On codes designed via algebraic lifts of graphs

46th Annual Allerton Conference on Communication, Control, and Computing

Volumn , Issue , 2008, Pages 1254-1261

  Kelley, Christine A ^a  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC METHODS; LDPC CODES; SIMULATION RESULTS; VOLTAGE ASSIGNMENTS; VOLTAGE GRAPHS;

ELEVATORS;

GRAPH THEORY;

EID: 64549150629     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ALLERTON.2008.4797704     Document Type: Conference Paper

References (26)

1. J. Thorpe, "LDPC codes constructed from protographs", IPN progress report, pp. 42-154, JPL, August 2003.
2. J. Thorpe, K. Andrews, and S. Dolinar, "Methodologies for designing LDPC codes using protographs and circulants.", in Proceedings of the IEEE International Symposium on Information Theory, p. 236, Chicago, June 2004.
3. D. Divsalar, S. Dolinar, and C. Jones, "Construction of protograph LDPC codes with minimum distance linearly growing with block size", IEEE Globecom, St. Louis, MO, Nov. 2005, pp. 1152?1156 2005.
4. J. L. Gross and T. W. Tucker, Topological graph theory, Wiley, NY, 1987.
5. C. A. Kelley and J. L. Walker, "LDPC codes from voltage graphs", in Proceedings of the International Symposium on Information Theory, Toronto, Canada, June 2008.
6. R. M. Tanner, D. Sridhara, and T. E. Fuja, "A class of group-structured LDPC codes", in Proc. of Intl. Symp. on Communication Theory and Applications, Ambleside, U. K., pp. 365-370, July 2001.
7. D. Sridhara, T. E. Fuja, and R. M. Tanner, "Low density parity check codes from permutation matrices", 2001 Conf. on Info. Sci. and Systems, Johns Hopkins University, March 2001.
8. J. L. Fan, "Array codes as low-density parity-check codes", in Proceedings of the 2nd International Symposium on Turbo Codes and their applications, Brest, France, Sept. 2000, pp. 543-546.
9. O. Milenkovic, N. Kashyap, and D. Leyba, "Shortened array codes of large girth," in IEEE Transactions on Information Theory, Vol. 5, No. 8, pp. 3707-3722, August 2006.
10. S. Song, L. Lan, S. Lin, and K. A-Ghaffar, "Construction of quasicyclic LDPC codes based on the primitive elements of finite fields", in Proc. of Conf. on Info. Systems and Sciences, March 22-24, 2006, pp. 835-838.
11. R. M. Tanner, "Quasi-cyclic repeat accumulate codes", in Proc. 37th Allerton Conference on Communication, Control and Computing, Monticello, IL, Oct. 1999, pp. 249?259.
12. N. Linial and E. Rozenman, "Random lifts of graphs: Perfect matchings", Combinatorica, vol. 25, pp. 407-424, 2005.
13. A. Amit and N. Linial, "Random lifts of graphs II: Edge expansion", Combinatorics Probability and Computing, vol. 15, pp. 317-332, 2006.
14. A. Amit, N. Linial, and J. Matousek, "Random lifts of graphs: independence and chromatic number", Random Structures and Algorithms, vol. 20, no. 1, pp. 1-22, Jan. 2002.
15. G. Exoo, "Voltage graphs, group presentations, and cages", The Electronic Journal of Combinatorics, vol. 11 (1), 2004.
16. L. Brankovic, M. Miller, J. Plesnik, J. Ryan, and J. Siran, "Large graphs with small degree and diameter: A voltage assignment approach", Jrnl. of Combinatorial Math. and Combinatorial Computing, vol. 24, pp. 161-176, 1997.
17. M. P. C. Fossorier, "Quasi-cyclic low-density parity-check codes from circulant permutation matrices", IEEE Transactions on Information Theory, vol. 50, no. 8, pp. 1788?1793, 2004.
18. D. J. C. MacKay and M. C. Davey, "Evaluation of Gallager codes for short block length and high rate applications", in Codes, Systems, and Graphical Models, B. Marcus and J. Rosenthal, Eds., vol. 123 of IMA Volumes in Mathematics and its Applications, pp. 113-130. Springer, New York, 2000.
19. R. Smarandache and P. O. Vontobel, "On regular quasi-cyclic LDPC codes from binomials", in Proceedings of the IEEE International Symposium on Information Theory, Chicago, IL, June 2004.
20. O. Y. Takeshita, "A new construction for LDPC codes using permutation polynomials over integer rings", arXiv:cs/0506091v1, 2005.
21. K. Yang and T. Helleseth, "On the minimum distance of array codes as LDPC codes", in IEEE Transactions on Information Theory, vol. 49, No. 12, December 2003.
22. J. Chen, R. M. Tanner, J. Zhang, M. P. C. Fossorier, "Construction of irregular LDPC codes by quasi-cyclic extension", IEEE Transactions on Information Theory, pp. 1479-1483, Vol. 53, No. 4, April 2007.
23. R. M. Tanner, "A recursive approach to low complexity codes," in IEEE Transactions on Information Theory, vol. IT-27, pp. 533-547, Sept. 1981.
24. D. Archdeacon, J-H. Kwak, J. Lee, and Y. Sohn, "Bipartite covering graphs", Discrete Mathematics, 214 (2000) pp. 51-63.
25. T. W. Hungerford, Algebra, Graduate Texts in Mathematics, vol. 73, Springer-Verlag, 1974.
26. P. J. Cameron, Permutation groups, London Mathematical Society Student Texts, vol. 45, Cambridge University Press, 1999.