Pseudo-Codeword Analysis and Design of Quasi-Cyclic and Convolutional Codes

准循环码和卷积码的伪码字分析与设计

• 批准号: 0708033
• 负责人: Roxana Smarandache
• 金额: $ 12万
• 依托单位: San Diego State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-15 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0708033&HistoricalAwards=false
• 关键词: Pseudo; Codeword; Analysis; Design; Quasi

Proposal: DMS - 0708033PI: Smarandache, RoxanaInstitution: San Diego State UniversityTitle: Pseudo-Codeword Analysis and Design of Quasi-Cyclic and Convolutional CodesAbstractThis project focuses on the mathematical aspects of modern digital communication systems --- in particular on the analysis and design of certain vector spaces over finite fields, called low-density parity-check (LDPC) codes, that have a set of "sparse'' vectors generating the dual space, and among these, on quasi-cyclic and convolutional LDPC codes. In conjunction with an iterative decoding algorithm based on passing probability estimates along the edges of a graph naturally associated to the code, these codes show great promise for current and future communication systems. The analysis consists of an analysis of the associated code graphs, fundamental cones (with implications in linear programming decoding and iterative decoding), pseudo-codeword sets (the culprits that prevent the convergence of iterative decoding) and pseudo-weights (a measure of performance under iterative decoding). The goals are: to develop a theory of finite-length LDPC codes and provide a comparison between different codes having related algebraic structures; to unify relevant notions like near-codewords, pseudo-codewords, girth, minimum distance, minimum pseudo-weight by studying the effect that each has on the others; to derive lower and upper bounds on the performance of LDPC block and convolutional codes based on these parameters and their influences; and to ultimately provide guidelines for designing finite-length LDPC codes that have predictably good performance under iterative decoding.The inclusion of LDPC block codes in emerging standards such as digital video broadcasting, Ethernet and third-generation (3G) mobile-telephone networks, which will allow wireless access from 3G phones to be over ten times faster than from an old-fashioned dial-up, has recently spurred interest in LDPC convolutional codes. Initial research on LDPC convolutional codes leads the PI to the belief that these codes have several potential practical advantages compared to LDPC block codes. The goal of this project is to analyze these codes and construct new ones with predictably good performance. This research will naturally integrate abstract theory and real-world applications, providing exciting opportunities for cross-cutting research. The PI's continuing collaboration with leading engineering experts from academia and industry enables a transition from the theoretical research findings in this project to practical communication systems. It is anticipated that the project will have an impact on the future information infrastructure and contribute to universal accessibility. This impact will extend to the areas of data compression and communication protocols and security, since their underlying theories are closely related to coding theory.

提案：DMS-0708033PI：Smarandache，Roxanainstitution：圣地亚哥州立大学题：伪代码分析和准环境和卷积的设计和卷积编码的设计，该项目的重点是对现代数字通信系统的数学方面的重点 - 尤其是在某些vector的数学方面 - 尤其是在某些范围的范围内 - 越来越局限于范围 - 在某些范围内 - 杂乱无章 - 局限于局限于局限于局限于（ codes, that have a set of "sparse'' vectors generating the dual space, and among these, on quasi-cyclic and convolutional LD​​PC codes. In conjunction with an iterative decoding algorithm based on passing probability estimates along the edges of a graph naturally associated to the code, these codes show great promise for current and future communication systems. The analysis consists of an analysis of the associated code graphs, fundamental cones （在线性编程解码和迭代解码中的影响），伪代码套件（防止迭代解码的收敛性的罪魁祸首）和伪重量（迭代解码下的性能度量）。目标是：开发有限长度的LDPC代码理论，并提供具有相关代数结构的不同代码之间的比较；统一相关概念，例如近代码，伪代码，围长，最小距离，最小伪重量，通过研究每个人对其他效果的影响；基于这些参数及其影响，在LDPC块和卷积代码的性能方面得出上限和上限；并最终提供了设计有限长度的LDPC代码的准则，这些代码在迭代解码下具有良好的性能。在新兴标准中包含了LDPC块代码，例如数字视频广播，以太网和第三代和第三代和第三代（3G）Mobile-Telephone网络，这将允许从3G Phone中无线访问中的兴趣，从而允许从3G的访问中进行兴趣。 LDPC卷积代码。关于LDPC卷积代码的初步研究使PI相信与LDPC块代码相比，这些代码具有几个潜在的实践优势。 该项目的目的是分析这些代码，并以可预测的良好性能构建新代码。这项研究将自然地整合抽象理论和现实世界的应用，为横切研究提供令人兴奋的机会。 PI与学术界和行业领先的工程专家的持续合作使从该项目的理论研究结果转变为实用通信系统。预计该项目将对未来的信息基础架构产生影响，并有助于普遍可访问性。由于其基本理论与编码理论密切相关，因此这种影响将扩展到数据压缩和通信协议和安全性领域。