LDPC编码算法研究

论文编号:TX353  论文字数:17120,页数:36

摘要

 低密度奇偶校验码（Low-Density-Parity-Check codes，简称LDPC码）是当前通信领域的热门研究课题之一，是第四代移动通信系统的信道编码技术中强有力的竞争者。LDPC码具有优秀的译码性能，迭代的概率译码算法使得LDPC码可以达到接近香农限的性能，而且译码的复杂度较低；译码算法本质上是并行算法，有利于硬件的并行实现，减少译码延时；它能够在迭代运行的过程中确定码字是否已译出，以决定译码过程能否结束，减少迭代次数；同时其译码错误是可以检测的；译码后的误码率可以随着信噪比的增加而任意减小，没有误码率下降减速的error floor现象。LDPC码编码的复杂度较高，同时在码长较长时，由于必须在接收到所有的信息比特后才能够进行编码，这就会给编码带来一定的延时。
 本文对LDPC码进行了系统的研究。首先介绍了LDPC码的定义和编译码原理，然后阐述了多种校验矩阵的构造方法；最后采用Gallager构造法构造LDPC码，并在MATLAB中进行仿真，给出了不同码长和不同码率的LDPC码在高斯白噪声信道下的误码率性能的仿真结果。
 

关键词：LDPC码，编码，Gallager构造

ABSTRACT

 Low-Density-Parity-Check-Codes is currently one of the pop researches in communication field. It is the powerful competition in the 4th generation of mobile communication system. The decoding performance of LDPC is excellent and can be near the Shannon limit by iterative probability decoding algorithm. It has low complexity, the decoding algorithm is essentially parallel, so it is suitable to realize on hardware in parallel and reduce the decoding delay time. It can make certain that if the codes are decoded in the iterative decoding process and if the process can be finished in order to reduce iterative times, at the same time the decoding error can be detected. Bit error rate(BER) after decoding can be decreased arbitrarily along with the increase of Signal-to-Noise rate(SNR), and the error floor phenomenon can not occur. The complexity of encoding is high. Because the encoding process begins after receiving all needed signal bits, it brings certain delay time while the length of the codes is very long.
 This paper gives a systematic investigation of LDPC codes. First, the definition of LDPC codes and the encoding methods are introduced. Then some parity check matrix construction methods of LDPC codes are illustrated; Finally, Gallager construction LDPC codes are simulated on MATLAB. The simulation results of BER performance of different length and rate for additive white Gaussian noise channels are presented.

Keywords: LDPC codes, encode, Gallager construction

目录

摘要 I
ABSTRACT II
第1章 绪论 1
 1.1数字通信与信道编码 1
 1.2纠错码的发展 1
 1.3 LDPC码发展历史和现状 3
 1.4本文主要工作 7
第2章 LDPC码的定义及编码原理 8
 2.1 LDPC码的定义及Tanner图 8
 2.1.1 LDPC码的定义及其描述 8
 2.1.2 LDPC码的Tanner图表示 9
 2.2 LDPC码的编码 11
 2.2.1 直接编码 12
 2.2.2 快速编码 12
 2.2.3 构造半随机校验矩阵H的编码 14
 2.2.4 具有循环码特性的LDPC码的编码 15
 2.2.5 基于删除信道LDPC码迭代译码算法的编码 15
 2.3 LDPC码的译码 15
第3章 LDPC码的校验矩阵的构造 16
 3.1 Gallager构造法 16
 3.2 Mackay构造法 17
 3.3超轻构造法 20
 3.4完全随机构造法 20
 3.5 Hu Xiao-Yu的PEG方法 21
 3.6 Bit-filling和Extended Bit-filling方法 23
 3.7非正则LDPC码的构造方法 23
 3.8其他的构造方法 24
第4章 LDPC码性能仿真 27
 4.1不同码长仿真图 27
 4.2不同码率仿真图 28
第5章 结束语 30
致谢 31
参考文献 32