Noise-shaped predictive coding for multiple descriptions of a colored Gaussian source

It was recently shown that the symmetric multiple-description (MD) quadratic rate-distortion function for memoryless Gaussian sources and two descriptions can be achieved by dithered Delta-Sigma quantization combined with memoryless entropy coding. In this paper, we generalize this result to stationary (colored) Gaussian sources by combining noise shaping and source prediction. We first propose a new representation for the test channel that realizes the MD rate-distortion function of a Gaussian source, both in the white and in the colored source case. We then show that this test channel can be materialized by embedding two source prediction loops, one for each description, within a common noise shaping loop. While the noise shaping loop controls the tradeoff between the side and the central distortions, the role of prediction (like in differential pulse code modulation) is to extract the source innovations from the reconstruction at each of the side decoders, and thus reduce the coding rate. Finally, we show that this scheme achieves the MD rate-distortion function at all resolutions and all side-to-central distortion ratios, in the limit of high dimensional quantization.