Design of Optimal Entropy-constrained Successively Refinable Unrestricted Polar Quantizer for Bivariate Circularly Symmetric Sources

This paper focuses on the design of entropy-constrained successively refinable unrestricted polar quantizer (EC-SRUPQ) for bivariate circularly symmetric sources. The proposed algorithm is globally optimal under the constraint that the magnitude quantizers’ thresholds are confined to finite sets. The optimization problem is formulated as the minimization of a weighted sum of distortions and entropies. The proposed solution consists of a series of steps including solving the minimum-weight path problem for multiple node pairs in certain weighted directed acyclic graphs. The asymptotical time complexity is $O(K_{1}K_{2}^{2}P_{max })$ , where $K_{1}$ and $K_{2}$ are the sizes of the sets of possible magnitude thresholds of the coarse UPQ and refined UPQ, respectively, while $P_{max }$ is the maximum number of phase levels in any phase quantizer of the coarse UPQ.