High-resolution source coding for non-difference distortion measures: the rate-distortion function
Tamás Linder, Ram Zamir · IEEE Transactions on Information Theory · 1999
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)=/spl par/W(x)(y-x)/spl par//sup 2/,y,x/spl isin/R/sup n/, the asymptotic expression for the rate-distortion function of X/spl isin/R/sup n/ at distortion level D equals h(X)-/sub 2///sup n/log(2/spl pi/eD/n)+Elog|detW(X)| where h(X) is the differential entropy of X. Extensions to stationary sources and to high-resolution remote ("noisy") source coding are also given.