A Unified Finite Field Approach for Constructing Quasi-Cyclic LDPC Codes for AWGN, Binary Erasure, and Burst Channels

为 AWGN、二进制擦除和突发信道构造准循环 LDPC 码的统一有限域方法

• 批准号: 0727478
• 负责人: Shu Lin
• 金额: $ 25万
• 依托单位: University of California-Davis
• 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: 2007-09-15 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0727478&HistoricalAwards=false
• 关键词: Unified; Finite; Field; Approach; Constructing

AbstractAs the demand of error-free data transmission and storage increases, error control becomes increasingly important in data communication and storage systems. Today very sophisticated error control mechanisms are being used in a broad range of communication and data storage systems to achieve reliable data transmission and storage, such as wireless, satellite, optical, digital video broadcast, network communications, hard disc drives, compact disks, and many others. This research is to devise methods for constructing good error control codes and developing efficient error control mechanisms that have great potential to achieve error-free information transmission and data storage for the future generation of data communication and storage systems.This research investigates several very promising algebraic methods for systematic construction of binary and q-ary high performance and efficiently encodable quasi-cyclic (QC) LDPC codes for AWGN, random erasure, erasure-burst and error-burst channels. Specical subjects investigated include: (1) a united approach based on nite fields for constructing binary and q-ary QC-LDPC codes; (2) a masking technique that adjusts column and row weights of the parity-check matrices of the constructed codes to yield performance close to Shannon limit; (3) construction of codes for both random and burst erasure channels thatyield good performance when decoded iteratively; and (4) a new simple algorithm for decoding cyclic codes, including LDPC codes, over error-burst channel. Preliminary results are impressive. The q-ary LDPC codes constructed significantly outperform comparable RS codes decoded with any existing algebraic soft-decision decoding algorithm.

摘要随着对无差错数据传输和存储要求的提高，差错控制在数据通信和存储系统中变得越来越重要。如今，非常复杂的差错控制机制被用于广泛的通信和数据存储系统中，以实现可靠的数据传输和存储，诸如无线、卫星、光学、数字视频广播、网络通信、硬盘驱动器、光盘以及许多其他系统。本研究的目的是设计构造良好的差错控制码的方法和开发有效的差错控制机制，为下一代数据通信和存储系统实现无差错的信息传输和数据存储提供巨大的潜力。本研究探讨了几种非常有前途的代数方法，用于系统地构造二进制和q进制高性能和有效可编码的准循环（QC）用于AWGN、随机擦除、擦除突发和错误突发信道的LDPC码。具体研究内容包括：（1）基于有限域的二进制和q进制QC-LDPC码的联合构造方法;（2）调整所构造码的校验矩阵的行和列权值以使性能接近香农限的掩蔽技术;（3）构造在随机和突发擦除信道下迭代译码性能良好的码;（4）提出了一种新的差错突发信道下循环码（包括LDPC码）的简单译码算法。初步结果令人印象深刻。所构造的q元LDPC码的译码性能明显优于现有的任何代数软判决译码算法。