Multi-resolution source coding theorems

Abstract

For stationary sources on Polish alphabets, we describe the family of achievable rate and distortion vectors (R1,…,RL) and (D1,…,DL) for an L-resolution source code, where the description at the first resolution is given at rate R1 and distortion D1, the description at the second resolution includes both the first description and a refining description of rate R2 and distortion D2, and so on. We consider performance bounds for fixed- and variable-rate source codes on discrete-time stationary ergodic and stationary nonergodic sources for any integer number of resolutions L ≥ 1. For L > 1, the results extend previous results for discrete memoryless sources.