Rate distortion function with a proportional mean-square error distortion measure

New bounds on the rate distortion function of certain stationary time-discrete and time-continuous 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 in the time-discrete case 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 upper bound.