An iterative method for optimal resolution-constrained polar quantizer design

This paper addresses the problem of polar quantization optimization. Particularly, the aim of this investigation is to find the method for the optimal resolution-constrained polar quantizer design. The new iterative algorithm for determination of the optimal decision and representation magnitude levels and algorithm for optimization of number of phase cells within each magnitude level, is proposed. At high rates, the new optimal polar quantizer outperforms the optimal polar compander for 0.2dB, while the more significant gain should be expected at lower rates. In this paper, in order to enable practical implementation of quantizer model, algorithm which transforms real values for the optimal numbers of phase cells within magnitude levels into integer ones is also proposed. Moreover, the approximate closed form of signal to quantization ratio (SQNR) is derived. Since circularly symmetric sources and complex presentation of signals arise in numerous applications, it can be concluded that the usage area of the suggested proposal is very wide (audio coding, image coding, spectral phase coding SPC, synthetic aperture radars systems SARs, coding of the discrete Fourier transform). It should be emphasized that in contrast to earlier work, where models have been designed under high-rate assumption, the obtained nonuniform unrestricted polar quantizer is optimal for all rates.