Optimization of random quantization

The present communication is devoted to the problem of the optimization of quantizers when transition points are random variables (Random Quantizers). The optimization is carried out with respect to the mean-squared error criterion when the Mean Transfer Function is imposed to be linear. The optimal solutions being dependent on the input variable statistics, we give it for two common laws (Gaussian and 1st order Laplacian). A simulation showing the validity of the theoretical results is also reported.