无小环大列重QC-LDPC短码的显式构造

Explicit Constructions of Short QC-LDPC Codes Free of Small Cycles and with Large Column Weight

针对列重较大的无4环且无6环的准循环(Quasi-Cyclic,QC)低密度奇偶校验(Low-Density Parity-Check,LDPC)码,本文提出了三种新的显式构造方法.新方法的指数矩阵由两个整数序列完全定义,其中第一个序列是从0开始且公差为1的等差序列,第二个序列是由符合最大公约数约束的整数组成的特殊序列.对于现有显式方法只能提供较大循环块尺寸的多种行重类型,新显式构造方法在这些行重类型下均获得了相当小的循环块尺寸,从而将最小循环块尺寸降低到大约只有原来的一半.与近期提出的基于搜索的对称结构法相比,新的显式构造方法具有类似或更优的译码性能、极低的描述复杂度且不需要计算机搜索.

Three new explicit constructions are proposed for quasi-cyclic(QC)low-density parity-check(LDPC)codes free of 4-cycles and 6-cycles with large column weights.The exponent matrices for these new methods are completely defined by two sequences of integers.The first sequence is an arithmetic sequence starting from zero with the common difference being one,and the second is a special sequence composed of integers satisfying the greatest-common-divisor(GCD)constraint.The new methods can produce rather small circulant sizes for many categories of row weights,while the existing explicit methods can only provide relatively large circulant sizes,thus the up-to-date smallest circulant sizes being nearly halved.Compared with the recently proposed symmetrical construction which relies upon extensive search,the new explicit constructions have similar or better decoding performance,possess extremely low description complexity and need no computer search.