Algebraic and Geometric Constructions of Shannon Limit Approaching Codes and Turbo Decoding of Reed-Solomon Codes

香农极限逼近码的代数和几何构造以及Reed-Solomon码的Turbo译码

• 批准号: 0117891
• 负责人: Shu Lin
• 金额: $ 51万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-10-01 至 2006-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0117891&HistoricalAwards=false
• 关键词: Algebraic; Geometric; Constructions; Shannon; Limit

As the demand for error-free data transmission and data storage increases, error control becomes increasingly important in data communication and datastorage systems. It has become an integral part in almost every data communication or storage system design. Today very sophisticated error control schemes are being used in a broad range of communication and datastorage systems to achieve reliable data transmission and storage, such aswireless communication, satellite communication, optical communication, hard disc drives, compact disks and many others. The objective of this research is to devise methods for constructing good error control codes and to develop efficient error control schemes which have great potential to achieve error-free communication and data storage for the future generationof data communication and storage systems.Recently, there have been dramatic developments in error control codes anddecoding algorithms. Two families of powerful codes, known as turbo andlow density parity check (lDPC) codes, have been discovered and rediscovered.These two families of codes with iterative decoding have been shown to perform close to Shannon's theoretical limits with reasonable implementationcomplexity. As a result of their amazing error performance and practicalimplementation, it is anticipated that these two classes of codes will havean enormous impact on virtually all applications of error control coding overthe next 10 years or so. This research involves in two important aspectsof these two classes of Shannon limit approaching codes: construction of LDPC codes and turbo decoding of Reed-Solomon (RS) codes. The construction of LDPC codes is based on combinatoric appraches, such as finite geometries overfinite fields, statistical experimental designs, permutation groups andgraphs. In these approaches, points, lines, hyperplanes in finite geometries, balanced incomplete block designs, affine permutation groups, and pathsand independent sets of graphs are used for constructing LDPC codes whoseTanner graphs do not contain short cycles. All the construction methodsare systematic and codes constructed have good structural properties whichsimplify encoding and decoding implementations. Turbo decoding of a RS code is based on binary decomposition of the code into a set of simple binary component codes and formulating the code as a self concatenated code with the RS code itself as the outer code and the component codes as inner codes in a turbo coding arrangement. The decoding is carried out in two stages, turbo inner decoding and outer algebraic soft-decision decoding.

随着对无错误数据传输和数据存储的需求增加，错误控制在数据通信和数据存储系统中变得越来越重要。 它几乎已成为几乎每个数据通信或存储系统设计的组成部分。 如今，非常复杂的错误控制方案已在广泛的通信和数据存储系统中使用，以实现可靠的数据传输和存储，例如无静电通信，卫星通信，光学通信，硬盘驱动器，紧凑型磁盘等。 这项研究的目的是设计用于构建良好错误控制代码的方法，并开发有效的错误控制方案，这些方案具有实现无误差通信和数据存储的巨大潜力，用于数据通信和存储系统的未来生成。 已经发现并重新发现了两个强大的代码家族，称为Turbo Andlow密度均衡检查（LDPC）代码。这两个具有迭代解码的代码家族已被证明可以与Shannon的理论限制进行合理的实施。 由于其惊人的错误性能和实践实现，预计这两类代码将对未来10年左右的几乎所有错误控制编码的应用产生巨大影响。 这项研究涉及这两个类别的香农限制的两个重要方面，即接近代码：LDPC代码的构建和芦苇 - 溶解（RS）代码的涡轮解码。 LDPC代码的构建基于组合的调查，例如有限的几何形状过滤场，统计实验设计，置换组和图形。 在这些方法中，有限几何形状，平衡的不完整块设计，仿射置换组以及路径和独立图集的均衡几何形状中的点，线条，超平面，用于构建LDPC代码WHOSETANNER图形不包含短周期。 所有构造方法系统的系统和构建的代码都具有良好的结构属性，可以简化编码和解码实现。 RS代码的Turbo解码基于将代码的二进制分解为一组简单的二进制组件代码，并将代码作为自我串联代码以RS代码本身作为外代码作为外代码，将组件代码作为涡轮编码安排中的内部代码作为内部代码。 解码分为两个阶段，涡轮内部解码和外部代数软性解码。