Construction Methods of High Performance LDPC Codes

高性能LDPC码的构造方法

基本信息

批准号：
18560368
负责人：
SAKANIWA Kohichi
金额：
$ 2.51万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18560368/
关键词：
LDPC codes Multi-Edge type symmetry property Density Evolution Modified Expander codes repetition decoding MDS array codes decodable in linear time 密度発展性繰り返し符号法

项目摘要

Though the LDPC (Low Density Parity Check) codes are known as the codes to attain very good and close performance to the Shannon's limit, there still remain some basic problems to be resolved: e.g., (1) to derive detailed described code ensembles and evaluate their performance efficiently, (2) to construct LDPC codes with algebraic structure which are important in practical implementation.To solve these two basic problems, we in this research have proposed (1) a new class of Multi-Edge type LDPC code ensembles and an efficient DE (Density Evolution) for the proposed ensembles, (2) new modified expander codes and MDS (Maximum Distance Separable) array codes which are easy to implement as well as high performance.In the fiscal year 2006, (1) we developed DE (Density Evolution) for the new class of Multi-Edge type LDPC code ensembles which are constructed based on the newly found symmetry property, (2) proposed Justesen like modified expander codes which are decodable in linear time with the minimum distance repeat decoding and having asymptotically good performance.In the fiscal year 2007, (1) for the proposed new class of Multi-Edge type LDPC code ensembles, we have derived the weight distributions and the Stopping Set distributions and confirmed the effectiveness of the proposed code ensembles, (2) by comparing the proposed codes with the corresponding conventional ones we have found that the proposed codes exhibit sufficiently good performance and are thought to be very effective in practice.

尽管LDPC（低密度奇偶校验）码被认为是获得非常好的且接近香农极限性能的码，但仍然存在一些有待解决的基本问题：例如，（1）导出详细描述的码系综并评估其性能高效，（2）构造具有代数结构的LDPC码，这在实际实现中很重要。为了解决这两个基本问题，我们在本研究中提出了（1）一类新的Multi-Edge类型LDPC码系综和所提议的系综的高效DE（密度演化），（2）新的修改扩展码和MDS（最大距离可分离）阵列码，它们易于实现且具有高性能。在2006财年，（ 1) 我们为新型多边型 LDPC 码系综开发了 DE（密度演化），该系综是基于新发现的对称性构建的，(2)提出了类似 Justesen 的改进扩展码，它可以在线性时间内以最小距离重复解码进行解码，并且具有渐近良好的性能。在 2007 财年，（1）对于提出的新一类多边型 LDPC 码系综，我们推导了权重分布和停止集分布，并确认了所提出的代码集成的有效性，（2）通过将所提出的代码与相应的传统代码进行比较，我们发现所提出的代码表现出足够好的性能，并且被认为在实践中非常有效。