This paper presents an algorithm for the optimal design of general entropy-constrained successively refinable unrestrictedpolar quantizer, i.e., with arbitrary number L of refinement levels, for bivariate circularly ...
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This paper presents an algorithm for the optimal design of general entropy-constrained successively refinable unrestrictedpolar quantizer, i.e., with arbitrary number L of refinement levels, for bivariate circularly symmetric sources. The optimization problem is formulated as the minimization of a weighted sum of distortions and entropies for the scenario where the magnitude quantizers' thresholds are confined to a predefined finite set. The proposed solution algorithm is globally optimal. It involves L stages, where each stage corresponds to an unrestrictedpolar quantizer (UPQ) level, and includes solving the minimum-weight path problem for multiple node pairs in a series of weighted directed acyclic graphs. Additionally, we derive an upper bound P-max((l)), l is an element of [1 : L], on the possible number of phase levels in any phase quantizer of the l-th level UPQ, which grows linearly with l. The time complexity of the proposed approach is O((LK3)-K-2 P-max((1))), where K is the cardinality of the predefined set of possible magnitude thresholds. Finally, the experimental results for L = 3 demonstrate the effectiveness in practice of the proposed scheme.
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