EAGER: Understanding cooperation through the zero-error relay channel

研究的目的是获得零错误容量，这是一种基本的性能限制，量化了原始中继信道可以可靠地无错误地通信的消息数量。在这个信道中，在带外中继存在的情况下，源与目标通信。由于中继信道容量已经开放了40多年，从理论上讲，了解源和中继如何在通信消息中合作是很有趣的。该研究着眼于零错误容量，它不同于更常见的研究小错误容量，并导致一个未探索的组合问题，涉及新的中继“压缩”图。从数学和结构的角度理解如何合作的进展有望通过从这种新颖的组合角度攻击中继信道来实现。了解如何最好地中继对于扩展无线网络的覆盖范围或增加无线网络的可靠性非常重要。中继是802.16j、802.11ah和4G LTE Advanced等现有标准的一部分。PI的外联和教育工作的重点是继续积极参与“科学中的妇女”留用和招募活动，并通过非专家讲座和教程扩大对信息论的认识。从技术上讲，研究首先要确定原始中继信道的零误差容量何时不为零。当容量为正时，将寻求表征原始中继通道总体容量的图的结构以及如何最佳地合作。预计这些是难以计算的组合量；然后，我们的目标是简化某些通道类的表达式，并将这些图的属性理解为块长度和节点数量的函数。

The research seeks to obtain the zero-error capacity a fundamental performance limit quantifying the number of messages that may be reliably communicated with no error of the primitive relay channel. In this channel, a source communicates with a destination in the presence of an out-of-band relay. Understanding how the source and relay may cooperate in communicating messages is interesting theoretically as the relay channel capacity has been open for over 40 years. The research looks at the zero-error capacity, which differs from the more commonly studied small-error capacity, and leads to an unexplored combinatorial problem involving new relaying "compression" graphs. Progress in understanding how to cooperate from a mathematical, structural perspective is expected to be made by attacking the relay channel from this novel combinatorial angle. Understanding how to best relay is important in extending coverage of, or adding reliability to, wireless networks. Relaying is a part of existing standards such as 802.16j, 802.11ah, and 4G LTE Advanced. The PI's outreach and educational efforts focus on remaining active in "women in science" retention and recruiting events and broadening awareness of information theory through non-specialist talks and tutorials. Technically, the research will first determine when the zero-error capacity of the primitive relay channel is non-zero. When the capacity is positive, the structure of the graphs that characterize the overall capacity of the primitive relay channel and how to best cooperate will be sought. These are expected to be difficult-to-compute combinatorial quantities; the goal will then be to simplify the expressions for certain classes of channels, and to understand the properties of these graphs as a function of the block length and number of nodes.