论文标题
用于分布式源编码的最佳测试通道的结构性特性，该源编码带有用于平方误差的多元高斯源的解码器侧信息
Structural Properties of Optimal Test Channels for Distributed Source Coding with Decoder Side Information for Multivariate Gaussian Sources with Square-Error Fidelity
论文作者
论文摘要
本文侧重于测试通道的结构属性，Wyner的操作信息率失真函数（RDF），$ \ overline {r}（Δ_x）$，是多变量相关的，共同独立且相同分布的高斯随机变量（rvs），$ \ \ \ \ \ w {x_t，y_t，y_t，y t，y tyt，$ \ wanty variables（RVS）的元素$ x_t：ω\ rightarrow {\ mathbb r}^{n_x} $，$ y_t：ω\ rightarrow {\ Mathbb r}^{n_y} $，在解码器上有平均均值错误e} \ sum_ {t = 1}^n || x_t - \ wideHat {x} _t ||^2 \leqΔ_x$，当$ \ {y_t \} _ {y_t \} _ {t = 1}^\ infty $是可用于解码器的侧面信息。我们构建了最佳测试渠道实现，该实现实现了信息RDF，$ \ operline {r}（δ_x）\ triangleq \ inf _ {{{\ cal m}（Δ_x）} i（x; z | y）$，其中$ {\ cal m}（Δ_x）$ a $ z $ z $ z $ Z $ p} _ {z | x，y} = {\ bf p} _ {z | x} $，$ \ wideHat {x} = f（y，z）$，和$ {\ bf e} \ {|| x- x- x- x- \ wideHat我们显示了基本结构属性：（1）实现RDF的最佳测试频道实现，$ \ overline {r}（Δ_x）$，满足条件独立性，$ {\ bf p} _ {x | \ wideHat {x}，y，z} = {\ bf p} _ {x | \ wideHat {x}，y}，y} = {\ bf p} e} \ big \ {x \ big | \ wideHat {x}，y，z \ big \ \} = {\ bf e} \ big \ \ {x \ big | \ big | \ big | \ wideHat {x} \ big \ big \ \} = \ wideHat {x} $ and（2） $ {r} _ {x | y}（Δ_x）\ triangleq \ inf _ {{\ bf p} _ {\ wideHat {x} | x，y}：{\ bf e} \ wideHat {x} | y）$，当$ \ {y_t \} _ {t = 1}^\ infty $都可以供索引和解码器，以及等值$ \ edline {r}（r}（δ_x）= {r} = {r} _ {x | y}（x | y}（x | y}（X | y}）$。
This paper focuses on the structural properties of test channels, of Wyner's operational information rate distortion function (RDF), $\overline{R}(Δ_X)$, of a tuple of multivariate correlated, jointly independent and identically distributed Gaussian random variables (RVs), $\{X_t, Y_t\}_{t=1}^\infty$, $X_t: Ω\rightarrow {\mathbb R}^{n_x}$, $Y_t: Ω\rightarrow {\mathbb R}^{n_y}$, with average mean-square error at the decoder, $\frac{1}{n} {\bf E}\sum_{t=1}^n||X_t - \widehat{X}_t||^2\leq Δ_X$, when $\{Y_t\}_{t=1}^\infty$ is the side information available to the decoder only. We construct optimal test channel realizations, which achieve the informational RDF, $\overline{R}(Δ_X) \triangleq\inf_{{\cal M}(Δ_X)} I(X;Z|Y)$, where ${\cal M}(Δ_X)$ is the set of auxiliary RVs $Z$ such that, ${\bf P}_{Z|X,Y}={\bf P}_{Z|X}$, $\widehat{X}=f(Y,Z)$, and ${\bf E}\{||X-\widehat{X}||^2\}\leq Δ_X$. We show the fundamental structural properties: (1) Optimal test channel realizations that achieve the RDF, $\overline{R}(Δ_X)$, satisfy conditional independence, $ {\bf P}_{X|\widehat{X}, Y, Z}={\bf P}_{X|\widehat{X},Y}={\bf P}_{X|\widehat{X}}, \hspace{.2in} {\bf E}\Big\{X\Big|\widehat{X}, Y, Z\Big\}={\bf E}\Big\{X\Big|\widehat{X}\Big\}=\widehat{X} $ and (2) similarly for the conditional RDF, ${R}_{X|Y}(Δ_X) \triangleq \inf_{{\bf P}_{\widehat{X}|X,Y}:{\bf E}\{||X-\widehat{X}||^2\} \leq Δ_X} I(X; \widehat{X}|Y)$, when $\{Y_t\}_{t=1}^\infty$ is available to both the encoder and decoder, and the equality $\overline{R}(Δ_X)={R}_{X|Y}(Δ_X)$.
