码长连续变化的QC-LDPC码的设计

该文基于有限多项式环的理论，提出了码长连续变化的准循环低密度奇偶校验(Quasi-Cyclic Low Density Parity Check, QC-LDPC)码的设计方法。当有限环基数大于某个门限值时，在此环内通过一定规则选择参数生成移位项，利用它们构造出的校验矩阵均可以达到较大的圈长(girth)值。在设计中，有限环基数为连续的整数，且基数与码长呈线性关系，因此能够在girth值不变的前提下实现码长的连续变化。该文分析并证明了该构造方法大大增加了可用的高性能QC-LDPC码数量，更好地服务于自适应链路系统。

Design of QC-LDPC Code with Continuously Variable Length

Based on the theory of finite polynomial ring, a novel code design method for Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes with continuously variable length is proposed. When the cardinal number of the ring is larger than a certain threshold, the shift offset values can be formulated by the parameters selected in the ring. Thus all H matrices constructed by them have larger girth. In the design, the cardinal number of the ring is a continuously variable integer, which has a linear relation with the code length, so that the code length can be increased continuously. Analyses and proofs show that, the method can enlarge the number of QC-LDPC codes greatly, which can serve the adaptive link systems better.