Design of Optimal Fixed-Rate Unrestricted Polar Quantizer for Bivariate Circularly Symmetric Sources

This letter presents an algorithm for the design of fixed-rate unrestricted polar quantizer (FUPQ) for bivariate circularly symmetric sources. The proposed algorithm is globally optimal for the class of FUPQs with the magnitude quantizer thresholds restricted to some predefined finite set. The solution algorithm is based on dynamic programming, which is further accelerated by exploiting the monotonicity property of the cost function. The time complexity of the accelerated algorithm is $O(KN^2)$, where $N$ is the number of target qunatizer levels and $K$ is the size of the predefined set of possible thresholds. The experimental results show that our approach outperforms the previous tractable designs when the total number of quantizer levels ranges between 25 and 256.