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首页> 外文期刊>IEEE Transactions on Information Theory >Information Rates of Densely Sampled Data: Distributed Vector Quantization and Scalar Quantization With Transforms for Gaussian Sources
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Information Rates of Densely Sampled Data: Distributed Vector Quantization and Scalar Quantization With Transforms for Gaussian Sources

机译：密集采样数据的信息速率：高斯源变换的分布式矢量量化和标量量化

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This paper establishes rates attainable by several lossy schemes for coding a continuous parameter source to a specified mean-squared-error distortion based on sampling at asymptotically large rates. First, a densely sampled, spatiotemporal, stationary Gaussian source is distributively encoded. The Berger-Tung bound to the distributed rate-distortion function and three convergence theorems are used to obtain an upper bound, expressed in terms of the source spectral density, to the smallest attainable rate at asymptotically large sampling rates. The bound is tighter than that recently obtained by Kashyap Both indicate that with ideal distributed lossy coding, dense sensor networks can efficiently sense and convey a field, in contrast to the negative result obtained by Marco for encoders based on scalar quantization and Slepian-Wolf distributed lossless coding. The second scheme is transform coding with scalar coefficient quantization. A new generalized transform coding analysis, as well as the aforementioned convergence theorems, is used to find the smallest attainable rate at asymptotically large sampling rates in terms of the source spectral density and the operational rate-distortion function of the family of quantizers, which in contrast to previous analyses need not be convex. The result shows that when a transform is used, scalar quantization need not cause the poor performance found by Marco As a corollary, the final result pursues an approach, originally proposed by Berger, to show that the inverse water-pouring formula for the rate-distortion function can be attained at high sampling rates by transform coding with ideal vector quantization to encode the coefficients. Also established in the paper are relations between operational rate-distortion and distortion-rate functions for a continuous parameter source and those for the discrete parameter source that results from sampling.
机译：本文建立了通过以渐进大速率采样为基础将连续参数源编码为指定的均方误差失真的几种有损方案可获得的速率。首先，对密集采样的时空平稳高斯源进行分布式编码。分布速率失真函数的Berger-Tung边界和三个收敛定理用于获得以源谱密度表示的上限，在渐近大采样速率下，该上限达到最小。该边界比Kashyap最近获得的边界更严格。两者都表明，与理想的分布式有损编码相比，密集的传感器网络可以有效地感测和传递磁场，这与Marco对基于标量量化和Slepian-Wolf分布的编码器得出的否定结果相反无损编码。第二种方案是具有标量系数量化的变换编码。一种新的广义变换编码分析以及上述收敛定理，用于根据源谱密度和量化器系列的工作速率失真函数来找到渐近大采样速率下的最小可实现速率。与以前的分析形成对比的不必是凸面的。结果表明，使用变换时，标量量化不必导致Marco发现的较差性能。作为推论，最终结果采用了Berger最初提出的方法，表明速率的反注水公式为通过采用理想的矢量量化对系数进行编码的变换编码，可以在高采样率下获得失真函数。本文还建立了连续参数源的操作率失真和失真率函数与采样产生的离散参数源的函数之间的关系。

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