On Scalar Quantizer Design with Decoder Side Information

In this work, we investigate the design of scalar quantizers for the Wyner-Ziv problem, where the decoder has access to a noisy copy of the source. Necessary conditions are given for the design of optimum quantizers with a fixed number of partitions for a criterion consisting of a linear combination of distortion and rate. A simple iterative algorithm is developed to tackle the new quantizer design problem. The new algorithm generalizes the well-known Lloyd type I algorithm. The new approach will, in general, yield different scalar quantizers than the traditional approaches and these new quantizers provide some advantages. We also develop approximations to simplify quantizer design for high rate cases. With such approximations, the traditional optimal fixed-rate and entropy-constrained scalar quantizers are shown to remain optimum under certain conditions.