Multiple Description Quantization via Gram-Schmidt Orthogonalization

Abstract

The multiple description (MD) problem has received considerable attention as a model of information transmission over unreliable channels. A general framework for designing efficient multiple description 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 that any point in the EGC 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 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 low-complexity MD scalar quantizers in the proposed general framework also is 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.

48 pages; submitted to IEEE Transactions on Information Theory

References in corpus (3)

• On the role of MMSE estimation in approaching the information-theoretic limits of linear Gaussian channels: Shannon meets Wiener
• Successive Wyner-Ziv Coding Scheme and its Application to the Quadratic Gaussian CEO Problem
• Shannon meets Wiener II: On MMSE estimation in successive decoding schemes

Cited by in corpus (7)

• Approximating the Gaussian Multiple Description Rate Region Under Symmetric Distortion Constraints
• Successive Wyner-Ziv Coding for the Binary CEO Problem under Logarithmic Loss
• Robust Distributed Compression of Symmetrically Correlated Gaussian Sources
• n-Channel Asymmetric Entropy-Constrained Multiple-Description Lattice Vector Quantization
• Achieving the Gaussian Rate-Distortion Function by Prediction
• Lattice-based Robust Distributed Source Coding
• Multiuser Successive Refinement and Multiple Description Coding