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)+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.
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机译：针对一类非差分失真测度，研究了随机向量的速率失真函数的渐近（即低失真）行为问题。主要结果是一个渐近紧表达式，它与差值失真度量的香农下限相似。例如，对于输入加权平方误差失真量度d（x，y）= / spl par / W（x）（yx）/ spl par // sup 2 /，y，x / spl isin / R / sup n /，在失真级别D时，X / spl的速率失真函数isin / R / sup n /的渐近表达式等于h（X）-/ sub 2 /// sup n / log（2 / spl pi / eD / n）+ Elog | detW（X）|其中h（X）是X的微分熵。还给出了对固定源和高分辨率远程（“噪声”）源编码的扩展。
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