Dithered lattice-based quantizers for multiple descriptions

Multiple description (MD) source coding is aimed at achieving graceful degradation in reconstruction with respect to losing portions of the code, with the cost of some redundancy. We examine MD schemes which use entropy-coded dithered lattice quantizers (ECDQ). We propose two techniques, one based on successive refinement (SR), and the other a dithered and periodic version of the NM scalar quantizer (MDSQ) with distributed cells proposed by Vaisbampayan. Similarly to the single description case, both techniques are universal in nature, and are equivalent to additive noise channels. This allows to derive analytical expressions for the rate-distortion performance for general sources, and to compare them to the optimal rate regions at both high and low resolutions. Among other results, we establish that while the dithered MDSQ scheme loses only the space filling loss of the scalar lattice at any resolution, the SR-based scheme loses an additional 0.5 bit at any lattice dimension. Possible improvements, such as "refinement time sharing" and "dependent dithering," are discussed.