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

随着无差错数据传输和存储需求的增加，差错控制在数据通信和存储系统中变得越来越重要。今天，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，例如无线、卫星、光、数字视频广播、网络通信、硬盘驱动器、光盘等。该研究旨在为下一代数据通信和存储系统设计构造良好的差错控制码和开发高效的差错控制机制，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极大的潜力。所研究的特殊课题包括：(1)基于Nite域的构造二进制和q元QC-LDPC码的统一方法；(2)调整所构造的码的奇偶校验矩阵的列和行权重以获得接近Shannon极限的性能的掩蔽技术；(3)为随机和突发擦除信道构造的码，在迭代译码时获得良好的性能；以及(4)在错误突发信道上对包括LDPC码在内的循环码进行译码的新的简单算法。初步结果令人印象深刻。所构造的q元LDPC码的性能明显优于任何现有的代数软判决译码算法译码的同类RS码。

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.