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Gholami, M., Mostafaiee, F. (2012). On the girth of Tanner (3,7) quasi-cyclic LDPC codes. Transactions on Combinatorics, 1(2), 1-16. doi: 10.22108/toc.2012.762
Mohammad Gholami; Fahime Sadat Mostafaiee. "On the girth of Tanner (3,7) quasi-cyclic LDPC codes". Transactions on Combinatorics, 1, 2, 2012, 1-16. doi: 10.22108/toc.2012.762
Gholami, M., Mostafaiee, F. (2012). 'On the girth of Tanner (3,7) quasi-cyclic LDPC codes', Transactions on Combinatorics, 1(2), pp. 1-16. doi: 10.22108/toc.2012.762
Gholami, M., Mostafaiee, F. On the girth of Tanner (3,7) quasi-cyclic LDPC codes. Transactions on Combinatorics, 2012; 1(2): 1-16. doi: 10.22108/toc.2012.762

On the girth of Tanner (3,7) quasi-cyclic LDPC codes

Article 1, Volume 1, Issue 2, June 2012, Page 1-16  XML PDF (338 K)
Document Type: Research Paper
DOI: 10.22108/toc.2012.762
Authors
Mohammad Gholami 1; Fahime Sadat Mostafaiee2
1Shahrekord University
2Malek Ashtar University
Abstract
‎‎S‎. ‎Kim et al‎. ‎have been analyzed the girth of some algebraically‎ ‎structured quasi-cyclic (QC) low-density parity-check (LDPC)‎ ‎codes‎, ‎i.e‎. ‎Tanner $(3,5)$ of length $5p$‎, ‎where $p$ is a prime of‎ ‎the form $15m+1$‎. ‎In this paper‎, ‎by extension this method to‎ ‎Tanner $(3,7)$ codes of length $7p$‎, ‎where $p$ is a prime of the‎ ‎form $21m‎+ ‎1$‎, ‎the girth values of Tanner $(3,7)$ codes will be‎ ‎derived‎. ‎As an advantage‎, ‎the rate of Tanner $(3,7)$ codes is‎ ‎about $0.17$ more than the rate of Tanner $(3,5)$ codes‎.
Keywords
LDPC codes; Tanner graph; Girth
Main Subjects
11T71 Algebraic coding theory; cryptography; 94C15 Applications of graph theory; 97K30 Graph theory
References
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S. Kim, J.-S. No, H. Chung, and D.-J.Shin (2006). On the girth of Tanner's $(3, 5)$ quasi-cyclic LDPC codes. IEEE Trans. Inf. Theory. 52 (4), 1739-1744
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