Worst-Case Source for Distributed Compression with Quadratic Distortion
  We consider the k-encoder source coding problem with a quadratic distortion measure. We show that among all source distributions with a given covariance matrix K, the jointly Gaussian source requires the highest rates in order to meet a given set of distortion constraints. 
Ilan Shomorony, A. Salman Avestimehr, Himanshu Asnani, Tsachy Weissman
cs.IT math.IT