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

职业生涯：图、因子图和迭代算法的代码本研究的主要重点是研究在适度错误控制技术的背景下可靠地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，没有纠错码，今天的许多技术都不可能实现。这项研究的重点是基于图的迭代译码算法，毫无疑问，这是过去十年来编码理论最重要的发展之一。研究人员的研究目标是开发一种广泛的、分析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。图上的编码与基于图的迭代算法、系统论和网络信息论等领域之间的相互作用是本研究的重点，目的是发现和利用这些领域之间的基本联系。本文提出了三个主要的研究方向。第一个主要目的是对有圈图和无圈图中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源于最近在码长趋于无穷大时对图上的码进行分析的成功，以及在相对简单的图上的短码的伪码字的概念。这两种方法都是通过在代码构造中大量利用底层图的性质而变得可行的。第二个主要推动力涉及图上代码的最小实现的泛化所引起的问题。这项工作对行为系统理论、网络信息理论和迭代译码都有重要的意义。其目标是推导出在图上实现代码的“最小”实现的算法。这个问题的解决方案与网络信息论中的重要问题和期望信息流在给定网络拓扑下的可达性密切相关。研究人员研究的第三个目标是在基于图的迭代设置中联合优化接收函数。因子图为基于图形模型的迭代信任传播算法的研究提供了一个自然和通用的框架。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。这项研究的重点是通过联合优化子系统实现对未来通信系统至关重要的收益的机会。

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.