Optimal designing scalar quantizers using a hybrid quantization method for the Laplacian source

This paper proposes new method for designing scalar quantizers. The proposed method, denoted as hybrid method, combines two quantization techniques, the companding technique and the Lloyd-Max's algorithm. In this paper an exact and complete analysis of the hybrid quantization method considering the Laplacian input signals is carried out. Furthermore, two approaches to the problem of finding the sets of parameters are considered. It is demonstrated that by using both approaches the hybrid quantization method provides optimal scalar quantizer design. Moreover, the designing complexity of the proposed method is considered and compared with the complexity of the other models in use. It is shown that, in case of average and large number of quantization levels, scalar quantizers designed by using the hybrid quantization method have less complexity than optimal Lloyd-Max's scalar quantizers. Also, it is demonstrated that the proposed quantization method has a little bit greater complexity than the method based on the companding technique, but provides optimal quantizer's performance.