Construction Methods of High Performance LDPC Codes

虽然LDPC(Low Density Parity Check，低密度奇偶校验)码被认为是性能非常好且接近香农极限的码，但仍然有一些基本问题需要解决：(1)推导出详细描述的码集并有效地评估其性能，(2)构造具有代数结构的LDPC码，这在实际实现中是重要的。为了解决这两个基本问题，我们在本研究中提出了(1)一类新的多边型LDPC码集和一种有效的密度进化算法，(2)易于实现且性能良好的新的修正扩展器码和MDS(最大距离可分)阵列码。在2006财年，(1)我们针对基于新发现的对称性质构造的新型多边型LDPC码集开发了密度进化算法，(2)提出了具有最小距离重复译码在线性时间内可译码且具有渐近良好性能的类Justesen修正扩展器码。在2007财年，(1)针对提出的新型多边沿型LDPC码集，推导了码集的重量分布和停止集分布，验证了所提出的码集的有效性。(2)通过与相应的传统码进行比较，我们发现所提出的码具有足够好的性能，在实践中被认为是非常有效的。

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.