基于CRT的低复杂度LDPC不规则码构造算法及理论研究

Irregular LDPC codes are the error-correcting codes who have the smallest gap to the Shannon limit. The error-correcting capability of irregular LDPC codes will be improved while the length of code and girth are inceased.The PEG algorithm is the most successful algorithm to construct irregular LDPC codes. However, there are two disadvantages with the PEG algorithm: 1) the girth decrease always the increase of the code length of the irregular LDPC code; 2) the complexity of PEG algorithm grows exponential with the code length. For these two problems, this project do research focusing on the following topics: 1) with the girth fixed, extend the code length of irregular LDPC codes based on CRT; 2) reduce the complexity of PEG algorithm based on CRT；3）reduce the hardware complexity of the decoder based on CRT. There are four significant values of this project: 1) with the girth fixed, the error correcting performance of irregular LDPC codes is improved via increasing the code length; 2)the complexity of the PEG algorithm is reduced; 3) the hardware complexity of the decoder of the irregular LDPC codes is reduced; 4) this project introduces the CRT into the construction algorithm of irregular LDPC codes,which has the positive impact on motivating the application of CRT into the areas of error correcting codes and communication system.

LDPC不规则码是目前距离Shannon限最近的纠错码,其纠错性能随着码长和girth的长度的增加而提高。PEG算法是LDPC不规则码最成功的构造算法.然而在PEG算法存在两个问题：1）girth往往随着LDPC不规则码的码长的增加而减小；2）PEG算法的复杂度随着码长的增加呈指数增长。本项目将针对以上两个问题重点研究如下内容：1)在girth不减小的前提下，基于CRT增加LDPC不规则码的码长；2）基于CRT降低PEG算法的复杂度；3）基于CRT降低译码器的硬件复杂度。本项目的研究将有四方面的意义：1）在girth不减小的前提下，通过增加码长提高了现有的LDPC不规则码的纠错性能；2）降低了PEG算法的复杂度；3）降低了LDPC不规则码译码器的硬件复杂度；4）本项目的工作将CRT引入到LDPC不规则码的构造算法中，对于推动CRT在纠错码以及通信领域的应用也有积极作用。

LDPC不规则码是目前距离Shannon限最近的纠错码,其纠错性能随着码长和girth的长度的增加而提高。PEG算法是LDPC不规则码最成功的构造算法.然而在PEG算法存在两个问题：1）girth往往随着LDPC不规则码的码长的增加而减小；2）PEG算法的复杂度随着码长的增加呈指数增长。本项目将针对以上两个问题重点研究如下内容：1)在girth不减小的前提下，基于CRT增加LDPC不规则码的码长；2）基于CRT降低PEG算法的复杂度；3）基于CRT降低译码器的硬件复杂度。本项目的研究将有四方面的意义：1）在girth不减小的前提下，通过增加码长提高了现有的LDPC不规则码的纠错性能；2）降低了PEG算法的复杂度；3）降低了LDPC不规则码译码器的硬件复杂度；4）本项目的工作将CRT引入到LDPC不规则码的构造算法中，对于推动CRT在纠错码以及通信领域的应用也有积极作用。