We consider the distributed source coding system for $L$ correlated Gaussianobservations $Y_i, i=1,2, ..., L$. Let $X_i,i=1,2, ..., L$ be $L$ correlatedGaussian random variables and $N_i,$ $i=1,2,... L$ be independent additiveGaussian noises also independent of $X_i, i=1,2,..., L$. We consider the casewhere for each $i=1,2,..., L$, $Y_i$ is a noisy observation of $X_i$, that is,$Y_i=X_i+N_i$. On this coding system the determination problem of the ratedistortion region remains open. In this paper, we derive explicit outer andinner bounds of the rate distortion region. We further find an explicitsufficient condition for those two to match. We also study the sum rate part ofthe rate distortion region when the correlation has some symmetrical propertyand derive a new lower bound of the sum rate part. We derive a sufficientcondition for this lower bound to be tight. The derived sufficient conditiondepends only on the correlation property of the sources and their observations.
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机译：我们考虑用于与$ L $相关的高斯观测B $ Y_i，i = 1,2，...，L $的分布式源编码系统。令$ X_i，i = 1,2，...，L $为相关的高斯随机变量和$ N_i，$ $ i = 1,2，... L $为独立加性高斯噪声也独立于$ X_i， i = 1,2，...，L $。我们考虑的情况是，每个$ i = 1,2，...，L $，$ Y_i $是$ X_i $的噪声观测值，即$ Y_i = X_i + N_i $。在该编码系统上，额定扭曲区域的确定问题仍然存在。在本文中，我们得出了速率失真区域的显式外边界和内边界。我们进一步找到了这两个匹配的显式充分条件。当相关具有一定的对称性时，我们还研究了速率失真区域的求和率部分，并得出了求和率部分的新下界。我们得出一个足够的条件来使这个下限变得严格。导出的充分条件仅取决于源及其观测值的相关属性。
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