Which codes have 4-cycle-free Tanner graphs?

IEEE Transactions on Information Theory

Volumn 52, Issue 9, 2006, Pages 4219-4223

  Halford, Thomas R ^a   Grant, Alex J ^b   Chugg, Keith M ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

Author keywords

Cycles; Girth; Graphical models of codes; Iterative decoding; Tanner graphs

Indexed keywords

GRAPH THEORY; ITERATIVE METHODS; MATHEMATICAL MODELS;

BINARY LINEAR BLOCK CODES; GRAPHICAL MODELS; ITERATIVE DECODING; TANNER GRAPHS;

CODES (SYMBOLS);

EID: 33748612991     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.880060     Document Type: Article

References (16)

1. R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inf. Theory, vol. IT-27, no. 5, pp. 533-547, Sept. 1981.
2. D. J. C. MacKay, "Good error correcting codes based on very sparse matrices," IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 399-431, Feb. 1999.
3. Y. Kou, S. Lin, and M. P. C. Fossorier, "Low-density parity-check codes based on finite geometries: A rediscovery and new results," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2711-2736, Nov. 2001.
4. J.-L. Kim, U. N. Peled, I. Perepelitsa, V. Pless, and S. Friedland, "Explicit construction of families of LDPC codes with no 4-cycles," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2378-2388, Oct. 2004.
5. J. S. Yedidia, J. Chen, and M. C. Fossorier, "Generating code representations suitable for belief propagation decoding," in Proc. Allerton Conf. Communication, Control, and Computing, Monticello, IL, Oct. 2002.
6. S. Sankaranarayanan and B. Vasić, "Iterative decoding of linear block codes: A parity-check orthogonalization approach," IEEE Trans. Inf. Theory, vol. 51, no. 9, pp. 3347-3353, Sep. 2005.
7. T. Etzion, A. Trachtenberg, and A. Vardy, "Which codes have cycle-free Tanner graphs?," IEEE Trans. Inf. Theory, vol. 45, no. 6, pp. 2173-2181, Sep. 1999.
8. S. Neuwirth, The size of bipartite graphs with girth eight. Feb. 2001 [Anline]. Available: ArXiv:math/0102210
9. I. Reiman, "Über ein Problem von K. Zarankiewicz," Acta Math. Acad. Sci. Hungary, vol. 9, pp. 269-273, 1958.
10. B. Bollobas, Extremal Graph Theory. New York: Academic, 1978.
11. T. Beth, D. Jungnickel, and H. Lenz, Design Theory. Cambridge, U.K.: Cambridge Univ. Press, 1999.
12. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1978.
13. S. Hoory, "The size of bipartite graphs with a given girth," J. Comb. Theory, Ser. B, vol. 86, no. 2, pp. 215-220, 2002.
14. S. J. Johnson and S. R. Weller, "Resolvable 2-designs for regular low-density parity-check codes," IEEE Trans. Commun., vol. 51, no. 9, pp. 1413-1419, Sep. 2003.
15. D. Augot and F. L. vit Vehel, "Bounds on the minimum distance of the duals of BCH codes," IEEE Trans. Inf. Theory, vol. 42, no. 4, pp. 1257-1260, Jul. 1996.
16. T. Schaub, "A linear complexity approach to cyclic codes," Ph.D. dissertation, ETHZ, Zurich, Switzerland, 1998.