Asymptotic performance of block quantizers with difference distortion measures

IEEE Transactions on Information TheoryPublished 1 January 1980

Y. Yamada, Saburo Tazaki, Robert M. Gray

DOI10.1109/tit.1980.1056142

Source URL

Citations152

SJR quartileQ1

SJR score1.46

SNIP1.76

TL;DR

Gersho's bounds on the asymptotic performance of block quantizers are valid for vector distortion measures that are powers of the Euclidean or l_{2} norm, and this generalization provides a k -dimensional generalization of Gish and Pierce's results for single-symbol quantizers.

Abstract

Gersho's bounds on the asymptotic (large rate or small distortion) performance of block quantizers are valid for vector distortion measures that are powers of the Euclidean or l_{2} norm. These results are generalized to difference distortion measures that are increasing functions of the seminorm of their argument, where any seminorm is allowed. This provides a k -dimensional generalization of Gish and Pierce's results for single-symbol quantizers. When the distortion measore is a power of a seminorm the bounds are shown to be strictly better than the corresponding bounds provided by the k th-order rate-distortion functions.

Keywords

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