On the Asymptotic Distribution of
On the Asymptotic Distribution of
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关于渐近分布
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
D. Neuhoff
中科院分区：
文献类型：
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作者：
D. Neuhoff
在最近的一篇论文中，Lee和Neuhoff发现了一个由具有许多量化点的矢量量化器产生的误差长度分布的渐近公式。该分布取决于源概率密度、量化器点密度和量化器形状轮廓。(The后者将量化单元的形状表征为位置的函数。本文的目的是通过确定精确的条件来给出这个公式的严格推导，在该条件下，表明如果具有给定维数和增加的点数的矢量量化器序列具有分别收敛到“模型”点密度和“模型”形状轮廓的“特定”点密度和“特定”形状轮廓，则量化误差的长度分布，适当地归一化，收敛于上述公式，其中模型点密度和模型形状轮廓被替代。
In a recent paper, Lee and Neuhoff found an asymp- totic formula for the distribution of the length of the errors produced by a vector quantizer with many quantization points. This distribution depends on the source probability density, the quantizer point density, and the quantizer shape profile. (The latter characterizes the shapes of the quantization cells as a function of position.) The purpose of this paper is to give a rigorous derivation of this formula by identifying precise conditions under which it is shown that if a sequence of vector quantizers with a given dimension and an increasing number of points has "specific" point densities and "specific" shape profiles converging to a "model" point density and a "model" shape profile, respectively, then the distribution of the length of the quantization error, suitably normalized, converges to the aforementioned formula, with the model point density and the model shape profile substituted.