论文标题
多元高斯来源的灰色智力率区域的表征：高斯辅助RV的最佳性
Characterization of the Gray-Wyner Rate Region for Multivariate Gaussian Sources: Optimality of Gaussian Auxiliary RV
论文作者
论文摘要
在本文中检查的是灰色和Wyner可实现的损耗率区域，用于相关的多元高斯随机变量（RVS）$ x_1：ω\ rightarrow {\ Mathbb r}^{p_1} $在两个解码器。结果表明，在由三倍的RVS $（x_1，x_2，w）$引起的所有联合分布中，$ w：ω\ rightarrow {\ mathbb w} $是辅助RV取得连续，可计数或有限的价值，灰色和wyner Achievable Achievable Achievable Achievable Achievable Achievable Achievable Achieven Achoraive at the the the the the the the the the the $ i is $ $ $ $ w $ w。 $ n $二维高斯房车。然后得出结论，可实现的速率区域由三个条件的协方差$ q_ {x_1，x_2 | w}，q_ {x_1 | w}，q_ {x_2 | w} $的共同高斯RVS。此外，如果RV $ W $制作$ x_1 $和$ x_2 $有条件地独立，则可以实现的速率区域的相应子集更简单，并且仅由两个条件的协方差$ q_ Q_ {x_1 | w}进行参数化，q_ {x_2 | w} $。本文还包括灰色速率区域的Pangloss平面以及相应速率失真函数的特征，其测试通道分布以及诱导这些分布的实现的结构特性。
Examined in this paper, is the Gray and Wyner achievable lossy rate region for a tuple of correlated multivariate Gaussian random variables (RVs) $X_1 : Ω\rightarrow {\mathbb R}^{p_1}$ and $X_2 : Ω\rightarrow {\mathbb R}^{p_2}$ with respect to square-error distortions at the two decoders. It is shown that among all joint distributions induced by a triple of RVs $(X_1,X_2, W)$, such that $W : Ω\rightarrow {\mathbb W} $ is the auxiliary RV taking continuous, countable, or finite values, the Gray and Wyner achievable rate region is characterized by jointly Gaussian RVs $(X_1,X_2, W)$ such that $W $ is an $n$-dimensional Gaussian RV. It then follows that the achievable rate region is parametrized by the three conditional covariances $Q_{X_1,X_2|W}, Q_{X_1|W}, Q_{X_2|W}$ of the jointly Gaussian RVs. Furthermore, if the RV $W$ makes $X_1$ and $X_2$ conditionally independent, then the corresponding subset of the achievable rate region, is simpler, and parametrized by only the two conditional covariances $Q_{X_1|W}, Q_{X_2|W}$. The paper also includes the characterization of the Pangloss plane of the Gray-Wyner rate region along with the characterizations of the corresponding rate distortion functions, their test-channel distributions, and structural properties of the realizations which induce these distributions.
