Abstract

The source coding theorem for stationary sources describes the optimal performance theoretically achievable by fixed- and variable-rate block quantizers. We here generalize the source coding theorem by considering the problem of multi-resolution or successive refinement source coding. In particular, given a distortion vector (D 1 ; : : : ; DL ), we describe the family of achievable rate vectors (R 1 ; : : : ; RL ) 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. We consider performance bounds for both 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 source coding ...

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