Theoretical Bounds for the Size of Elementary Trapping Sets by Graphic Methods
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912705499103232 |
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| author | Xiong, Haoran Ye, Zicheng Zhang, Huazi Wang, Jun Liu, Ke Yin, Dawei Wang, Guanghui Yan, Guiying Ma, Zhiming |
| author_facet | Xiong, Haoran Ye, Zicheng Zhang, Huazi Wang, Jun Liu, Ke Yin, Dawei Wang, Guanghui Yan, Guiying Ma, Zhiming |
| contents | Elementary trapping sets (ETSs) are the main culprits for the performance of LDPC codes in the error floor region. Due to the large quantity, complex structures, and computational difficulties of ETSs, how to eliminate dominant ETSs in designing LDPC codes becomes a pivotal issue to improve the error floor behavior. In practice, researchers commonly address this problem by avoiding some special graph structures to free specific ETSs in Tanner graph. In this paper, we deduce the accurate Turán number of $θ(1,2,2)$ and prove that all $(a,b)$-ETSs in Tanner graph with variable-regular degree $d_L(v)=γ$ must satisfy the bound $b\geq aγ-\frac{1}{2}a^2$, which improves the lower bound obtained by Amirzade when the girth is 6. For the case of girth 8, by limiting the relation between any two 8-cycles in the Tanner graph, we prove a similar inequality $b\geq aγ-\frac{a(\sqrt{8a-7}-1)}{2}$. The simulation results show that the designed codes have good performance with lower error floor over additive white Gaussian noise channels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02737 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Theoretical Bounds for the Size of Elementary Trapping Sets by Graphic Methods Xiong, Haoran Ye, Zicheng Zhang, Huazi Wang, Jun Liu, Ke Yin, Dawei Wang, Guanghui Yan, Guiying Ma, Zhiming Information Theory Elementary trapping sets (ETSs) are the main culprits for the performance of LDPC codes in the error floor region. Due to the large quantity, complex structures, and computational difficulties of ETSs, how to eliminate dominant ETSs in designing LDPC codes becomes a pivotal issue to improve the error floor behavior. In practice, researchers commonly address this problem by avoiding some special graph structures to free specific ETSs in Tanner graph. In this paper, we deduce the accurate Turán number of $θ(1,2,2)$ and prove that all $(a,b)$-ETSs in Tanner graph with variable-regular degree $d_L(v)=γ$ must satisfy the bound $b\geq aγ-\frac{1}{2}a^2$, which improves the lower bound obtained by Amirzade when the girth is 6. For the case of girth 8, by limiting the relation between any two 8-cycles in the Tanner graph, we prove a similar inequality $b\geq aγ-\frac{a(\sqrt{8a-7}-1)}{2}$. The simulation results show that the designed codes have good performance with lower error floor over additive white Gaussian noise channels. |
| title | Theoretical Bounds for the Size of Elementary Trapping Sets by Graphic Methods |
| topic | Information Theory |
| url | https://arxiv.org/abs/2307.02737 |