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

职业：图形编码、因子图和迭代算法本研究的主要重点是在现代误差控制技术的背景下研究可靠传输信息的创造性新方法。纠错码是现代通信和存储系统的重要组成部分，没有它们，今天的许多技术都不可能实现。本研究的重点是基于图的迭代解码算法，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个广泛的，分析的，建设性的方法来研究和教育，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之间的相互作用，如迭代的基于图的算法、系统理论和网络信息理论，是本研究的重点，目的是发现和利用这些领域之间的基本联系。本研究的中心思想是“图上码”和“因子图”的框架。目前有三个主要的研究重点。第一个重点是对有循环和无循环图中的迭代解码算法进行分析和理论研究。这项研究的主要工具源于最近在图码长度接近无穷大时的码分析方面的成功，以及相对简单图上短码的伪码字概念。这两种方法都是通过在代码构造中大量使用底层图的属性来实现的。第二个主要推力涉及图上代码的最小实现泛化所引起的问题。该工作对行为系统理论、网络信息理论和迭代译码具有重要的借鉴意义。目标是推导出在图上实现代码“最小”实现的算法。这一问题的解决与网络信息论中的重要问题以及给定网络拓扑中期望信息流的可实现性密切相关。研究者研究的第三个目标是在基于图形的迭代设置中共同优化接收函数。因子图为图模型上的迭代、信念传播算法的研究提供了一个自然而通用的框架。因子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合并到联合优化中的可能性。该研究的重点是实现联合优化子系统的机会，这对未来的通信系统至关重要。

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.