Multiple Description Quantization via Gram-Schmidt Orthogonalization

TL;DR

This paper introduces a systematic framework for multiple description quantization, leveraging Gram-Schmidt orthogonalization, to achieve optimal rate-distortion performance for Gaussian and other sources, with practical low-complexity schemes.

Contribution

It presents a new successive quantization scheme linked to Gram-Schmidt orthogonalization, achieving the entire Gaussian MD rate-distortion region and offering universal, high-performance quantization methods.

Findings

Achieves the entire Gaussian MD rate-distortion region with lattice-based quantization.

Provides a universal scheme applicable to all i.i.d. smooth sources.

Develops low-complexity scalar quantizers with improved high-resolution performance.

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.