Design of Successively Refinable Unrestricted Polar Quantizer
Huihui Wu, Sorina Dumitrescu · IEEE Transactions on Communications · 2019
This paper addresses the design of two-stage successively refinable unrestricted polar quantizers for bivariate circularly symmetric sources in the entropy-constrained and fixed-rate cases. The proposed solutions are globally optimal when the thresholds of the magnitude quantizers are confined to finite discretizations of the interval [0, ∞). The algorithm developed for the entropy-constrained case involves a series of stages, including solving the minimum-weight path problem for multiple node pairs in certain weighted directed acyclic graphs. The asymptotical time complexity is O(K1K22Pmax), where K1and K2are the sizes of the sets of possible magnitude thresholds of the coarse and refined unrestricted polar quantizers (UPQs), respectively, while Pmaxis an upper bound on the number of phase levels in any phase quantizer of the coarse UPQ. The solution algorithm for the fixed-rate case is based on solving a succession of dynamic programming problems for multiple coarse quantizer bins. The time complexity in the fixed-rate case amounts to O(K1K2N2N1), where N1is the number of cells of the coarse UPQ and N is the ratio between the number of bins of the fine and coarse UPQs. The extensive experimental results on a bivariate circularly symmetric Gaussian source show the effectiveness of the proposed schemes.