Multiple-Description Coding by Dithered Delta-Sigma Quantization

TL;DR

This paper introduces a novel multiple-description coding scheme based on dithered Delta-Sigma quantization, which asymptotically achieves the optimal rate-distortion trade-off for Gaussian sources by leveraging noise shaping and redundancy.

Contribution

It establishes a connection between multiple-description coding and Delta-Sigma quantization, proposing a symmetric, time-invariant scheme with asymptotic optimality.

Findings

Asymptotic approach to the MD rate-distortion function for Gaussian sources.

Optimal noise shaping filter must be minimum phase with a specific spectral profile.

The scheme is symmetric, eliminating the need for source splitting.

Abstract

We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.