项目名称: 准循环LDPC码校验矩阵的秩和冗余行分析及码的性能优化
项目编号: No.61201156
项目类型: 青年科学基金项目
立项/批准年度: 2013
项目学科: 电子学与信息系统
项目作者: 黄勤
作者单位: 北京航空航天大学
项目金额: 27万元
中文摘要: 近年来准循环(QC)LDPC 码的重要进展是将有限域离散Fourier 矩阵变换用于分析某些代数准循环LDPC 码的性质,如校验矩阵的秩,最小码间距离以及最小环路长度(girth)。但是目前的分析有很强的局限性,仅限于特定的四类代数码,并且必须满足某些约束条件。本研究拟深入分析QC-LDPC 码校验矩阵的秩,从共轭矩阵出发,利用Fourier 变换及近世代数理论来首次尝试得出通用的矩阵分析。其意义在于:一方面校验矩阵的秩是设计码时最基本的考虑因素;另一方面秩与冗余行紧密相关(矩阵的行数减去秩等于矩阵的冗余行),而恰当的冗余行不仅能提高LDPC 码在低信噪比下的纠错性能,而且能够有效降低错误平台。深入研究冗余行及其在不同信道下对LDPC 码性能的影响将为码的构造提供新的优化准则。本研究的开展不仅能促进现有LDPC 码的理论分析,而且将对未来通信系统和存储系统制定LDPC 码标准有指导意义。
中文关键词: 准循环;LDPC码;秩;编码;生成矩阵
英文摘要: Recent development in QC-LDPC codes is the introduction of a matrix-theoretic approach for studying these codes based on matrix transformation via Fourier transforms over finite fields. Ranks of certain classes of algebraic QC-LDPC codes are derived, but some constraints may have to be applied. Starting from conjugate matrices, this research will be concerned with general analysis on the rank of an array of circulants whose null space defines a QC-LDPC code, which is based on the Fourier transform and modern algebra theory. The benefits of a general analysis are two aspects. First, the rank of the parity-check matrix is one of the most essential factors in code design; Second, the number of rows minus rank is the number of redundant (dependent) rows. It is well-known that well-designed redundnat rows have positive impacts on the error performance of LDPC codes,e.g., waterfall threshold and error floor. Thus, it will be a potential way to improve the performance of QC-LDPC codes, which may result in new code constructions from the view of transform domain. In a word, this research not only will advance the analysis of QC-LDPC codes, but also will provide guidelines for LDPC code designs for future communication systems and storage systems.
英文关键词: Quasi cyclic;LDPC code;rank;encode;generator matrix