Multiple-Description Coding by Dithered Delta–Sigma Quantization

Jan Ostergaard, Ram Zamir
2009 IEEE Transactions on Information Theory  
We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linearadditive noise model resulting from dithered lattice quantization, allow us to construct a symmetric MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer
more » ... order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. We further show that the optimal noise-shaping filter of any order can be found by solving a set of Yule-Walker equations, and we present an exact rate-distortion analysis for any filter order, lattice vector quantizer dimension and bit rate. An important advantage of the proposed design is that it is symmetric in rate by construction, and there is therefore no need for source splitting.
doi:10.1109/tit.2009.2027528 fatcat:2xcxf2cqyrghnhzal2gasgo63u