Colored Gaussian Multiple Descriptions: Spectral-Domain Characterization and Time-Domain Design
Jan Stubbe Østergaard, Yuval Kochman, Ram Zamir · arXiv (Cornell University) · 2010
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. We also show that the symmetric colored QG MD RDF can be achieved by combining oversampled noise-shaped predictive coding, dithered quantization, and memoryless entropy coding. In particular, the MD test channel can be materialized by embedding two source prediction loops, one for each description, within a common noise shaping loop, whose parameters are explicitly found from a spectral-domain characterization. Index Terms Multiple-description coding, rate-distortion theory, predictive coding, noise shaping, delta-sigma quantization, optimization, KKT optimality conditions