[IEEE Trans. on Information Theory, September 1999, pp. 2110-2115]
On the Rate-Distortion Function of Random Vectors and
Stationary Sources with Mixed Distributions
András György, Tamás Linder, and Kenneth Zeger
Abstract
The asymptotic (small distortion) behavior of the rate-distortion
function of an n-dimensional source vector with mixed distribution
is derived. The source distribution is a finite mixture of components
such that under each component distribution a certain subset of the
coordinates have a discrete distribution while the remaining
coordinates have a joint density. The expected number of coordinates
with a joint density is shown to equal the rate-distortion dimension
of the source vector. Also, the exact small distortion asymptotic
behavior of the rate-distortion function of a special but interesting
class of stationary information sources is determined.