Construction of Low-rank Circulant Matrices and Their Associated Nonbinary LDPC Codes

Hengzhou XU; Hai ZHU; Dan FENG; Bo ZHANG; Manjie ZHOU

doi:10.11999/JEIT200351

Volume 43 Issue 1

Jan. 2021

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Article Navigation > Journal of Electronics & Information Technology > 2021 > 43(1): 85-91

Hengzhou XU, Hai ZHU, Dan FENG, Bo ZHANG, Manjie ZHOU. Construction of Low-rank Circulant Matrices and Their Associated Nonbinary LDPC Codes[J]. Journal of Electronics & Information Technology, 2021, 43(1): 85-91. doi: 10.11999/JEIT200351

Citation:

Hengzhou XU, Hai ZHU, Dan FENG, Bo ZHANG, Manjie ZHOU. Construction of Low-rank Circulant Matrices and Their Associated Nonbinary LDPC Codes[J]. Journal of Electronics & Information Technology, 2021, 43(1): 85-91. doi: 10.11999/JEIT200351

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Construction of Low-rank Circulant Matrices and Their Associated Nonbinary LDPC Codes

doi: 10.11999/JEIT200351

1.
School of Network Engineering, Zhoukou Normal University, Zhoukou 466001, China
2.
School of Communications and Information Engineering, Xi’an University of Post and Telecommunications, Xi’an 710121, China

Funds: The National Natural Science Foundation of China (61801527,11971311), The TianYuan Special Funds of the National Natural Science Foundation of China (12026230, 12026231), The Training Program for Young Core Instructor of Henan Universities (2018GGJS137), The Key Scientific Research Projects of Henan Educational Committee (20A510017), The Natural Science Foundation of Henan (202300410523), The Project of Youth Talent Lift Program of Shaanxi Association for Science and Technology (20200116), The Scientific Research Program Funded by Shaanxi Provincial Education Department (20JK0918)

Received Date: 2020-05-08
Rev Recd Date: 2020-10-26

Available Online: 2020-11-19

Publish Date: 2021-01-15

Abstract

Abstract

In image processing, the redundant information of low-rank matrices can be used for image recovery and image feature extraction, and redundant rows of the parity-check matrices can accelerate the convergence rate in iterative decoding. A class of low-rank circulant matrices with easy hardware implementation is studied. Circulant matrices are first converted into position sets, the search space of position sets is pruned based on isomorphism theory, and then construction of circulant matrices is proposed based on the bit shift method. Considering the relationship between the column assignment of non-zero field elements and the matrix rank, circulant matrices whose Tanner graphs have no cycles of length 4 are chosen, and according to the column assignment of non-zero field elements, construction of nonbinary LDPC codes over various finite fields and with different code rates is presented. Numerical simulation results show that, compared with binary LDPC codes constructed based on the PEG algorithm, the proposed nonbinary LDPC codes have 0.9 dB gain at Word Error Rate (WER) of 10^-5 when the modulation is BPSK, and the performance gap becomes large by combining with high order modulations. Furthermore, the performance gap of the proposed codes between 5 iterations and 50 iterations is negligible, and it provides a promising coding scheme for low-latency and high-reliability communications.
- LDPC code,
- Low-rank matrix,
- Circulant matrix,
- Isomorphism theory,
- Girth

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