http://iet.metastore.ingenta.com
1887

## Recursive method for generating column weight 3 low-density parity-check codes based on three-partite graphs

• Author(s):
• DOI:

$19.95 (plus tax if applicable) ##### Buy Knowledge Pack 10 articles for$120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:

IET Communications — Recommend this title to your library

## Thank you

In this study, a method is presented to construct column weight 3 (CW3) low-density parity-check (LDPC) codes using three-partite graphs. Let Gb be a bipartite graph and Ng be the set of all minimum length cycles in Gb . Using Gb and Ng , a three-partite graph denoted G(Gb , Ng ), or simply Gt , is formed. Let T be the set of length 3 cycles in Gt and Ta be the set of three element subsets of vertices in Gt such that each of these subsets form a subgraph with no edges in Gt and has precisely one element in each section of Gt . Furthermore, let H be the binary matrix in which the set of rows represent the set of vertices of Gt , the columns represent the elements of V:= TTa , and hij = 1 if and only if the ith vertex of Gt belongs to the jth three element set in V. Then H is a CW3 binary matrix. Using the Tanner graph representing H , a recursive construction for CW3 LDPC codes is provided. Applying a simple restriction on T and Ta , codes free of length 4 cycles are generated. Euclidean and finite geometry codes are used as the base codes for generating new CW3 LDPC codes. Results are presented which show that these new codes perform well in an additive white Gaussian noise (AWGN) channel with the iterative sum-product decoding algorithm.

Inspec keywords:

Subjects:

### References

1. 1)
2. 2)
3. 3)
4. 4)
5. 5)
6. 6)
7. 7)
8. 8)
9. 9)
10. 10)
11. 11)
• 11. Malema, G.A., Liebelt, M.: ‘High girth column-weight-two LDPC codes based on distance graphs’, Eurasip J. Wirel. Commun. Networking, 2007, 2007, Article ID 48158, doi: 10.1155/2007/48158.
12. 12)
13. 13)
14. 14)
• 14. Fan, J., Xiao, Y.: ‘A method of counting the number of cycles in LDPC codes’. Proc. Int. Conf. Signal Processing, Beijing, China, November 2006, pp. 14.
15. 15)
16. 16)
17. 17)
18. 18)
• 18. Salahshouri, Z.: ‘Construction of LDPC codes based on finite fields and algebraic structures’. MS Thesis, Faculty of Applied Sciences, Malek Ashtar University of Technology, Iran, 2011.
19. 19)
• 19. Ahmadi, M.: ‘Graph based regular LDPC codes’. MS Thesis, Faculty of Applied Sciences, Malek Ashtar University of Technology, Iran, 2011.
20. 20)
21. 21)
22. 22)
23. 23)
24. 24)
25. 25)
26. 26)
27. 27)
• 27. Zhou, B., Zhang, L., Huang, Q., Lin, S., Xu, M.: ‘Constructions of high performance non-binary QC-LDPC codes’. Proc. IEEE Inf. Theory Workshop, Porto, Portugal, May 2008, pp. 7175.
28. 28)
• 28. Neal, R.M.: ‘Software for LDPC Codes’ (Dept. of Statistics and Department of Computer Science, University of Toronto), http://www.cs.toronto.edu/~radford/ftp/LDPC-2006-02-08/index.html.
29. 29)
30. 30)
31. 31)
32. 32)
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-com.2014.0235

### Related content

content/journals/10.1049/iet-com.2014.0235
pub_keyword,iet_inspecKeyword,pub_concept
6
6
This is a required field