High-resolution Source Coding for Non-diierence Distortion Measures: the Rate Distortion Function
نویسنده
چکیده
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-diierence distortion measures. The main result is an asymptotically tight expression which parallels the Shannon lower bound for diierence distortion measures. For example, for an input-weighted squared error distortion measure d(x; y) = kW(x)(y ? x)k 2 , y; x 2 R n , the asymptotic expression for the rate distortion function of X 2 R n at distortion level D equals h(X) ? n 2 log(2eD=n) + Elog j det W (X)j where h(X) is the diierential entropy of X. An extension to stationary sources is also given. Applications include the study of the rate distortion function and the structure of the optimal encoder for high resolution remote source coding and the development of a high resolution quantization theory for non-diierence distortion measures.
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تاریخ انتشار 1998