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.

A conjectural expression of the asymptotic gap between the rate-distortion function of an arbitrary generalized Gaussian multiterminal source coding system and that of its centralized counterpart in the high-resolution regime is proposed. The validity of this expression is verified when the number of sources is no more than 3.