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突破性范例。当今的商用网络是为了避免干扰而构建的，因此给定的资源一次只能由一个用户使用。通过干扰对齐，所有用户同时接入信道，每个用户获得一半的无干扰速率，从而实现网络吞吐量随用户数量线性扩展。两种最常研究的干扰对齐方法是线性和非线性方案。在前一种情况下，对齐问题可以表述为求解关于未知数子集的超定方程组，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入成果。目前不存在包含这两种方法的统一框架。 这项研究使用现代代数中的模理论（关于留数环或多项式环）作为干扰对齐的统一框架。首先介绍了该框架，并展示了通过选择适当的环来减少众所周知的线性和非线性干扰对准。然后，根据子模块分解和评估的自由度对通道进行分类。最后，通过一种新颖的方法设计实际的代码，其中目的地解码与接收信号最接近（在嵌套格链中）的格码。后一项任务与最近提出的计算转发中继方法有关。还探讨了两者之间的联系。所提出的工作的核心影响源于其对干扰对齐的统一理论处理。目前尚不存在这样的统一框架或方法。尽管人们经常发现经典的线性代数工具不足以解决网络问题，但迄今为止，模块理论还没有出现作为解释、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颖基础，将为社区提供极其丰富的工具集来设计和分析代码，预计这将影响并有益于其他网络问题，例如网络编码和计算转发中继。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、分散式干扰网络的网络科学综合理论迈出重要一步。这项研究的结果将在主要的国内和国际专业场所、信息论和通信网络社区中展示，并预计将立即用于工业部门。