Design of General Entropy-Constrained Successively Refinable Unrestricted Polar Quantizer

This paper presents an algorithm for the optimal design of general entropy-constrained successively refinable unrestricted polar 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 unrestricted polar 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 ∈ [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(L
²
K
³
P
_max
^(l)
), 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.