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首页> 外文期刊>IEEE Transactions on Information Theory >A vector quantization approach to universal noiseless coding and quantization
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A vector quantization approach to universal noiseless coding and quantization

机译：通用无噪编码和量化的矢量量化方法

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摘要

A two-stage code is a block code in which each block of data is coded in two stages: the first stage codes the identity of a block code among a collection of codes, and the second stage codes the data using the identified code. The collection of codes may be noiseless codes, fixed-rate quantizers, or variable-rate quantizers. We take a vector quantization approach to two-stage coding, in which the first stage code can be regarded as a vector quantizer that "quantizes" the input data of length n to one of a fixed collection of block codes. We apply the generalized Lloyd algorithm to the first-stage quantizer, using induced measures of rate and distortion, to design locally optimal two-stage codes. On a source of medical images, two-stage variable-rate vector quantizers designed in this way outperform standard (one-stage) fixed-rate vector quantizers by over 9 dB. The tail of the operational distortion-rate function of the first-stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two-stage codes. We show that there exist two-stage universal noiseless codes, fixed-rate quantizers, and variable-rate quantizers whose per-letter rate and distortion redundancies converge to zero as (k/2)n/sup -1/ log n, when the universe of sources has finite dimension k. This extends the achievability part of Rissanen's theorem from universal noiseless codes to universal quantizers. Further, we show that the redundancies converge as O(n/sup -1/) when the universe of sources is countable, and as O(n/sup -1+/spl epsiv//) when the universe of sources is infinite-dimensional, under appropriate conditions.
机译：两阶段代码是一种分组代码，其中，每个数据块按两个阶段进行编码：第一阶段对一组代码中的分组代码的身份进行编码，第二阶段使用所标识的代码对数据进行编码。码的集合可以是无噪声码，固定速率量化器或可变速率量化器。我们采用矢量量化方法进行两阶段编码，其中第一级代码可以被视为矢量量化器，可以将长度为n的输入数据“量化”为固定的一组块码。我们将广义Lloyd算法应用于第一级量化器，使用率和失真的诱导量度来设计局部最优的两级代码。在医学图像的来源上，以这种方式设计的两级可变速率矢量量化器的性能优于标准（一级）固定速率矢量量化器的9 dB以上。第一级量化器的运算失真率函数的尾部确定两级代码通用序列的冗余度的最佳收敛速率。我们表明存在两阶段通用无噪声代码，固定速率量化器和可变速率量化器，当（k / 2）n / sup -1 / log n时，每个字母的速率和失真冗余收敛为零。源的宇宙具有有限的维数k。这将Rissanen定理的可实现性部分从通用无噪声代码扩展到通用量化器。此外，我们显示，当源的宇宙可数时，冗余度收敛为O（n / sup -1 /），而当源的宇宙无限时，则收敛为O（n / sup -1 + / spl epsiv //）。尺寸，在适当条件下。

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