The problem of asymptotic (i.e., low-distortion) behavior of the rate-distortion function of a random vector is investigated for a class of non-difference distortion measures. The main result is an asymptotically tight expression which parallels the Shannon lower bound for difference distortion measures. For example, for an input-weighted squared error distortion measure d(x,y) -\\W(x)(y -x)\\2, y, x 6 R, the asymptotic expression for the rate-distortion function of X 6 R" at distortion level D equals h(X) - | log (2-KeD/n) + B log |det W(X)\ where h(X) is the differential entropy of X. Extensions to staionary sources and to high-resolution remote ("noisy") source coding are also given. In a companion paper in this issue these results are applied to develop a high-resolution quantization theory for non-difference distortion measures.
- Asymptotic quantization theory
- Non-difference distortion measures
- Rate-distortion function
- Remote source coding
- Shannon lower bound