无小环的结构化低密度校验码的构造方法

The Design of Structured Low-Density Parity-Check Codes With Large Girth

提出了一种基于代数方法和图的高度结构化的低密度校验(LDPC)码构造方法.该方法通过设计一个有3类特殊线路的连接图,来保证由此连接图映射而得的校验矩阵对应的Tanner图无小环.此方法可构造最小环长分别为8和12的两类(3,k)准循环(QC)规则LDPC码.对该方法进一步扩展,还可构造两类列重为2最小环长分别为16和24的结构化LDPC码.仿真结果表明在加性高斯白噪声(AWGN)信道下,用迭代译码算法,在误比特率为10-5时,新提出的(3,k)准循环规则LDPC码优于对应的随机构造的LDPC码0.1dB,而新提出的列重为2的结构化LDPC码优于对应的随机构造的LDPC码2dB.

This paper, based on algebra and graph, proposes a method for constructing structured low-density parity-check （LDPC） codes. In this method, the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles. The construction method results in two classes of （3,κ）-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively. Furthermore, by extending this construction method, two classes of LDPC codes with column weight 2, whose girths are respectively 16 and 24, can be obtained. The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding. At the BER of 10^-5, the new proposed （3,κ）-regular （4356,2205） QC-LDPC code performs 1.48dB from the Shannon limit. Moreover, it outperforms the random regular LDPC code of comparable parameters by 0.1dB. For the new proposed structured LDPC codes with column weight 2, they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.