Multi-resolution source coding theorems

For stationary sources on Polish alphabets, we describe the family of achievable rate and distortion vectors (R₁,…,R_L) and (D₁,…,D_L) 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