LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure Analysis
In this paper, we investigate the cycle structure inherent in the Tanner graphs of low-density parity-check (LDPC) codes constructed from balanced incomplete block designs (BIBDs). We begin by delineating the incidence structure of BIBDs and propose a methodology for constructing LDPC codes based on...
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MDPI AG
2025-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/5/476 |
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| author | Hengzhou Xu Xiaodong Zhang Mengmeng Xu Haipeng Yu Hai Zhu |
| author_facet | Hengzhou Xu Xiaodong Zhang Mengmeng Xu Haipeng Yu Hai Zhu |
| author_sort | Hengzhou Xu |
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| description | In this paper, we investigate the cycle structure inherent in the Tanner graphs of low-density parity-check (LDPC) codes constructed from balanced incomplete block designs (BIBDs). We begin by delineating the incidence structure of BIBDs and propose a methodology for constructing LDPC codes based on these designs. By analyzing the incidence relations between points and blocks within a BIBD, we prove that the resulting LDPC codes possess a girth of 6. Subsequently, we provide a detailed analysis of the cycle structure of the constructed LDPC codes and introduce a systematic approach for enumerating their short cycles. Using this method, we determine the exact numbers of cycles of lengths 6 and 8. Simulation results demonstrate that the constructed LDPC codes exhibit excellent performance. |
| format | Article |
| id | doaj-art-65e1f868259140e8bb775da2784c8cec |
| institution | OA Journals |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-65e1f868259140e8bb775da2784c8cec2025-08-20T02:33:54ZengMDPI AGEntropy1099-43002025-04-0127547610.3390/e27050476LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure AnalysisHengzhou Xu0Xiaodong Zhang1Mengmeng Xu2Haipeng Yu3Hai Zhu4School of Computer, Henan University of Engineering, Zhengzhou 451191, ChinaSchool of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, ChinaSchool of Computer, Henan University of Engineering, Zhengzhou 451191, ChinaSchool of Computer, Henan University of Engineering, Zhengzhou 451191, ChinaSchool of Computer, Henan University of Engineering, Zhengzhou 451191, ChinaIn this paper, we investigate the cycle structure inherent in the Tanner graphs of low-density parity-check (LDPC) codes constructed from balanced incomplete block designs (BIBDs). We begin by delineating the incidence structure of BIBDs and propose a methodology for constructing LDPC codes based on these designs. By analyzing the incidence relations between points and blocks within a BIBD, we prove that the resulting LDPC codes possess a girth of 6. Subsequently, we provide a detailed analysis of the cycle structure of the constructed LDPC codes and introduce a systematic approach for enumerating their short cycles. Using this method, we determine the exact numbers of cycles of lengths 6 and 8. Simulation results demonstrate that the constructed LDPC codes exhibit excellent performance.https://www.mdpi.com/1099-4300/27/5/476LDPC codesbalanced incomplete block designs (BIBDs)Tanner graphcyclegirth |
| spellingShingle | Hengzhou Xu Xiaodong Zhang Mengmeng Xu Haipeng Yu Hai Zhu LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure Analysis Entropy LDPC codes balanced incomplete block designs (BIBDs) Tanner graph cycle girth |
| title | LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure Analysis |
| title_full | LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure Analysis |
| title_fullStr | LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure Analysis |
| title_full_unstemmed | LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure Analysis |
| title_short | LDPC Codes on Balanced Incomplete Block Designs: Construction, Girth, and Cycle Structure Analysis |
| title_sort | ldpc codes on balanced incomplete block designs construction girth and cycle structure analysis |
| topic | LDPC codes balanced incomplete block designs (BIBDs) Tanner graph cycle girth |
| url | https://www.mdpi.com/1099-4300/27/5/476 |
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