M. Effros et al., VARIABLE-RATE SOURCE-CODING THEOREMS FOR STATIONARY NONERGODIC SOURCES, IEEE transactions on information theory, 40(6), 1994, pp. 1920-1925
Citations number
10
Categorie Soggetti
Information Science & Library Science","Engineering, Eletrical & Electronic
For a stationary ergodic source, the source coding theorem and its con
verse imply that the optimal performance theoretically achievable by a
fixed-rate or variable-rate block quantizer is equal to the distortio
n-rate function, which is defined as the infimum of an expected distor
tion subject to a mutual information constraint. For a stationary none
rgodic source, however, the distortion-rate function cannot in general
be achieved arbitrarily closely by a fixed-rate block code. We show,
though, that for any stationary nonergodic source with a Polish alphab
et, the distortion-rate function can be achieved arbitrarily closely b
y a variable-rate block code. We also show that the distortion-rate fu
nction of a stationary nonergodic source has a decomposition as the av
erage of the distortion-rate functions of the source's stationary ergo
dic components, where the average is taken over points on the componen
t distortion-rate functions having the same slope. These results exten
d previously known results for finite alphabets.