Binary representation of cycle Tanner-graph GF(2b) codes

IEEE International Conference on Communications

Volumn 1, Issue , 2004, Pages 528-532

  Hu, Xiao Yu ^a   Eleftheriou, Evangelos ^a  

^a IBM RESEARCH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DECODING; ERROR ANALYSIS; GRAPH THEORY; ITERATIVE METHODS; RANDOM PROCESSES;

BINARY REPRESENTATION; BLOCK LENGTH; NOISY CHANNELS; RANDOM ENSEMBLES;

CODES (SYMBOLS);

EID: 4143097079     PISSN: 05361486     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. R.G. Gallager, Law Density Parity Check Codes Cambridge, MA: MIT Press, 1963.
2. D.J.C. MacKay, "Good error-correcting codes based on very sparse matrices," IEEE Trans. Inform. Theory, vol. 45, pp. 399-431, Mar. 1999.
3. T. Richardson, A. Shokrollahi, and R. Urbanke, "Design of provably good low-density parity-check codes," IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, Feb. 2001.
4. R.M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inform. Theory, vol. 27, pp. 533-547, Sept. 1981.
5. M.C. Davey and D. MacKay, "Low-density parity-check codes over GF(q)," IEEE Commun. Lett., vol. 2, pp. 165-167, June 1999.
6. M.C. Davey, Error-Correction Using Low-Density Parity-Check codes. PhD thesis, University of Cambridge, Cambridge, UK, Dec. 1999.
7. X.-Y. Hu, E. Eleftheriou, and D.-M. Arnold, "Irregular progressive edge-growth Tanner graphs," in Proc. 4th Intl. ITG Conf. on Source and Channel Coding, Berlin, ITG-Fachbericht 170, Berlin, Offenbach: VDE-Verlag, 2002, pp. 61-68.
8. X.-Y. Hu, E. Eleftheriou, and D.-M. Arnold, "Progressive edge-growth Tanner graphs," in Proc. IEEE Global Telecommun. Conf. (GLOBE-COM), San Antonio, Texas, USA, Nov. 2001.
9. W.W. Peterson and E.J. Weldon. Jr., Error-Correcting Codes, Cambridge, MA: MIT Press, 1972.
10. D. Jungnickel and S.A. Vanstone, "Graphical codes revisited," IEEE Trans. Inform. Theory, vol. 43, pp. 136-146, Jan. 1997.
11. J. Blomer, R. Karp, and E. Welzl, "The rank of sparse random matrices over finite fields," Research Report, International Computer Science Institute, Berkeley, CA, 1996.
12. S.J. MacMullan and O.M. Collins, "A comparison of known codes, random codes, and the best codes," IEEE Trans. Inform. Theory, vol. 44, pp. 3009-3022, Nov. 1998.
13. A. Lubotzky, R. Phillips, and P. Sarnak, "Ramanujan graphs," Combinatorica, vol. 8, pp. 261-277, 1988.
14. G.A. Margulis, "Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators," Problemy Peredachi Inform., vol. 24, pp. 51-60, 1988.
15. M. Sipser and D.A. Spielman, "Expander codes," IEEE Trans. Inform. Theory, vol. 42, pp. 1710-1722, Nov. 1996.
16. J. Lafferty and D. Rockmore, "Codes and iterative decoding on algebraic expander graphs," in Proc. IEEE Intl. Symp. Inform. Theory and Applications (ISITA) Honolulu, Hawaii, 2000.
17. J. Rosenthal and P.O. Vontobel, "Construction of LDPC codes based on Ramanujan graphs and ideas from Margulis," in Proc. 38th Annual Allerton Conf. on Communication, Computing and Control, Monticello, IL, Oct. 2000.
18. C. Schlegel and L. Perez, "On error bounds and turbo codes," IEEE Commun. Lett., vol. 3, pp. 205-207, July 1999.
19. C.E. Shannon, R.G. Gallager, and E.R. Berlekamp, "Lower bounds to error probability for coding on discrite memoryless channels: Part I and II," Inform. Control., vol. 10, pp. 65-103 and 527-552, Jan. and May 1967.
20. G. Poltyrev, "Bounds on the decoding error probability of binary linear codes via their spectra," IEEE Trans. Inform. Theory, vol. 40, pp. 1284-1292, July 1994.
21. H. Herzberg and G. Poltyrev, "The error probability of M-ary PSK block coded modulation schemes," IEEE Trans. Commun., vol. 44, pp. 427-433, Apr. 1996.
22. I. Sason and S. Shamai (Shitz), "Improved upper bounds on the ensemble performance of ML decoded low-density parity-check codes," IEEE Commun. Lett., vol. 4, pp. 89-91, Mar. 2000.
23. H. Song and J.R. Cruz, "Reduced-complexity decoding of Q-ary LDPC codes for magnetic recording," IEEE Trans. Magnetics, vol. 39, pp. 1081-1087, Mar. 2003.
24. q)," in Proc. IEEE Workshop on Inform. Theory, Paris, France, 2003.