Colored Gaussian Multiple Descriptions: Spectral-Domain Characterization and Time-Domain Design

Details Colored Gaussian Multiple Descriptions: Spectral-Domain Characterization and Time-Domain Design Colored Gaussian Multiple Descriptions: Spectral-Domain Characterization and Time-Domain Design

2010-06-10

arxiv.org/abs/1006.2002v2

Computer Science

Information Theory

Submitted to IEEE Transactions on Information Theory. For clarity, sections has been rewritten and several propositions has be

Scientific paper

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 via two Lagrangian variables. To establish this result, we use two key ideas. First, we propose a new representation for the MD test channel, and show that the minimum mutual information rate across this channel coincide with the QG MD RDF. Second, we use variational calculus to obtain a spectral domain representation of the test channel's optimal side and central distortion spectra given the source spectral density and the side and central distortion constraints. The distortion spectra are specified via two Lagrangian parameters, 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 noise-shaped predictive coding, dithered quantization, and memoryless entropy coding. In particular, we show that the proposed 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 the spectral-domain characterization. The source prediction loops exploit the source memory, and thus reduce the coding rate. The noise-shaping loop, controls the trade-off between the side and the central distortions by shaping the quantization noise.

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