Variable-rate source coding theorems for stationary nonergodic sources
The source coding theorem and its converse imply that the optimal performance theoretically achievable by a fixed- or variable-rate block quantizer on a stationary ergodic source equals the distortion-rate function. While a fixed-rate block code cannot achieve arbitrarily closely the distortion-rate function on an arbitrary stationary nonergodic source, the authors show for the case of Polish alphabets that a variable-rate block code can. They also show that the distortion-rate function of a stationary nonergodic source has a decomposition as the average over points of equal slope on the distortion-rate functions of the source's stationary ergodic components. These results extend earlier finite alphabet results.
© Copyright 1994 IEEE. Reprinted with permission. This material is based upon work partially supported by an AT&T Ph.D. Scholarship, by a grant from the Center for Telecommunications at Stanford, and by an NSF Graduate Fellowship.