基于EETS与GC的非规则QC-LDPC码低错误平层构造方法

A Novel Construction Method with the Low Error Floor of Irregular QC-LDPC Codes Based on the Elimination of the ETS and Girth Constraints

摘要:

针对准循环低密度奇偶校验(QC-LDPC)码在高信噪比区域可能出现的错误平层现象,提出了一种基于消除基本陷阱集(Eliminating Elementary Trapping Sets, EETS)和围长约束(girth constraints, GC)的非规则QC-LDPC码构造方法。该方法通过巧妙选取度分布,利用基本陷阱集搜索和围长约束改进渐进边增长(Progressive Edge Growth, PEG)算法构造基矩阵,然后通过等差(Arithmetic Progression, AP)序列扩展得到所需的校验矩阵。该方法仅需对简单环形式的ETS进行搜索和消除,就能确保构造的基矩阵中不存在设置范围内的绝大多数ETS,从而降低错误平层现象,且该方法计算复杂度相对较低,可灵活设计码长码率。仿真结果表明,由所提出构造方法所构造的非规则QC-LDPC码比其他五种QC-LDPC码的纠错性能更为优越,且没有明显的错误平层现象。

Abstract:

In order to improve the phenomena that there may be an error floor of quasi-cyclic low-density parity-check (QC-LDPC) codes in high signal to noise ratio (SNR) region, a novel construction method of irregular QC-LDPC codes based on eliminating elementary trapping sets(EETS) and girth constraints(GC) is proposed. The proposed method constructs the basic matrix by means of selecting the degree distribution dexterously and using the ETS search and girth constraints to modify the progressive edge growth (PEG) algorithm, and then obtains the final check matrix by means of expanding the arithmetic progression sequence (APS). Furthermore, only by simply searching and eliminating the ETS in the form of the simple cycles, the proposed method assures that the majority of the ETS in the set range do not exist in the constructed basic matrix, thus the error floor phenomenon is reduced. The proposed method can flexibly adjust and design the code-length and code-rate with relatively low complexity. The simulation results show that the error-correction performance of the irregular QC-LDPC code constructed by the proposed construction method, compared with the five QC-LDPC codes, is more superior and has no error floor phenomenon.