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JOURNAL OF ELECTRONICS INFORMATION TECHNOLOGY

Construction of Non-binary QC-LDPC Codes

Min Yang, Wenyan Zhang, Jie Zhong, Jie Wu

Published Feb 18, 2014• 1 citation
Publisher

Abstract

该文研究准循环多进制LDPC码的构造，给出多进制LDPC码的设计流程和构造方法。详细讨论了多进制LDPC码的性能影响因素，综合考虑了环长和环的连通性对性能的影响，研究了母矩阵扩展中偏移因子的选择以及GF(q)上非零元素替代。同时提出了次优解的搜索方法，以降低搜索复杂度。最后，将提出的方法用于不同阶数下LDPC码的构造。仿真结果表明，通过新方法构造得到的多进制LDPC码与二进制码相比，在BPSK调制方式下在误帧率10-4附近有0.2 dB的性能提升；在有限域阶数与调制阶数匹配的情况下，有更大的性能提升。与相近码长，相同码率的多进制循环码相比，该文构造得到的多进制LDPC码在误帧率10-4附近有0.25 dB的性能提升。

DOI
10.3724/sp.j.1146.2012.00403

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Non-binary (NB) low-density parity-check (LDPC) codes offer superior error-correcting performance compared to binary LDPC codes, especially for short and medium lengths. Constructing such codes with large girth remains challenging due to various combinatorial constraints. We present a novel algebraic and graph-theoretic construction of non-binary quasi-cyclic (QC) LDPC codes with column weight two and girth 12, which is known to be largest achievable girth for array-based QC-LDPC codes. In constructing girth-12 (2, dc) NB-QC-LDPC codes, our method attains the minimum possible code length for dc < 10. Motivated by the fact that non-binary spatially coupled (SC) QC-LDPC codes achieve optimal performance at column weight three, we further construct NB-SC-QC-LDPC codes with girth ≥ 8 while effectively reducing the number of 8-cycles. Specifically, for (3, dc) codes, our design eliminates dominant absorbing sets such as the (3, 3) and (4, 2), eliminates the (5, 1) elementary absorbing sets (EAS), and eliminates almost all (6, 2) EAS, thereby directly enhancing the error-correction performance. The proposed NB-QC-LDPC codes achieve performance comparable to NB-LDPC codes used in the BeiDou satellite navigation system, while requiring a significantly smaller parity-check matrix storage footprint, for instance, around a 44× reduction in storage requirements with respect to BeiDou rate-1/2 (88, 44) code. Also, the proposed rate-1/2 code with length n = 684 provide a 0.4 dB gain over non-binary near-regular QC-LDPC code with same parameters proposed by Huang et al. [IEEE Trans. Commun.] while requiring a smaller parity-check matrix storage footprint. Furthermore, the proposed rate-1/2 NB-SC-QC-LDPC code having length n = 4608 achieve 0.1 dB coding gain compared to existing protograph constructions while requiring a significantly smaller parity-check matrix storage footprint, i.e., around a 192× reduction.
Repeat Accumulate (RA) codes are subclass of low-density parity-check (LDPC) codes with fast encoder structures. QC-LDPC codes are also a class of LDPC codes and easy to be implemented. There were some paper had researched that non-binary LDPC codes have better performance cover binary ones. In this paper, It constructed non-binary RA codes with linear encoding method and non-binary QC-LDPC codes with algebraic constructions method. The BER performance of RA and QC-LDPC codes over GF(q) were compared by simulation over the Additive White Gaussian Noise (AWGN) channels. The simulation results concluded when code length and code rate are same, the BER performance of this two non-binary LDPC codes are very close, but they still have a little different point.
This paper considers the algebraic construction and performance of non-binary spatially-coupled low density parity check (LDPC) codes. A replicate-and-mask approach is presented to construct finite-length algebraic quasi-cyclic (QC) spatially-coupled (SC) LDPC codes. Numerical results show the superiority of non-binary algebraic SC QC LDPC codes over the corresponding random non-binary (block and SC) LDPC codes. In this paper, it is demonstrated that the threshold saturation phenomenon, previously demonstrated for binary SC LDPC codes, also holds for non-binary SC LDPC codes over the binary-input AWGN channel with BPSK modulation.