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首页> 外文期刊>IEEE Transactions on Information Theory >Rates of convergence in the source coding theorem, in empirical quantizer design, and in universal lossy source coding
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Rates of convergence in the source coding theorem, in empirical quantizer design, and in universal lossy source coding

机译：源编码定理，经验量化器设计和通用有损源编码中的收敛速率

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摘要

Rate of convergence results are established for vector quantization. Convergence rates are given for an increasing vector dimension and/or an increasing training set size. In particular, the following results are shown for memoryless real-valued sources with bounded support at transmission rate R. (1) If a vector quantizer with fixed dimension k is designed to minimize the empirical mean-square error (MSE) with respect to m training vectors, then its MSE for the true source converges in expectation and almost surely to the minimum possible MSE as O(/spl radic/(log m/m)). (2) The MSE of an optimal k-dimensional vector quantizer for the true source converges, as the dimension grows, to the distortion-rate function D(R) as O(/spl radic/(log k/k)). (3) There exists a fixed-rate universal lossy source coding scheme whose per-letter MSE on a real-valued source samples converges in expectation and almost surely to the distortion-rate function D(R) as O((/spl radic/(loglog n/log n)). (4) Consider a training set of n real-valued source samples blocked into vectors of dimension k, and a k-dimension vector quantizer designed to minimize the empirical MSE with respect to the m=[n/k] training vectors. Then the per-letter MSE of this quantizer for the true source converges in expectation and almost surely to the distortion-rate function D(R) as O(/spl radic/(log log n/log n))), if one chooses k=[(1/R)(1-/spl epsiv/)log n] for any /spl epsiv//spl isin/(0.1).
机译：建立收敛速度以进行矢量量化。对于增加的向量维数和/或增加的训练集大小，给出了收敛速度。特别是，对于传输速率为R的有限支持的无记忆实值源，显示了以下结果。（1）如果设计了固定维数k的矢量量化器以最小化相对于m的经验均方误差（MSE）训练向量，则其对真实源的MSE会在期望值上收敛，并且几乎可以肯定地将MSE最小化为O（/ spl radic /（log m / m））。 （2）对于真实源，最佳k维矢量量化器的MSE随着维数的增长收敛为O（/ spli radic /（log k / k））的畸变率函数D（R）。 （3）存在一种固定速率通用有损源编码方案，该方案的实值源样本上的每个字母MSE均符合期望值，并且几乎可以肯定地将失真率函数D（R）收敛为O（（（/ spl radic / （loglog n / log n）。（4）考虑一个训练集合，其中包含训练成组的n个实值源样本，这些样本被分成维数为k的矢量，以及一个k维矢量量化器，该量化器旨在将m = [ [n / k]个训练向量。然后，此量化器针对真实源的每个字母的MSE会按预期收敛，并且几乎可以肯定地收敛到失真率函数D（R）为O（/ spl radic /（log log n / log n ））），如果对于任何/ spl epsiv // spl isin /（0.1）选择k = [（1 / R）（1- / spl epsiv /）log n]。

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