Optimal Design of A Two-stage Wyner-Ziv Scalar Quantizer with Degraded Side Information

This work addresses the optimal design of a two-stage Wyner-Ziv scalar quantizer with degraded side information (SI). We assume that binning is performed optimally and address the design of the nested quantizer partitions. The optimization problem is formulated as minimizing a weighted sum of distortions and rates. The proposed solution algorithm is globally optimal when the source and SI are discrete, while the partition cells are contiguous. The algorithm is based on solving the single source or the all-pairs minimum-weight path problem in certain weighted directed acyclic graphs. A so-called partial Monge property is additionally introduced and a faster solution algorithm exploiting this property is proposed. Experimental results assess the practical performance of the proposed scheme.