一种基于超分箱的分布式计算量化器设计
A Distributed Computationally Aware Quantizer Design via Hyper Binning
摘要：
我们设计了一个分布式函数感知量化方案的分布式函数压缩。我们认为$2$相关的源$X_1$和$X_2$和目的地，寻求一个连续函数$f(X_1,\,X_2)$的结果的估计$\hat{f}$。我们开发了一种压缩方案，称为超分仓，以通过最小化联合源分割的熵来压缩$f$。超合并是Cover的随机码构造的自然推广，用于使用正交合并的渐进最优Slepian-Wolf编码方案。这种方法背后的关键思想是使用线性判别分析，以表征不同的源特征组合。该方案捕获源和函数结构之间的相关性作为降维的手段。我们调查的性能超分仓不同的源分布，并确定哪些类的源需要更多的分区，以实现更好的函数近似。我们的方法带来了信息论的角度来看，传统的矢量量化技术从信号处理。
英文摘要：
We design a distributed function-aware quantization scheme for distributed functional compression. We consider $2$ correlated sources $X_1$ and $X_2$ and a destination that seeks an estimate $\hat{f}$ for the outcome of a continuous function $f(X_1,\,X_2)$. We develop a compression scheme called hyper binning in order to quantize $f$ via minimizing the entropy of joint source partitioning. Hyper binning is a natural generalization of Cover's random code construction for the asymptotically optimal Slepian-Wolf encoding scheme that makes use of orthogonal binning. The key idea behind this approach is to use linear discriminant analysis in order to characterize different source feature combinations. This scheme captures the correlation between the sources and the function's structure as a means of dimensionality reduction. We investigate the performance of hyper binning for different source distributions and identify which classes of sources entail more partitioning to achieve better function approximation. Our approach brings an information theory perspective to the traditional vector quantization technique from signal processing.
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