Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms
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.
Cite
@article{arxiv.1006.2002,
title = {Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms},
author = {Jan Ostergaard and Yuval Kochman and Ram Zamir},
journal= {arXiv preprint arXiv:1006.2002},
year = {2016}
}
Comments
Accepted for publications in the IEEE Transactions on Information Theory. Title have been shortened, abstract clarified, and paper significantly restructured