基于马尔可夫的LDPC码围长检测研究

Girth detection of LDPC based on Markov process

LDPC码是目前最好的信道编码技术之一,由于其校验矩阵中存在短环,采用和积等迭代译码算法时将会降低译码性能。因此,围长是目前设计LDPC码的一个很重要的方面,检测与消除短环已成为提高LDPC码译码性能的重要措施。在基于校验矩阵的环路检测定理基础上,根据马氏链的特点和最大熵原理,将校验矩阵转化为转移概率矩阵,给出了一种基于转移概率矩阵的围长检测方法,在理论上给予证明,且进行了仿真,结果表明该方法对不同的校验矩阵具有很好的围长检测效果,且能对其状态进行分类判别。

LDPC is one of the best channel code techniques. For the short girth in the its check matrix, using sumproduct decoding arithmetic can reduce the decoding performance. Girth is a very important aspect in LDPC code designing. Girth detecting and eliminating short girth become very important method in improving LDPC decoding performance. Based on the cycles detection theorem of check matrix,Markov process and maximum entropy principle,a new way of girth detection is proposed in the paper where the check matrix is replaced by transition probability matrix to prove it in theory. The simulation results show that girth detection has good results and some practical value to different check matrixes and can classify the state according to simulation.