Information rates of Pre/Post-filtered dithered quantizers

We consider encoding of a source with pre-specified second-order statistics, but otherwise arbitrary, by Entropy-Coded Dithered (lattice) Quantization (ECDQ) incorporating linear pre- and post-filters. In the design and analysis of this scheme we utilize the equivalent additive-noise channel model of the ECDQ. For Gaussian sources and square error distortion measure, the coding performance of the pre/post filtered ECDQ approaches the rate-distortion function, as the dimension of the (optimal) lattice quantizer becomes large; actually, in this case the proposed coding scheme simulates the optimal forward channel realization of the rate-distortion function. For non-Gaussian sources and finite-dimensional lattice quantizers, the coding rate exceeds the rate-distortion function by at most the sum of two terms: the "information divergence of the source from Gaussianity" and the "information divergence of the quantization noise from Gaussianity." Additional bounds on the excess rate of the scheme from the rate distortion function are also provided.