Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms

TL;DR

This paper extends the understanding of colored Gaussian multiple descriptions by providing a spectral domain parametrization with two Lagrangian variables and proposing a time-domain scheme combining delta-sigma and differential pulse-code modulation.

Contribution

It introduces a spectral domain parametrization for the two-description case and a practical time-domain scheme achieving the RDF using delta-sigma and differential pulse-code modulation.

Findings

Spectral domain parametrization with two Lagrangian variables for two-description RDF.

Time-domain scheme design combining delta-sigma modulation and differential pulse-code modulation.

Explicit parameter determination from spectral analysis for practical implementation.

Abstract

It is well known that Shannon's rate-distortion function (RDF) in the colored quadratic Gaussian (QG) case can be parametrized via a single Lagrangian variable (the "water level" in the reverse water filling solution). In this work, we show that the symmetric colored QG multiple-description (MD) RDF in the case of two descriptions can be parametrized in the spectral domain via two Lagrangian variables, which control the trade-off between the side distortion, the central distortion, and the coding rate. This spectral-domain analysis is complemented by a time-domain scheme-design approach: we show that the symmetric colored QG MD RDF can be achieved by combining ideas of delta-sigma modulation and differential pulse-code modulation. Specifically, two source prediction loops, one for each description, are embedded within a common noise shaping loop, whose parameters are explicitly found from the spectral-domain characterization.