CIF: Small: Fundamental Limits of Robust Interference Management -- Between the Extremes

无线干扰网络的容量是网络信息论中最重要的开放性问题之一。在过去的十年里，在这个问题上取得了很大的进展。然而，最初的焦点是两极分化：渠道知识要么无限精确，要么完全不存在；当干扰太强或太弱时；信道要么是完全恒定的，要么是独立变化的。以往的研究主要集中在极端情况下，得出截然不同的结论，而本研究通过解决存在的不兼容性和尽可能利用协同效应来调和不同的极端情况。这项研究由三个主要部分组成。逐步探索全范围的部分渠道知识、渠道优势和渠道一致性模式。这三个推力的垫脚石包括拓扑干扰管理的最新进展，将干扰作为噪声处理的最优性，以及盲干扰对准。这项研究的最后一个关键因素是鲁棒外边界的突破，称为对齐图像集（AIS）方法。一种新颖的组合参数，它根据发送器可用的信道知识的数量，限定一组码字在不同接收器上投射的图像的相对大小。该研究结合了理论对容量极限的追求和对鲁棒性的实际关注。了解无线通信网络在稳健环境下的能力，对于工业界、学术界、政府机构和整个社会来说都是至关重要的，这样才能对未来的网络有现实的期望。

The capacity of wireless interference networks is one of the most important open problems of network information theory. Much progress has been made on this problem within the past decade. However, the initial focus has been on divergent extremes: where channel knowledge is available either with infinite precision or entirely absent; where the interference is either too strong or too weak; where channels are either perfectly constant or independently varying. Where previous studies have focused on extreme scenarios to arrive at radically divergent conclusions, this research reconciles the divergent extremes by resolving incompatibilities wherever they exist and exploiting synergies everywhere possible.The research is comprised of three main components ? exploring progressively, the full range of partial channel knowledge, channel strengths, and channel coherence patterns. The stepping stones for the three thrusts include recent advances in topological interference management, the optimality of treating interference as noise, and blind interference alignment. The final critical ingredient of this research is a breakthrough in robust outer bounds, called the Aligned Image Sets (AIS) approach ? a novel combinatorial argument that bounds the relative size of the images cast by a set of codewords at different receivers based on the amount of channel knowledge available to the transmitters. The research combines the theoretical pursuit of capacity limits with the practical concern for robustness. Understanding the capabilities of wireless communication networks in robust settings is essential for the industry, the academia, the government agencies and the society in general to have realistic expectations from the networks of the future.