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.

干涉对齐是无线网络的突破范式，其中几个用户共享相同的频道资源。当今的市售网络是建立的，以避免干扰，因此一次只有一个用户使用给定资源。通过干扰对齐，所有用户同时访问了通道，每个用户获得了无干扰率的一半，从而获得了与用户数量线性扩展的网络吞吐量。两种最常见的干扰一致性方法是线性和非线性方案。在前一种情况下，可以将对齐问题提出为解决未知子集的过度确定方程系统的问题，并且可以将其放入向量空间的熟悉语言中。后者需要对数字理论的深度结果，即通过理性数字近似一个非理性数字。目前尚无统一框架，包括这两种方法。 这项研究使用现代代数的模块（在残基环或多项式环上）的理论作为干扰一致性的统一框架。首先，引入并显示该框架通过选择适当的环将其减少到众所周知的线性和非线性干扰对齐。然后，渠道是根据其子模块分解和评估的自由度对渠道进行分类的。最后，实际代码是通过一种新颖的方法设计的，该方法将目的地解码为接收信号的壁橱（嵌套晶格链中）的晶格代码。后一个任务与最近提出的反向继电器方法有联系。还探索了两者之间的联系。拟议的工作的核心影响源于其对干扰一致性的统一理论处理。目前尚无这样的统一框架或方法论。尽管经常观察到经典的线性代数工具不足以解决网络问题，但对于解释，分析和设计干扰网络的工具而言，模块的理论并未出现。这项研究通过探索新颖的干扰结算基础，将为社区提供极为丰富的工具集，以设计和分析代码，预计将影响和受益于其他网络问题，例如网络编码和计算和向前的继电器，从技术角度来看，该研究中提出的新范式将为网络的范围提供一项研究的范围，并将其综合的范围用于综合网络处理，以扩大网络处理的范围，从而使网络处理范围，从而使网络的范围扩大了重要的范围。分布式，分散的，干扰网络。这项研究的结果将在信息理论和通信网络社区的主要国家和国际专业场所介绍，并有望立即对工业部门使用。