  New bounds on the rate distortion function of certain non-Gaussian sources,
with a proportional-weighted mean-square error (MSE) distortion measure, are
given. The growth, g, of the rate distortion function, as a result of changing
from a non-weighted MSE distortion measure to a proportional-weighted
distortion criterion is analyzed. It is shown that for a small distortion, d,
the growth, g, and the difference between the rate distortion functions of a
Gaussian memoryless source and a source with memory, both with the same
marginal statistics and MSE distortion measure, share the same lower bound.
Several examples and applications are also given.
