Rational Dither Modulation using logarithmic quantization with optimum parameter

In this paper, a new logarithmic quantization for Rational Dither Modulation (RDM) is presented. It can be shown that the μ-law function produces quantization levels which are in best accordance with the noise characteristics in RDM. However, since the μ-law function cannot be used in its original form, as in, we use it with slight modifications. In order to obtain the optimum quantizer arrangement, which results in minimum error probability, the analytical error probability is obtained and then minimized with respect to μ, which defines the compression level of the logarithmic function. The embedding distortion for the proposed method is also derived. Simulation results show that, using logarithmic quantization, better performance can be achieved in comparison with conventional RDM. Furthermore, as will be shown, the proposed method is more suitable in practice due to its perceptual advantages.