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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l_{2}</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> -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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> th-order rate-distortion functions.
Keywords
Distortion (music)MathematicsRate distortionGeneralizationNorm (philosophy)AlgorithmDiscrete mathematicsComputer scienceStatisticsCoding (social sciences)Mathematical analysisTelecommunicationsBandwidth (computing)
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Publication Info
- Year
- 1980
- Type
- article
- Volume
- 26
- Issue
- 1
- Pages
- 6-14
- Citations
- 152
- Access
- Closed
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Cite This
Y. Yamada,
Saburo Tazaki,
Robert M. Gray
(1980).
Asymptotic performance of block quantizers with difference distortion measures.
IEEE Transactions on Information Theory
, 26
(1)
, 6-14.
https://doi.org/10.1109/tit.1980.1056142
Identifiers
- DOI
- 10.1109/tit.1980.1056142