A Distributed Computationally Aware Quantizer Design via Hyper Binning
A Distributed Computationally Aware Quantizer Design via Hyper Binning
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DOI：
10.1109/tsp.2023.3238888
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发表时间：
2020-09
影响因子：
5.4
通讯作者：
Derya Malak;Muriel M'edard
中科院分区：
文献类型：
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作者：
Derya Malak;Muriel M'edard
设计了一种分布式函数感知的分布式函数压缩量化方案。我们考虑两个相关的源$X_{1}$和$X_{2}$，以及寻找连续函数$f(X_{1}，\，X_{2})$的结果的估计$HAT{f}$的目的地。我们开发了一种称为超级入库的压缩方案，通过最小化联合信源划分的熵来量化$f$。超分组码是Cover随机码构造的自然推广，它利用了正交分组码的渐近最优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来表征不同的源特征组合。该方案捕捉源和函数结构之间的相关性作为降维的一种手段。我们研究了不同信源分布的超库的性能，并确定了哪类信源需要更多的划分才能实现更好的函数逼近。我们的方法从信号处理的角度给传统的矢量量化技术带来了信息论的视角。
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.