Tail-Biting Trellis Realizations for Block Codes

该奖项将支持旨在加深我们对分组代码图形表示的理解的研究。这种表示在现代编码理论中起着基本作用，其中图上的代码用于采用迭代解码算法。这些算法的强大性能引起了人们对代码的最佳图形表示的浓厚兴趣。咬尾格架形成了这种图形模型的一种特殊类型。本项目重点研究给定代码的各种咬尾网格实现之间的关系，例如最小实现和不可约实现，并分析迭代解码算法在这些图上的性能。编码理论是应用数学与通信系统工程相结合的学科。它涉及通过卫星、互联网、手机等确保数据传输的完整性。其基本思想是对要发送的消息进行预处理，以便在发送之后，接收方有很好的机会从接收到的（通常是错误的）消息中恢复原始消息。预处理称为编码，恢复过程称为解码。该奖项将支持针对代码的最佳图形表示的研究，这反过来又与设计有效的解码算法密切相关。该奖项还将支持肯塔基大学的研究生项目，因为将有两名博士生参与该项目。

This award will support research aimed at deepening our understanding of graphical representations of block codes. Such representations play a fundamental role in modern coding theory, where codes on graphs are used in order to employ iterative decoding algorithms. The powerful performance of these algorithms has led to a vivid interest in optimal graphical representations of codes. Tail-biting trellises form a particular type of such graphical models. This project focuses on studying the relation between various tail-biting trellis realizations of a given code, such as minimal realizations and irreducible ones, as well as on analyzing the performance of iterative decoding algorithms on these graphs.Coding theory is at the interface of applied mathematics and engineering of communication systems. It deals with ensuring the integrity of data transmission via satellite, internet, cell phones etc. The basic idea is to preprocess the to-be-sent messages in such a way that, after sending, the receiver has a good chance to recover the original message from the received, and generally erroneous, message. The preprocessing is called the encoding, and the recovering process is the decoding. This award will support research geared toward optimal graphical representations of codes, which in turn is closely related to designing efficient decoding algorithms. The award will also support the graduate program at the University of Kentucky because two Ph.D. students will be involved in the project.