论文标题
通过混合量和涵盖一般渠道的问题
Minoration via Mixed Volumes and Cover's Problem for General Channels
论文作者
论文摘要
我们为1987年的托马斯覆盖率开放问题提供了完整的解决方案，内容涉及一般离散无内存设置中继电器通道的能力，而无需任何其他假设。我们方法中的关键步骤是通过凸几何方法来降低随机过程的某些软效果，这是基于两个思想的：首先，通过近似带有界面数量的colytope的凸面集，软触发是按照另一个过程的最高限制的。其次，使用Pajor的结果，该过程的最高因素通过混合体积不平等（Minkowski的第一个不等式）而在包装数字方面处于较低的限制。
We give a complete solution to an open problem of Thomas Cover in 1987 about the capacity of a relay channel in the general discrete memoryless setting without any additional assumptions. The key step in our approach is to lower bound a certain soft-max of a stochastic process by convex geometry methods, which is based on two ideas: First, the soft-max is lower bounded in terms of the supremum of another process, by approximating a convex set with a polytope with bounded number of vertices. Second, using a result of Pajor, the supremum of the process is lower bounded in terms of packing numbers by means of mixed-volume inequalities (Minkowski's first inequality).
