A distributed lossy compression network with $L$ encoders and a decoder is considered. Each encoder observes a source and sends a compressed version to the decoder. The decoder produces a joint reconstruction of target signals with the mean squared error distortion below a given threshold. It is assumed that the observed sources can be expressed as the sum of target signals and corruptive noises which are independently generated from two symmetric multivariate Gaussian distributions. The minimum compression rate of this network versus the distortion threshold is referred to as the rate-distortion function, for which an explicit lower bound is established by solving a minimization problem. Our lower bound matches the well-known Berger-Tung upper bound for some values of the distortion threshold. The asymptotic gap between the upper and lower bounds is characterized in the large $L$ limit.
翻译:使用美元编码器和解码器的分布式损耗压缩网络。 每一个编码器都观察源, 并发送压缩版本到解码器。 解码器将联合重建目标信号, 并在给定阈值下进行平均平方误差扭曲。 假设观察到的源可以以目标信号和腐蚀性噪声的总和表示, 这些信号和噪声是两个对称多变量高斯分布所独立产生的。 这个网络相对于扭曲阈值的最低压缩速率被称为速率扭曲函数, 通过解决最小化问题来确定明确的较低限值。 我们的下限匹配著名的卑尔格- 东上界值的扭曲阈值。 上界和下界之间的孔隙以大L$限值为特征。