CIF: Small: Modules as a Framework for Interference Alignment in Networks

CIF：小型：模块作为网络中干扰对齐的框架

• 批准号: 1218635
• 负责人: Daniela Tuninetti
• 金额: $ 11.7万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1218635&HistoricalAwards=false
• 关键词: CIF; Small; Modules; Framework; Interference

Interference Alignment is a breakthrough paradigm for wireless networks where several users share the same channel resources. Today's commercially available networks are built so as to avoid interference, so that a given resource is used by only one user at a time. With interference alignment, all users access the channel simultaneously and each user obtains half the interference-free rate, thereby achieving a network throughput that scales linearly with the number of users. The two most commonly studied approaches to interference alignment are the linear and non-linear schemes. In the former case the alignment problem can be formulated as that of solving an overdetermined system of equations with respect to a subset of the unknowns, and can be cast into the familiar language of vector spaces. The latter requires deep results in number theory on approximating an irrational number by a rational one. At present no unifying framework exists that encompasses both approaches. This research uses the theory of modules (on residue rings or polynomial rings) from modern algebra as a unifying framework for interference alignment. First the framework is introduced and shown to reduce to well known linear and non-linear interference alignment by choosing proper rings. Then, channels are classified in terms of their submodule decomposition and their degrees of freedom evaluated. Finally, actual codes are designed through a novel method where a destination decodes the lattice code that is the closet (in a nested lattice chain) to the received signal. This latter task has connections with the recently proposed compute-and-forward method of relaying. Connections among the two are also explored.The central impact of the proposed work stems from its unified theoretical treatment of interference alignment. No such unified framework or methodology exists at present. Although it has been often observed that classical linear algebra tools are insufficient for network problems, the theory of modules has not emerged so far as a tool to explain, analyze and design codes for interference networks. This research, by exploring novel foundations of interference alignment, will provide the community with an extremely rich toolset to design and analyze codes, which is expected to impact and benefit other network problem such as network coding and compute-and-forward relaying.From a technical perspective the new paradigm proposed in this research will enlarge the scope of information processing in interference networks, and provide an important step forward into the consolidation of a comprehensive theory of network science for distributed, decentralized, interfering networks. The results of this research will be presented at major national and international professional venues, in the information theory and communication networks communities and are expected to be of immediate use to the industrial sector.

干扰对齐是多个用户共享相同信道资源的无线网络的一个突破性范例。今天商业上可用的网络是为了避免干扰而建立的，因此一次只有一个用户使用给定的资源。在干扰对齐的情况下，所有用户同时接入信道，每个用户获得一半的无干扰速率，从而实现随用户数量线性扩展的网络吞吐量。干扰对齐的两种最常用的研究方法是线性和非线性方案。在前一种情况下，对齐问题可以表示为关于未知数的子集求解超定方程组的问题，并且可以转化为熟悉的向量空间语言。后者需要数论中关于用有理数逼近无理数的深刻结果。目前还不存在涵盖这两种方法的统一框架。本研究使用现代代数中的模理论(在剩余环或多项式环上)作为干扰对齐的统一框架。首先介绍了该框架，并通过选择合适的环将其归结为众所周知的线性和非线性干扰对齐。然后，根据信道的子模分解对信道进行分类，并对其自由度进行评估。最后，通过一种新颖的方法来设计实际的码，其中目的地对格码进行解码，该格码是(在嵌套的格链中)与接收信号最接近的格码。后一项任务与最近提出的计算转发继电保护方法有关。文中还探讨了两者之间的联系。这项工作的核心影响来自于它对干扰对齐的统一理论处理。目前还没有这种统一的框架或方法。虽然人们经常注意到，经典的线性代数工具不足以解决网络问题，但模理论还没有出现，成为解释、分析和设计干扰网络代码的工具。这项研究通过探索干扰对齐的新基础，将为社区提供一个极其丰富的工具集来设计和分析代码，这有望影响和受益于其他网络问题，如网络编码和计算转发转发。从技术角度来看，本研究提出的新范式将扩大干扰网络中信息处理的范围，并为巩固分布式、分散、干扰网络的综合网络科学理论向前迈出重要的一步。这项研究的结果将在国家和国际主要专业场所、信息理论和通信网络社区公布，预计将立即用于工业部门。