论文标题
LDPC代码中循环的一种理论方法
A Number Theoretic Approach to Cycles in LDPC Codes
论文作者
论文摘要
由排列矩阵构建的LDPC代码最近引起了许多研究人员的兴趣。处理此类代码时的关键点是试图避免相关的坦纳图中短长度的循环，即获得可能的围栏。在本文中，我们提供了一个框架来获得此类代码的构造。我们将某个长度的周期存在的标准与某些数字理论概念有关，尤其是所谓的Sidon集。通过这种方式，我们获得了具有一定周长的LDPC代码的示例。最后，我们扩展了我们的结构，以获得不规则的LDPC代码。
LDPC codes constructed from permutation matrices have recently attracted the interest of many researchers. A crucial point when dealing with such codes is trying to avoid cycles of short length in the associated Tanner graph, i.e. obtaining a possibly large girth. In this paper, we provide a framework to obtain constructions of such codes. We relate criteria for the existence of cycles of a certain length with some number-theoretic concepts, in particular with the so-called Sidon sets. In this way we obtain examples of LDPC codes with a certain girth. Finally, we extend our constructions to also obtain irregular LDPC codes.
