Design of Optimal Scalar Quantizer for Sequential Coding of Correlated Sources

This paper addresses the design of a sequential scalar quantizer (SSQ) for finite-alphabet correlated sources in the fixed-rate (FR) and entropy-constrained (EC) cases. The optimization problem is formulated as the minimization of a weighted sum of distortions and rates. The proposed solution is globally optimal for the class of SSQs with convex cells and is based on solving the minimum-weight path (MWP) problem in the EC case, respectively, a length-constrained MWP problem in the FR case, in a series of weighted directed acyclic graphs. The asymptotic time complexity is $O(K_{1}^{2}K_{2}^{2})$ , where $K_{1}$ and $K_{2}$ are the respective sizes of the alphabets of the two sources. Additionally, it is proved that, by applying the proposed algorithms to discretizations of correlated sources with continuous joint probability density function, the performance approaches that of the optimal EC-SSQ, respectively, FR-SSQ, with convex cells for the original sources as the accuracy of the discretization increases. Extensive experiments performed with correlated Gaussian sources validate the effectiveness in practice of the proposed approach in approximating the optimal SSQ for the case of continuous-alphabet sources.