Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources
Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources
复制标题
通过矢量值高斯源滤波实现零延迟率失真
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
C. Charalambous
中科院分区：
文献类型：
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作者：
Photios A. Stavrou;Jan Østergaard;C. Charalambous
我们处理零延迟源编码的向量值高斯马尔可夫源的均方误差（MSE）的保真度标准，其特征在于操作零延迟向量值高斯率失真函数（RDF）。我们解决这个问题，考虑非预期RDF（NRDF），这是一个下界的因果最佳性能理论上可达到的功能（或简单的因果RDF）和操作零延迟RDF。我们记得实现对应于最佳的高斯NRDF的“测试通道”，当考虑向量高斯-马尔可夫源在有限的时间范围内的MSE失真。然后，我们引入了充分条件，以证明该问题的解的存在性在无限的时间水平（或渐近制度）。对于渐近制度，我们使用的高斯NRDF的渐近特性提供了一个新的等价实现方案的反馈，其特征在于跨维度的向量源的资源分配（反向注水）问题。我们利用新的实现，通过格量化与减法抖动和联合无记忆熵编码来获得一个预测编码方案。这种编码方案提供了一个上界的操作零延迟向量值高斯RDF。当我们使用标量量化时，则对于矢量高斯-马尔可夫源的$r$有效维度，所获得的下限和理论上限之间的差距差距小于或等于$0.254 r + 1$ bits/vector。然而，我们进一步表明，当我们使用矢量量化时，并假设无限维高斯-马尔可夫源使先前的间隙可以忽略不计，即，高斯NRDF近似于操作零延迟高斯RDF。我们还将我们的结果扩展到向量值高斯源的任何有限的记忆在温和的条件下。我们的理论框架与说明性的数值实验证明。
We deal with zero-delay source coding of a vector-valued Gauss–Markov source subject to a mean-squared error (MSE) fidelity criterion characterized by the operational zero-delay vector-valued Gaussian rate distortion function (RDF). We address this problem by considering the nonanticipative RDF (NRDF), which is a lower bound to the causal optimal performance theoretically attainable function (or simply causal RDF) and operational zero-delay RDF. We recall the realization that corresponds to the optimal “test-channel” of the Gaussian NRDF, when considering a vector Gauss–Markov source subject to a MSE distortion in the finite time horizon. Then, we introduce sufficient conditions to show existence of solution for this problem in the infinite time horizon (or asymptotic regime). For the asymptotic regime, we use the asymptotic characterization of the Gaussian NRDF to provide a new equivalent realization scheme with feedback, which is characterized by a resource allocation (reverse-waterfilling) problem across the dimension of the vector source. We leverage the new realization to derive a predictive coding scheme via lattice quantization with subtractive dither and joint memoryless entropy coding. This coding scheme offers an upper bound to the operational zero-delay vector-valued Gaussian RDF. When we use scalar quantization, then for $r$ active dimensions of the vector Gauss–Markov source the gap between the obtained lower and theoretical upper bounds is less than or equal to $0.254r + 1$ bits/vector. However, we further show that it is possible when we use vector quantization, and assume infinite dimensional Gauss–Markov sources to make the previous gap to be negligible, i.e., Gaussian NRDF approximates the operational zero-delay Gaussian RDF. We also extend our results to vector-valued Gaussian sources of any finite memory under mild conditions. Our theoretical framework is demonstrated with illustrative numerical experiments.