On calculating Sakrison's rate distortion function for classes of parameterized sources

Abstract

Sakrison extended Shannon's notion of the rate distortion function to parameterized classes of sources by taking a minimax approach and defining a measure of the minimum rate required for information reconstruction subject to a prescribed fidelity level D. Unfortunately, calculation of Sakrison's rate distortion function may be very difficult because analytic solutions do not generally exist and there has been a lack of a constructive method for finding the rate. However, an approach presented in this correspondence may be used to calculate an approximation to Sakrison's rate distortion function for classes of sources with a finite, discrete input space and a continuous parameter space. The approach gives rise to an algorithm which is shown to be convergent and numerical examples are studied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>