Distortion-rate bounds for fixed- and variable-rate multiresolution sourcecodes

The source coding theorem for stationary sources describes the optimal perf ormance theoretically achievable by fixed- and variable-rate block quantize rs. The source coding theorem may be generalized by considering the problem of multiresolution or successive refinement source coding, which is the to pic of this work. Given a distortion vector (D-1, ..., D-L), this work desc ribes the family of achievable rate vectors (R-1, ..., R-L) for describing a stationary source at L resolutions, where the description at the first re solution is given at rate R-1 and achieves an expected distortion no greate r than D-1, the description at the second resolution includes both the firs t 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 bo unds for both fixed- and variable-rate source codes on discrete-time statio nary ergodic sources and discrete-time stationary nonergodic sources for an y integer number of resolutions L greater than or equal to 1, For L = 1, th e source coding theorems for stationary sources result, For L > 1, the resu lts extend previous theorems for discrete-alphabet memoryless sources.