Tree encoding for symmetric sources with a distortion measure

A simple algorithm is developed for mapping the outputs of a source into a set of code sequences generated by a tree code. The algorithm is analyzed for the case of a source producing discrete independent equiprobable letters when the distortion measure satisfies a certain symmetry condition. It is shown that the algorithm is capable of achieving an average distortion as close as desired to the minimum average distortion for the code rate given by Shannon's rate-distortion theorem.