[论文解读] Fundamental Limits of Communications in Interference Networks-Part III: Information Flow in Strong Interference Regime

Reza Khosravi-Farsani, Farokh Marvasti|arXiv (Cornell University)|Jul 12, 2012

Wireless Communication Security Techniques参考文献 25被引用 4

一句话总结

该论文首次为具有任意拓扑结构的多用户经典干扰信道（CICs）建立了非平凡的强干扰区域，通过统一的外界界限定位了容量达到条件。通过引入新颖的技术引理推导出一般性干扰条件，该研究首次给出了多用户CICs在超过两用户情况下的精确容量结果，统一了已知的两用户CIC、认知无线电以及具有认知中继的广播信道的结果。

ABSTRACT

This third part of the paper is related to the study of information flow in networks with strong interference. First, the two-receiver networks are considered. A unified outer bound for the capacity region of these networks is established. It is shown that this outer bound can be systematically translated into simple capacity outer bounds for special cases such as the two-user Classical Interference Channel (CIC) and the Broadcast Channel with Cognitive Relays (BCCR) with common information. For these channels, special cases are presented where our outer bounds are tight, which yield the exact capacity. More importantly, by using the derived outer bounds, a strong interference regime is identified for the general two-receiver interference networks with any arbitrary topology. This strong interference regime, which is represented by only two conditions, includes all previously known results for simple topologies such as the two-user CIC, the cognitive radio channel, and many others. Then, networks with arbitrary number of receivers are considered. Finding non-trivial strong interference regime for such networks, specifically for the CICs with more than two users, has been one of the open problems in network information theory. In this paper, we will give a solution to this problem. Specifically, a new approach is developed based on which one can obtain strong interference regimes not only for the multi-user CICs but also for any interference network of arbitrary large sizes. For this development, some new technical lemmas are proved which have a central role in the derivations. As a result, this paper establishes the first non-trivial capacity result for the multi-user classical interference channel. A general formula is also presented to derive strong interference conditions for any given network topology.

研究动机与目标

• 识别具有任意拓扑结构的一般两接收机干扰网络的强干扰区域。
• 将强干扰特征刻画扩展至具有任意数量接收机的网络，解决网络信息论中长期存在的开放问题。
• 推导适用于任意干扰网络拓扑的一般性强干扰条件公式。
• 为超过两用户的多用户CICs建立精确容量结果，该问题此前一直未解决。
• 在单一理论框架下统一并推广两用户CIC、认知无线电以及具有认知中继的广播信道的已有结果。

提出的方法

• 利用信息论不等式，为两接收机干扰网络的容量区域推导出统一的外边界。
• 系统性地将统一的外边界转化为特定情形下的紧致容量外边界，包括两用户CIC和具有公共信息的BCCR。
• 提出两个关键条件，以定义适用于所有拓扑结构的一般两接收机网络的强干扰区域。
• 开发新的技术引理，以实现强干扰条件向具有任意数量接收机的网络的扩展。
• 提出一个通用公式，基于推导出的外边界和引理，用于推导任意给定网络拓扑的强干扰条件。
• 将该框架应用于多用户CICs，证明了此类信道在超过两用户情况下的首次非平凡容量结果。

实验结果

研究问题

• RQ1 在具有任意拓扑结构的一般两接收机干扰网络中，强干扰区域的必要且充分条件是什么？
• RQ2 强干扰区域能否扩展至多用户CICs（超过两用户）？若能，其条件是什么？
• RQ3 如何构建并专门化统一的外边界，以获得已知干扰信道模型的紧致容量边界？
• RQ4 能否推导出一个通用公式，以确定任意干扰网络拓扑的强干扰条件？
• RQ5 所推导的外边界对多用户CICs精确容量有何影响？

主要发现

• 为两接收机干扰网络的容量区域建立了一个统一的外边界，该边界可推广至已知的特殊情况，如两用户CIC和具有公共信息的BCCR。
• 该论文识别出仅由两个条件定义的强干扰区域，该区域涵盖了所有先前已知的简单拓扑结果。
• 首次为超过两用户的多用户CICs建立了非平凡的强干扰区域，实现了精确容量表征。
• 所提出的框架首次为多用户经典干扰信道提供了精确容量结果，解决了长期存在的开放问题。
• 推导出一个通用公式，用于计算任意给定网络拓扑的强干扰条件，从而可系统性分析任意干扰网络。
• 论文中开发的技术引理在将强干扰特征刻画扩展至两用户场景之外的过程中起到了核心作用。