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High-resolution source coding for non-difference distortion measures: the rate-distortion function

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2 Author(s)
T. Linder ; Dept. of Math. & Stat., Queen's Univ., Kingston, Ont., Canada ; R. Zamir

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∈Rn, the asymptotic expression for the rate-distortion function of X∈Rn at distortion level D equals h(X)-2 /nlog(2πeD/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

Published in:

IEEE Transactions on Information Theory  (Volume:45 ,  Issue: 2 )