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，Roxana机构：圣地亚哥州立大学标题：准循环码和卷积码的伪码字分析和设计摘要该项目重点关注现代数字通信系统的数学方面——特别是有限域上某些向量空间的分析和设计，称为低密度奇偶校验（LDPC） 代码，具有一组生成对偶空间的“稀疏”向量，其中包括准循环和卷积 LDPC 代码。结合基于沿与代码自然关联的图的边缘传递概率估计的迭代解码算法，这些代码在当前和未来的通信系统中显示出巨大的前景。该分析包括对相关代码图、基本锥体的分析。 （涉及线性编程解码和迭代解码）、伪码字集（阻止迭代解码收敛的罪魁祸首）和伪权重（迭代解码下的性能度量）。目标是：发展有限长度 LDPC 码的理论，并提供具有相关代数结构的不同码之间的比较；统一相关 通过研究每个概念对其他概念的影响，得出近码字、伪码字、周长、最小距离、最小伪权重等概念；根据这些参数及其影响导出 LDPC 块和卷积码性能的下限和上限；并最终为设计有限长度 LDPC 码提供指导，这些码在迭代下具有可预测的良好性能 LDPC 块码被纳入数字视频广播、以太网和第三代 (3G) 移动电话网络等新兴标准中，这将使 3G 手机的无线访问速度比老式拨号快十倍以上，最近激发了人们对 LDPC 卷积码的兴趣。对 LDPC 卷积码的初步研究使 PI 相信这些代码 与 LDPC 块码相比，具有几个潜在的实际优势。 该项目的目标是分析这些代码并构建具有可预测的良好性能的新代码。这项研究将自然地整合抽象理论和现实应用，为跨领域研究提供令人兴奋的机会。 PI 与学术界和工业界领先工程专家的持续合作使该项目的理论研究成果能够过渡到实际的通信系统。预计该项目将 对未来的信息基础设施产生影响，并有助于普及信息。这种影响将扩展到数据压缩、通信协议和安全领域，因为它们的底层理论与编码理论密切相关。