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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 l₂ 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.
Yamada et al. (Tue,) studied this question.