Multi-resolution source coding theorems

For stationary sources on Polish alphabets, we describe the family of achievable rate and distortion vectors (R/sub 1/,...,R/sub L/) and (D/sub 1/,...,D/sub L/) for an L-resolution source code, where the description at the first resolution is given at rate R/sub 1/ and distortion D/sub 1/, the description at the second resolution includes both the first description and a refining description of rate R/sub 2/ and distortion D/sub 2/, 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/spl ges/1. For L>1, the results extend previous results for discrete memoryless sources.