Network Compression: Worst Case Analysis

IEEE Trans Inf Theory. 2015 Jul;61(7):3980-3995. doi: 10.1109/tit.2015.2434829. Epub 2015 Jun 12.


We study the problem of communicating a distributed correlated memoryless source over a memoryless network, from source nodes to destination nodes, under quadratic distortion constraints. We establish the following two complementary results: 1) for an arbitrary memoryless network, among all distributed memoryless sources of a given correlation, Gaussian sources are least compressible, that is, they admit the smallest set of achievable distortion tuples and 2) for any memoryless source to be communicated over a memoryless additive-noise network, among all noise processes of a given correlation, Gaussian noise admits the smallest achievable set of distortion tuples. We establish these results constructively by showing how schemes for the corresponding Gaussian problems can be applied to achieve similar performance for (source or noise) distributions that are not necessarily Gaussian but have the same covariance.

Keywords: Worst-case source; joint source-channel coding; network compression; worst-case noise.