Upper bounds on the rate of LDPC codes as a function of minimum distance

IEEE Transactions on Information Theory

Volumn 52, Issue 5, 2006, Pages 2092-2100

  Ben Haim, Yael ^a   Litsyn, Simon ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Distance distribution; Linear programming; Low density parity check (LDPC) codes; Minimum distance

Indexed keywords

COMBINATORIAL MATHEMATICS; INFORMATION THEORY; LINEAR PROGRAMMING; MATRIX ALGEBRA;

DISTANCE DISTRIBUTION; GILBERT-VARSHAMOV BOUND; LOW-DENSITY PARITY-CHECK (LDPC) CODES; MINIMUM DISTANCE; PARITY-CHECK MATRICES; UPPER BOUNDS;

CODES (SYMBOLS);

EID: 33646046794     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.872972     Document Type: Article

References (13)

1. R. Gallager, Low Density Parity Check Codes. Cambridge, MA: MIT Press, 1963.
2. R. J. McEliece, E. R. Rodemich, H. Rumsey, and L. R. Welch, "New upper bounds on the rate of a code via the Delsarte-Macwilliams inequalities," IEEE Trans. Inf. Theory, vol. IT-23, no. 2, pp. 157-166, Mar. 1977.
3. C. Di, "Asymptotic and finite length analysis of low-density parity-check codes," Ph.D. dissertation, EPFL, Lausanne, Switzerland, 2004.
4. C. Di, T. Richardson, and R. Urbanke, "Weight distribution of iterative coding systems: How deviant can you be?," in Proc. IEEE Int Symp. Information Theory, Washington, DC, Jun. 2001, p. 50.
5. S. Litsyn and V. Shevelev, "On ensembles of low-density parity check codes: Asymptotic distance distributions," IEEE Trans. Inf. Theory, vol. 48, no. 4, pp. 887-908, Apr. 2002.
6. S. Litsyn and V. Shevelev, "Distance distributions in ensembles of irregular low-density parity-check codes," IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3140-3159, Dec. 2003.
7. G. Miller and D. Burshtein, "Asymptotic enumeration method for analyzing LDPC codes," IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 1115-1131, Jun. 2004.
8. A. Orlitsky, K. Viswanathan, and J. Zhang, "Stopping set distribution of LDPC code ensembles," IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 929-953, Mar. 2005.
9. D. Burshtein, M. Krivelevich, S. Litsyn, and G. Miller, "Upper bounds on the rate of LDPC codes," IEEE Trans. Inf. Theory, vol. 48, no. 9, pp. 2437-2449, Sep. 2002.
10. P. Delsarte, "An algebraic approach to the association schemes of coding theory," Philips Res. Repts. Suppl., vol. 10, pp. 1-97, 1973.
11. I. Krasikov and S. Litsyn, "Survey of binary Krawtchouk polynomials," in Codes and Association Schemes. ser. DIMACS Ser. Discrete Math. Theoret. Comput. Sci., A. Barg and S. Litsyn, Eds. Providence, RI: Amer. Math. Soc, 2001, vol. 56, pp. 199-211.
12. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1977.
13. A. Ashikhmin, I. S. Honkala, T. K. Laihonen, and S. Litsyn, "On relations between covering radius and dual distance," IEEE Trans. Inf. Theory, vol. 45, no. 6, pp. 1808-1816, Sep. 1999.