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 (D-1, ..., D-L), this work describes the family of achievable rate vectors (R-1, ..., R-L) for describing a stationary source at L resolutions, where the description at the first resolution is given at rate R-1 and achieves an expected distortion no greater than D-1, the description at the second resolution includes both the first description and a refining description of rate R-2 and achieves expected distortion no greater than D-2, 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 greater than or equal to 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.
successive refinement embedded ergodic and nonergodic source coding theorems multiuser information theory progressive transmission