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A Note on the Girth of (3, 19)-Regular Tanner’s Quasi-Cyclic LDPC Codes
- Source :
- IEEE Access, Vol 9, Pp 28582-28590 (2021)
- Publication Year :
- 2021
- Publisher :
- IEEE, 2021.
-
Abstract
- In this article, we study the cycle structure of (3, 19)-regular Tanner’s quasi-cyclic (QC) LDPC codes with code length $19p$ , where $p$ is a prime and $p\equiv 1~(\bmod ~57)$ , and transform the conditions for the existence of cycles of lengths not more than 10 into polynomial equations in a 57th root of unity of the prime field $\mathbb {F}_{p}$ . By employing the Euclidean division algorithm to check whether these equations have solutions over the prime field $\mathbb {F}_{p}$ , the girth values of (3, 19)-regular Tanner’s QC-LDPC codes of code length $19p$ are determined. In order to show the good performance of this class of QC-LDPC codes, numerical results are also provided.
Details
- Language :
- English
- ISSN :
- 21693536
- Volume :
- 9
- Database :
- Directory of Open Access Journals
- Journal :
- IEEE Access
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.3995a10cd8544c47b6070cf79c5661a0
- Document Type :
- article
- Full Text :
- https://doi.org/10.1109/ACCESS.2021.3058732