基于LU分解的LDPC编码改进算法研究

Research on Modified LDPC Encoding Algorithm Based on LU Decomposition

为了使低密度奇偶校验码(Low Density Parity-check Code,LDPC)的校验矩阵H满足系统码的形式,同时降低校验矩阵的复杂度,减少编码时的存储空间,提出改进的优化准则,设计一种基于LU分解的算法。通过用全主元策略对校验矩阵进行高斯消元、行列交换等调整,使之具有系统码的形式,分解后得到的矩阵具有更好的稀疏性,从而可以进一步简化编码设计、减小存储空间占用和降低计算复杂度。所采用的算法与校验矩阵的构造无关,对性能无影响,且利于硬件实现,具有较好的应用前景。

In order to make the check matrix H of Low Density Parity-check Codes （LDPC） meet the form of systematic code, reduce the complexity of LDPC and the storage space during coding, this paper proposes improved optimal criteria, and designs an algorithm based on LU decomposition. This algorithm uses complete pivot strategy to perform Gaussian elimination and row and column exchange to make the H have the form of systematic code. The decomposed matrix has better sparsity to further simplify code design and reduce storage space and computation complexity. The simulation results show that the modified algorithm is independent of the constitution of check matrix and favourable to hardware implementation, and has no influence on performance, so it has better application prospect.