Tanner (3, 23)-Regular QC-LDPC Codes: Cycle Structure and Girth Distribution
This paper studies a class of quasi-cyclic LDPC (QC-LDPC) codes, i.e., Tanner (3, 23)-regular QC-LDPC codes of code length <inline-formula> <tex-math notation="LaTeX">$23p$ </tex-math></inline-formula> with <inline-formula> <tex-math notation="LaTeX&qu...
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| Format: | Article |
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10409168/ |
| _version_ | 1797296331284283392 |
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| author | Qi Wang Jingping Che Huaan Li Zhen Luo Bo Zhang Hui Liu |
| author_facet | Qi Wang Jingping Che Huaan Li Zhen Luo Bo Zhang Hui Liu |
| author_sort | Qi Wang |
| collection | DOAJ |
| description | This paper studies a class of quasi-cyclic LDPC (QC-LDPC) codes, i.e., Tanner (3, 23)-regular QC-LDPC codes of code length <inline-formula> <tex-math notation="LaTeX">$23p$ </tex-math></inline-formula> with <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> being a prime and <inline-formula> <tex-math notation="LaTeX">$p \equiv 1 (\mathrm {mod} 69)$ </tex-math></inline-formula>. We first analyze the cycle structure of Tanner (3, 23)-regular QC-LDPC codes, and divide their cycles of lengths 4, 6, 8, and 10 into five equivalent types. We propose the sufficient and necessary condition for the existence of these five types of cycles, i.e., the polynomial equations in a 69th unit root of the prime field <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{p}$ </tex-math></inline-formula>. We check the existence of solutions for such polynomial equations by using the Euclidean division algorithm and obtain the candidate girth values of Tanner (3, 23)-regular QC-LDPC codes. We summarize the results and determine the girth distribution of Tanner (3, 23)-regular QC-LDPC codes. |
| first_indexed | 2024-03-07T22:03:05Z |
| format | Article |
| id | doaj.art-3fc1cb1ccd154cc9b981c5724edb4f2e |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-07T22:03:05Z |
| publishDate | 2024-01-01 |
| publisher | IEEE |
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| series | IEEE Access |
| spelling | doaj.art-3fc1cb1ccd154cc9b981c5724edb4f2e2024-02-24T00:00:28ZengIEEEIEEE Access2169-35362024-01-0112265912660910.1109/ACCESS.2024.335592610409168Tanner (3, 23)-Regular QC-LDPC Codes: Cycle Structure and Girth DistributionQi Wang0https://orcid.org/0009-0009-6925-255XJingping Che1Huaan Li2https://orcid.org/0000-0003-3779-4505Zhen Luo3Bo Zhang4https://orcid.org/0000-0003-3779-4505Hui Liu5School of Network Engineering, Zhoukou Normal University, Zhoukou, ChinaSchool of Network Engineering, Zhoukou Normal University, Zhoukou, ChinaSchool of Physics and Telecommunication Engineering, Zhoukou Normal University, Zhoukou, ChinaSchool of Network Engineering, Zhoukou Normal University, Zhoukou, ChinaHenan Provincial Research Center of Wisdom Education and Intelligent Technology Application Engineering Technology, Zhengzhou Railway Vocational Technical College, Zhengzhou, ChinaHenan Provincial Research Center of Wisdom Education and Intelligent Technology Application Engineering Technology, Zhengzhou Railway Vocational Technical College, Zhengzhou, ChinaThis paper studies a class of quasi-cyclic LDPC (QC-LDPC) codes, i.e., Tanner (3, 23)-regular QC-LDPC codes of code length <inline-formula> <tex-math notation="LaTeX">$23p$ </tex-math></inline-formula> with <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> being a prime and <inline-formula> <tex-math notation="LaTeX">$p \equiv 1 (\mathrm {mod} 69)$ </tex-math></inline-formula>. We first analyze the cycle structure of Tanner (3, 23)-regular QC-LDPC codes, and divide their cycles of lengths 4, 6, 8, and 10 into five equivalent types. We propose the sufficient and necessary condition for the existence of these five types of cycles, i.e., the polynomial equations in a 69th unit root of the prime field <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{p}$ </tex-math></inline-formula>. We check the existence of solutions for such polynomial equations by using the Euclidean division algorithm and obtain the candidate girth values of Tanner (3, 23)-regular QC-LDPC codes. We summarize the results and determine the girth distribution of Tanner (3, 23)-regular QC-LDPC codes.https://ieeexplore.ieee.org/document/10409168/LDPC codesquasi-cyclic (QC)girthEuclidean division algorithmprime field |
| spellingShingle | Qi Wang Jingping Che Huaan Li Zhen Luo Bo Zhang Hui Liu Tanner (3, 23)-Regular QC-LDPC Codes: Cycle Structure and Girth Distribution IEEE Access LDPC codes quasi-cyclic (QC) girth Euclidean division algorithm prime field |
| title | Tanner (3, 23)-Regular QC-LDPC Codes: Cycle Structure and Girth Distribution |
| title_full | Tanner (3, 23)-Regular QC-LDPC Codes: Cycle Structure and Girth Distribution |
| title_fullStr | Tanner (3, 23)-Regular QC-LDPC Codes: Cycle Structure and Girth Distribution |
| title_full_unstemmed | Tanner (3, 23)-Regular QC-LDPC Codes: Cycle Structure and Girth Distribution |
| title_short | Tanner (3, 23)-Regular QC-LDPC Codes: Cycle Structure and Girth Distribution |
| title_sort | tanner 3 23 regular qc ldpc codes cycle structure and girth distribution |
| topic | LDPC codes quasi-cyclic (QC) girth Euclidean division algorithm prime field |
| url | https://ieeexplore.ieee.org/document/10409168/ |
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