Performance of Nonuniform PAM Constellations for Gaussian Channel

In this paper, the Gaussian source quantization is done by using three different quantization methods[1,2]. The Gaussian source is an optimal information source, with average power as a constraint. We analyzed Pulse Amplitude Modulation (PAM) signal constellation obtained by means of different quantization methods for Gaussian channel. We quantized the Gaussian source applying the method given in [2], which gives the equiprobable appearance of signal constellations points, then, we quantized the same source using Lloyd-Max’s iterative quantization method and finally we performed Re-optimal quantization [1]. Re-optimal quantization is utilised because of minimization of average distortion for transmission through binary symetric channel [1], but we utilize Re-optimal quantization because of design of signal constellation for transmission through Gaussian channel in this paper. The first two methods are designed for noisefree transmission whereas the noise influence is considered by the third method. Also this paper presents the analysis method for the determination of the optimal signal constellation points disposition after quantization, when the error probability is minimized under the power constraint[3,4]. The combined method for the signal constellation design is considered in this paper. This method has two steps: the first step is the application nonuniform quantization (quantization methods of the noiseless transmission) and the second one is the nonlinear point transformation. The quantization methods of the noiseless transmission for the signal constellation design are considered in paper [5]. The nonlinear transformation is considered in [6] taking, the equiprobable transmission and great constellation points into account. In this paper, a method for determining, the conditional minimum is used. The minimum of the average error probability caused by the channel noise ( in dependence on the information source is discrete or continual) is determined [3,4]. The average transmission power is a constraint in determining the conditional minimum. The analysis for the sixteen points PAM signal constellation is presented. Nonuniform quantization of Gaussian source