Network compression: Worst-case analysis

We consider the problem of communicating a distributed correlated memoryless source over a memoryless network, from source nodes to destination nodes, under quadratic distortion constraints. We show the following two complementary results: (a) for an arbitrary memoryless network, among all distributed memoryless sources with a particular correlation, Gaussian sources are the worst compressible, that is, they admit the smallest set of achievable distortion tuples, and (b) for any arbitrarily distributed memoryless source to be communicated over a memoryless additive noise network, among all noise processes with a fixed correlation, Gaussian noise admits the smallest achievable set of distortion tuples. In each case, given a coding scheme for the corresponding Gaussian problem, we provide a technique for the construction of a new coding scheme that achieves the same distortion at the destination nodes in a non-Gaussian scenario with the same correlation structure.