Design of optimal quantizers for distributed coding of noisy sources

We investigate the design of optimal quantizers for individual encoding of several noisy observations of an unseen source, which is jointly decoded with the help of side information available at the decoder only. The joint statistics of the source data, the noisy observations and the side information are known, and exploited in the design. A variety of lossless coders for the quantization indices, including ideal Slepian-Wolf coders, are allowed. We present the optimality conditions such quantizers must satisfy, together with an extension of the Lloyd algorithm for a locally optimal design. Experimental results for Wyner-Ziv quantization of noisy Gaussian sources confirm the high-rate quantization theory established in our previous work.