Distortion-rate bounds for fixed- and variable-rate multiresolution source codes

The source coding theorem for stationary sources describes the optimal performance theoretically achievable by fixed- and variable-rate block quantizers. The source coding theorem may be generalized by considering the problem of multiresolution or successive refinement source coding, which is the topic of this work. Given a distortion vector (D₁,...,D_L), this work describes the family of achievable rate vectors (R₁,...,R_L) for describing a stationary source at L resolutions, where the description at the first resolution is given at rate R₁ and achieves an expected distortion no greater than D₁, the description at the second resolution includes both the first description and a refining description of rate R₂ and achieves expected distortion no greater than D₂, and so on. The work includes performance bounds for both fixed- and variable-rate source codes on discrete-time stationary ergodic sources and discrete-time stationary nonergodic sources for any integer number of resolutions L⩾1. For L=1, the source coding theorems for stationary sources result. For L>1, the results extend previous theorems for discrete-alphabet memoryless sources