Abstract: Irregular Low-Density Parity-Check（LDPC） codes have good error correcting performance，but their encoding complexities are high.In order to solve the problem above，a construction of irregular LDPC codes with low encoding complexities is proposed.And the encoding algorithms are designed，whose complexities are linear equations of code length.The construction and encoding algorithms are derived from the effectively encoding characteristics of Repeat-Accumulate（RA） codes and masking technique.Firstly，the new construction modifies parity-check matrices of RA codes to eliminate error floors of RA codes.Secondly，the new constructed parity-check matrices are based on Vandermonde matrices，this algebraic structure is easy for hardware implementation.Theoretic analyses and experimental results show that，at a bit-error rate of 1.0×10^-4，the new codes with lower encoding complexities outperform Mackay’s random LDPC codes by 0.4~0.6 dB over an Additive White Gauss Noise（AWGN） channel.

Key words: Low-Density Parity-Check（LDPC） codes, quasi-cyclic, Repeat-Accumulate（RA） codes, masking, Vandermonde matrices

摘要： 针对不规则低密度奇偶校验码（LDPC码）误码性能好，但编码复杂度高的问题，利用重复积累码（RA码）能有效编码的特性和掩模技术，提出了一种不规则LDPC码的构造方法，该码具有线性复杂度的编码算法。该构造方法，首先对RA码的校验矩阵进行了改进，消除了RA码常产生的错误平层效应；然后基于范德蒙矩阵构造了一种新的校验矩阵，该校验矩阵具有代数结构，易于硬件实现。理论分析和实验结果表明，构造的不规则LDPC码的编码复杂度低于Mackay随机码，在加性高斯白噪声（AWGN）信道条件下，误码率为1.0×10^-4时，比Mackay随机码性能提高约0.4~0.6 dB。

关键词: 低密度奇偶校验码, 准循环, 重复积累码, 掩模技术, 范德蒙矩阵