Asnani Himanshu, Shomorony Ilan, Avestimehr A Salman, Weissman Tsachy
Ericsson Research and Development Sillicon Valley, San Jose, CA 95134 USA.
Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720 USA.
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.
我们研究在二次失真约束下，通过无记忆网络从源节点向目的节点传输分布式相关无记忆源的问题。我们建立了以下两个互补的结果：1）对于任意无记忆网络，在给定相关性的所有分布式无记忆源中，高斯源的可压缩性最低，即它们允许的可实现失真元组集合最小；2）对于要通过无记忆加性噪声网络传输的任何无记忆源，在给定相关性的所有噪声过程中，高斯噪声允许的可实现失真元组集合最小。我们通过展示如何将相应高斯问题的方案应用于具有相同协方差但不一定是高斯分布的（源或噪声）分布来建设性地建立这些结果，以实现相似的性能。
