Distributed Information Processing for Battlespace Awareness---Ergodic and Non-Ergodic Interplay.

摘要

Our primary accomplishment is that we cracked the problem of determining the rate region of the vector Gaussian 'one-helper' source coding problem. This was one of the most fundamental open problems in information theory, and had withstood repeated attacks by several groups around the world, starting with Liu and Viswanath (2007). The problem is similar to that of determining the capacity region of the Gaussian MIMO broadcast channel, whose solution won two awards from the IEEE Information Theory Society, but the compression version of the problem turned out to be significantly harder. Our proof technique used the method introduced to solve that problem but also used a fundamentally new technique that we call 'distortion projection,' which essentially involves projecting the problem into a lower-dimensional space where it is easier to analyze. Our results imply that a very simple compression algorithm is optimal for this problem.