handle 3D holoscopic video are necessary. In this context, this paper discusses the requirements and challenges for 3D holoscopic video coding, and presents an efficient 3D holoscopic coding scheme based on High Efficiency Video Coding (HEVC). The proposed 3D holoscopic codec makes use of the self-similarity (SS) compensated prediction concept to efficiently explore the inherent correlation of the 3D holoscopic content in Intra- and Inter-coded frames, as well as a novel vector prediction scheme to take advantage of the peculiar characteristics of the SS prediction data. Extensive experiments were conducted, and have shown that the proposed solution is able to outperform HEVC as well as other coding solutions proposed in the literature. Moreover, a consistently better performance is also observed for a set of different quality metrics proposed in the literature for 3D holoscopic content, as well as for the visual quality of views synthesized from decompressed 3D holoscopic content.