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Gholami, Mohammad, Mostafaiee, Fahime. (1391). On the girth of Tanner (3,7) quasi-cyclic LDPC codes. , 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". , 1, 2, 1391, 1-16. doi: 10.22108/toc.2012.762
Gholami, Mohammad, Mostafaiee, Fahime. (1391). 'On the girth of Tanner (3,7) quasi-cyclic LDPC codes', , 1(2), pp. 1-16. doi: 10.22108/toc.2012.762
Gholami, Mohammad, Mostafaiee, Fahime. On the girth of Tanner (3,7) quasi-cyclic LDPC codes. , 1391; 1(2): 1-16. doi: 10.22108/toc.2012.762

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

Transactions on Combinatorics
مقاله 1، دوره 1، شماره 2، شهریور 2012، صفحه 1-16    اصل مقاله (337.95 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2012.762
نویسندگان
Mohammad Gholami* 1؛ Fahime Sadat Mostafaiee2
1Shahrekord University
2Malek Ashtar University
چکیده
‎‎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.
کلیدواژه‌ها
LDPC codes؛ Tanner graph؛ Girth
مراجع
M. P. C. Fossorier (2004) Quasi-cyclic low-density parity-check codes from circulant permutation matrices IEEE Trans. Inf. Theory 50 (8), 1788-1793
R. G. Gallager (1963) Low-Density Parity-Check Codes Cambridge, MA: MIT. Press
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
R. Lucas, M. P. C Fossorier, and Y. Kou, S. Lin (2000) Iterative decoding of onestep majority logic decodable codes based on belief propagation 48 (6), 931-937
D. J. C. Mackay (1999) Good error-correcting codes based on very sparse matrices IEEE Trans. Info. Theory 45 (2), 399-431
C. E. Shannon (1949) The Mathematical Theory of Information Urbana, IL:University of IllinoisPress, (reprinted 1998)
R. M. Tanner, D. Sridhara, and T. E. Fuja (2001) A class of group-structured LDPC codes in Proc. Int. Symp. Communication Theory and Applications, Ambleside, U.K., Jul.
R. M. Tanner (1981) A recursive approach to low complexity codes IEEE Trans. Inform. Theory 27, 533-547
R. M. Tanner, D. Sridhara, A. Sridharan, T. E. Fuja, and D. J. Costello (2004) LDPC Block and Convolutional Codes Based on Circulant Matrices IEEE Trans. Inf. Theory 50 (12), 2966-2984
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