TY - JOUR

T1 - High-resolution source coding for non-difference distortion measures

T2 - The rate-distortion function

AU - Linder, Tamâs

AU - Zamir, Ram

N1 - Funding Information:
Manuscript received January 15, 1997; revised April 1, 1998. This work was supported in part by the Joint Program between the Hungarian Academy of Sciences and the Israeli Academy of Science and Humanities, and by the National Science Foundation and OTKA under Grant F 014174. This work was presented in part at ISIT-97, Ulm, Germany, June 1997. T. Linder is with the Department of Mathematics and Statistics, Queen’s University, Kingston, Ont. K7L 3N6 Canada (e-mail: linder@mast.queensu.ca). R. Zamir is with the Department of Electrical Engineering–Systems, Tel-Aviv University, Ramat-Aviv, 69978, Israel (e-mail: zamir@eng.tau.ac.il). Communicated by N. Merhav, Associate Editor for Source Coding. Publisher Item Identifier S 0018-9448(99)01398-X.

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

KW - Asymptotic quantization theory

KW - Non-difference distortion measures

KW - Rate-distortion function

KW - Remote source coding

KW - Shannon lower bound

UR - http://www.scopus.com/inward/record.url?scp=0033099498&partnerID=8YFLogxK

U2 - 10.1109/18.749001

DO - 10.1109/18.749001

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AN - SCOPUS:0033099498

SN - 0018-9448

VL - 45

SP - 533

EP - 547

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 2

ER -