CAREER: Codes on Graphs, Factor Graphs, and Iterative Algorithms

职业：图、因子图和迭代算法的代码

• 批准号: 9984515
• 负责人: Ralf Koetter
• 金额: $ 22.5万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-05-15 至 2005-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9984515&HistoricalAwards=false
• 关键词: CAREER; Codes; Graphs; Factor; Iterative

CAREER: Codes on Graphs, Factor Graphs, and Iterative AlgorithmsThe primary focus of this research is the investigation of creative newmethods for reliable transmission of information in the context of modernerror-control techniques. Error-correcting codes are an essential part ofmodern communication and storage systems and much of today's technologywould not be possible without them. This study is focused on graph-based,iterative decoding algorithms, which, without doubt, are one of the mostsignificant coding-theoretic developments of the last decade. The goal ofthe investigator's research is to develop a broad, analytical, andconstructive approach to research and education, unifying graphicalmodels, coding theory, and iterative algorithms. The interplay betweencodes on graphs and other areas, like iterative graph-based algorithms,system theory, and network information theory, is in the focus of thisinvestigation with the goal of discovering and utilizing fundamentalconnections between these fields.The central notion of this research is the framework of "codes on graphs"and "factor graphs". Three main thrusts of research are present. The firstmain thrust is directed towards the analysis and theoretical study ofiterative decoding algorithms in graphs with and without cycles. The maintools for this research originate in recent successes in the analysis ofcodes on graphs as the codelength approaches infinity, and in the notion ofpseudo-codewords for short codes on relatively simple graphs. Bothapproaches are made viable by drawing heavily on the properties of theunderlying graph in the code construction.The second main thrust involves problems arising from generalizations ofminimal realizations of codes on graphs. This work has importantramifications to behavioral system theory, network information theory anditerative decoding. The goal is to derive algorithms that achieve a"minimal" realization of a code on a graph. A solution to this question isclosely related to important problems in network information theory and theachievability of desired information flows in a given network topology.The third objective of the investigator's study is aimed at jointlyoptimized receiver functions in a graph-based iterative setup. Factorgraphs provide a natural and generic framework for the study of iterative,belief propagation algorithms on graphical models. One of the mostexciting opportunities offered by the factor graph framework is thepossibility of incorporating a variety of different estimation tasks intoa joint optimization. The research focuses on opportunities to realize, injointly optimized subsystems, the gains that are essential for futurecommunication systems.

职业：图上的代码，因子图和迭代图本研究的主要重点是在现代控制技术的背景下，可靠的信息传输的创造性的新方法的调查。纠错码是现代通信和存储系统的重要组成部分，如果没有它们，今天的许多技术都是不可能的。本研究的重点是基于图的迭代译码算法，毫无疑问，这是过去十年中最重要的编码理论发展之一。研究者的研究目标是开发一种广泛的，分析性的和建设性的研究和教育方法，统一图形模型，编码理论和迭代算法。图上的编码与其他领域（如基于迭代图的算法、系统论和网络信息论）之间的相互作用是本研究的重点，其目标是发现和利用这些领域之间的基本联系。本研究的中心概念是“图上的编码“和“因子图”的框架。目前的研究主要有三个方面。第一个主要目标是对有圈图和无圈图的迭代译码算法进行分析和理论研究。这项研究的主要工具起源于最近的成功，在分析的代码在图的codelength接近无穷大，并在概念ofpseudo-codewords短代码相对简单的图。这两种方法都是可行的，通过大量绘制的基础图形的属性在代码construction.The第二个主要推力涉及的问题，从最小实现的代码的图形上的推广。这一工作对行为系统理论、网络信息理论和迭代解码都有重要的指导意义。我们的目标是推导出实现图上代码的“最小”实现的算法。这个问题的解决方案是密切相关的重要问题，在网络信息理论和所需的信息流在一个给定的网络topology.The第三个目标的研究者的研究旨在jointlyoptimized接收功能，在一个基于图形的迭代设置。因子图提供了一个自然和通用的框架，研究迭代，信念传播算法的图形模型。因素图框架提供的最令人兴奋的机会之一是将各种不同的估计任务纳入联合优化的可能性。该研究的重点是机会，实现，联合优化的子系统，收益是必不可少的未来通信系统。