Semi–logarithmic and hybrid quantization of Laplacian source inwide range of variances

Abstract

A novel semilogarithmic hybrid quantizer for non-uniform scalar quantization of Laplacian source, which consist of uniform quantizer and companding quantizer is introduced. Uniform quantizer has unit gain in area around zero. Companding quantizer is defined with a novel logarithm characteristic. Also an analysis of classic semilogarithmic A-law for various values of A parameter is provided. Comparation with classic semilogarithmic A-law is performed. The main advantage of hybrid quantizer is that number of representation levels for both uniform and companding quantizer are not unambiguously determined function of the A parameter value, as it is the case with classic semilogarithmic A companding characteristic. It is shown that by using hybrid quantizer, average of signal-to-quantization noise ratio SQNR quality obtained by using classic A companding law can be overachieved for 0.47 dB. Numbers of representation levels of hybrid quantizer are adapted to the input signal variances, in order to achieve high SQNR in a wide range of signal volumes (variances). By using this adaptation higher average SQNR quality of 2.52 dB could be achieved compared to classic A companding law. Forward adaptation of hybrid quantizer is analyzed and obtained performances correspond to adaptive classic A companding law case but possible advantage arises in simpler practical realization of hybrid quantizers. Obtained performances correspond to classic A -law companding case, because during the adaptation process, optimal values of parameter A are chosen. For each other A parameter values proposed hybrid quantizer provides better results. For value of A = 50 hybrid model has higher SQNR value for 0.79 dB.K e y w o r d s: hybrid semilogarithmic quantizer, forward adaptive quantization, Laplacian source