Semi-analytical solution for rate distortion function and OPTA for sources with arbitrary distribution

The rate distortion function is a widely used theoretical bound which describes the minimum mean square error (MMSE) distortion for a given number of quantization bits when quantizing a scalar random variable. An analytical solution for this function is only available for a small number of probability density functions (pdf), such as the Gaussian pdf. For arbitrary pdfs, the Blahut-Arimoto algorithm needs to be applied to iteratively estimate the rate distortion function. We propose a novel (semi-)analytical and non-iterative method to calculate the rate distortion function for sources with arbitrary pdfs. This method is based on the Guo-Shamai-Verdu¿ (GSV) theorem. Furthermore, it is possible to apply the proposed method for calculating the optimum performance theoretically attainable (OPTA) for arbitrarily distributed input symbols observed through an AWGN channel.