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

Document Type : Research Paper

Authors

1 Shahrekord University

2 Malek 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

Main Subjects

References

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

Files

Share

How to cite

Statistics