论文标题
从立方对称图构建的LDPC代码
LDPC codes constructed from cubic symmetric graphs
论文作者
论文摘要
低密度平价检查（LDPC）代码一直引起人们的关注，因为它们可以在香农限制附近执行。在本文中，我们提出了来自立方对称图的LDPC代码的结构。构造的代码为$（3,3）$ - 常规，绝大多数相应的坦纳图大于四个。我们分析了所获得的代码的属性，并为代码参数，维度和最小距离提供了边界。此外，我们给出了构造代码综合征重量的方差的表达。还提供了有关由少于200个顶点的双方立方对称图构建的LDPC代码的信息。某些构造的代码是最佳的，有些代码具有互补双重（LCD代码）的自动式或线性代码的附加属性。
Low-density parity-check (LDPC) codes have been the subject of much interest due to the fact that they can perform near the Shannon limit. In this paper we present a construction of LDPC codes from cubic symmetric graphs. The constructed codes are $(3,3)$-regular and the vast majority of the corresponding Tanner graphs have girth greater than four. We analyse properties of the obtained codes and present bounds for the code parameters, the dimension and the minimum distance. Furthermore, we give an expression for the variance of the syndrome weight of the constructed codes. Information on the LDPC codes constructed from bipartite cubic symmetric graphs with less than 200 vertices is presented as well. Some of the constructed codes are optimal, and some have an additional property of being self-orthogonal or linear codes with complementary dual (LCD codes).
