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

Abstract

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,...,DL), this work describes the family of achievable rate vectors (R1,...,RL) 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.