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

摘要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，非常复杂的误差控制机制被广泛应用于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、光学、数字视频广播、网络通信、硬盘驱动器、光盘等等。本研究旨在为未来一代的数据通信与存储系统设计出构建良好的错误控制代码和开发高效的错误控制机制的方法，这些机制具有实现无错误信息传输和数据存储的巨大潜力。本文研究了几种很有前途的代数方法，用于系统地构造用于AWGN、随机擦除、擦除突发和错误突发信道的二进制和q元高性能高效可编码的准循环（QC） LDPC码。具体研究内容包括：(1)基于nite域的二进制和q元QC-LDPC码的统一构造方法；(2)一种屏蔽技术，调整构造码的奇偶校验矩阵的列和行权重，使性能接近香农极限；(3)构建随机和突发擦除信道的编码，在迭代解码时产生良好的性能；(4)在突发错误信道上对包括LDPC码在内的循环码进行简单译码的新算法。初步结果令人印象深刻。所构建的q元LDPC码明显优于任何现有代数软判决译码算法解码的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.