Multiple Description Quantization Via Gram–Schmidt Orthogonalization

The multiple description (MD) problem has received considerable attention as a model of information transmission over unreliable channels. A general framework for designing efficient MD quantization schemes is proposed in this paper. We provide a systematic treatment of the El Gamal–Cover (EGC) achievable MD rate–distortion region, and show it can be decomposed into a simplified-EGC (SEGC) region and a superimposed refinement operation. Furthermore, any point in the SEGC region can be achieved via a successive quantization scheme along with quantization splitting. for the quadratic Gaussian case, the proposed scheme has an intrinsic connection with the Gram–Schmidt orthogonalization, which implies that the whole Gaussian MD rate–distortion region is achievable with a sequential dithered lattice-based quantization scheme as the dimension of the (optimal) lattice quantizers becomes large. Moreover, this scheme is shown to be universal for all independent and identically distributed (i.i.d.) smooth sources with performance no worse than that for an i.i.d. Gaussian source with the same variance and asymptotically optimal at high resolution. A class of MD scalar quantizers in the proposed general framework is also constructed and is illustrated geometrically; the performance is analyzed in the high-resolution regime, which exhibits a noticeable improvement over the existing MD scalar quantization schemes.