Graph-based convolutional and block LDPC codes

Problems of Information Transmission

Volumn 45, Issue 4, 2009, Pages 357-377

  Bocharova, I E ^a   Kudryashov, B D ^a   Satyukov, R V ^a  

^a ITMO UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

CONVOLUTIONAL LDPC CODES; GRAPH-BASED; LDPC CODES; LONG CODES; LOWER BOUNDS; MINIMUM DISTANCE; OPTIMAL CODES; TAIL-BITING CONVOLUTIONAL CODES; VOLTAGE GRAPHS;

CONVOLUTIONAL CODES;

CONVOLUTION;

EID: 75649100861     PISSN: 00329460     EISSN: 16083253     Source Type: Journal    
DOI: 10.1134/S0032946009040061     Document Type: Article

References (27)

1. Gallager, R.G., Low-Density Parity-Check Codes, Cambridge: MIT Press, 1963. Translated under the title Kody s maloi plotnost'yu proverok na chetnost', Moscow: Mir, 1966.
2. Berrou, C., Glavieux, A., and Thitimajshima, P., Near-Shannon-Limit Error-Correcting Coding and Decoding: Turbo-Codes. 1, in Proc. IEEE Int. Conf. on Communications (ICC'93), Geneva, Switzerland, 1993, vol. 2, pp. 1064-1070.
3. T.J. Richardson M.A. Shokrollahi R.L. Urbanke 2001 Design of Capacity-Approaching Irregular Low-Density Parity-Check Codes IEEE Trans. Inform. Theory 47 2 619 637 1019.94034 10.1109/18.910578 1820480 (Pubitemid 32318093)
4. X.-Y. Hu E. Eleftheriou D.M. Arnold 2003 Regular and Irregular Progressive Edge-Growth Tanner Graphs IEEE Trans. Inform. Theory 51 1 386 398 2234601 (Pubitemid 40151893)
5. Tanner, R.M., Sridhara, D., and Fuja, T., A Class of Group-Structured LDPC Codes, in Proc. 6th Int. Sympos. on Communication Theory and Applications (ISTCA-2001), Ambleside, Lake District, UK, 2001.
6. R.M. Tanner D. Sridhara A. Sridharan T.E. Fuja D.J. Costello Jr. 2004 LDPC Block and Convolutional Codes Based on Circulant Matrices IEEE Trans. Inform. Theory 50 12 2966 2984 10.1109/TIT.2004.838370 2103477
7. M.P.C. Fossorier 2004 Quasi-cyclic Low-Density Parity-Check Codes from Circulant Permutation Matrices IEEE Trans. Inform. Theory 50 8 1788 1793 10.1109/TIT.2004.831841 2096847
8. R.M. Tanner 1981 A Recursive Approach to Low Complexity Codes IEEE Trans. Inform. Theory 27 5 533 547 0474.94029 10.1109/TIT.1981.1056404 650686
9. Malema, G. and Liebelt, M., High Girth Column-Weight-Two LDPC Codes Based on Distance Graphs, EURASIP J. Wireless Commun. Networking, 2007, no. 1, Art. ID 48158, 5 pp.
10. Malema, G. and Liebelt, M., Quasi-cyclic LDPC Codes of Column-Weight Two Using a Search Algorithm, EURASIP J. Adv. Signal Process., 2007, no. 4, Art. ID 45768, 8 pp.
11. H. Zhang J. Moura 2003 The Design of Structured Regular LDPC Codes with Large Girth Proc. IEEE 2003 Global Telecommunications Conf. (GLOBECOM'03), San Francisco, USA 7 4022 4027
12. Bocharova, I.E., Kudryashov, B.D., Johannesson, R., and Zyablov, V.V., Asymptotically Good Woven Codes with Fixed Constituent Convolutional Codes, in Proc. 2007 IEEE Int. Sympos. on Information Theory (ISIT'2007), Nice, France, 2007, pp. 2326-2330.
13. Hu, X.-Y., Fossorier, M.P.C., and Eleftheriou, E., On the Computation of the Minimum Distance of Low- Density Parity-Check Codes, in Proc. IEEE Int. Conf. on Communications (ICC'04), Paris, France, 2004, vol. 2, pp. 767-771.
14. G. Solomon H.C.A. van Tilborg 1979 A Connection Between Block and Convolutional Codes SIAM J. Appl. Math. 37 2 358 369 0415.94008 10.1137/0137027 543955
15. H. Ma J. Wolf 1986 On Tail Biting Convolutional Codes IEEE Trans. Commun. 34 2 104 111 0586.94020 10.1109/TCOM.1986.1096498
16. Biggs, N., Constructions for Cubic Graphs with Large Girth, Electron. J. Combin., 1998, vol. 5,Art. A1, 25 pp.
17. Exoo, G. and Jajcay, R., Dynamic Cage Survey, Electron. J. Combin., 2008, vol. 15, Dynamic Survey DS16, 48 pp.
18. Lentmaier, M., Fettweis, G.P., Zigangirov, K.Sh., and Costello, D.J., Jr., Convolutional Codes for Iterative Decoding, in Proc. IEEE 10th Int. Sympos. on Spread Spectrum Techniques and Applications (ISSSTA'08), Bologna, Italy, 2008, pp. 785-789.
19. Pusane, A.E., Smarandache, R., Vontobel, P.O., and Costello, D.J., Jr., On Deriving Good LDPC Convolutional Codes from QC LDPC Block Codes, in Proc. 2007 IEEE Int. Sympos. on Information Theory (ISIT'2007), Nice, France, 2007, pp. 1221-1225.
20. Exoo, G., Voltage Graphs, Group Presentations and Cages, Electron. J. Combin., 2004, vol. 11, no. 1, Art. N2, 7 pp.
21. MacKay, D.J.C. and Davey, M.C., Evaluation of Gallager Codes for Short Block Length and High Rate Applications, Codes, Systems and Graphical Models (Proc. IMA Workshop, Minneapolis, USA, 1999, Marcus, B. and Rosenthal, J., Eds., IMA Vols. Math. Appl., vol. 123, New York: Springer, 2001, pp. 113-130.
22. V.K. Wei 1991 Generalized Hamming Weights for Linear Codes IEEE Trans. Inform. Theory 37 5 1412 1418 0735.94008 10.1109/18.133259 1136673 (Pubitemid 21704767)
23. S. Kim J.-S. No H. Chung D.-J. Shin 2007 Quasi-cyclic Low-Density Parity-Check Codes with Girth Larger than 12 IEEE Trans. Inform. Theory 53 8 2885 2891 10.1109/TIT.2007.901171 2400586 (Pubitemid 47249844)
24. Hall, M., Jr., Combinatorial Theory, Waltham: Blaisdell, 1967. Translated under the title Kombinatorika, Moscow: Mir, 1970.
25. G.A. Margulis 1982 Explicit Constructions of Graphs without Short Cycles and Low Density Codes Combinatorica 2 1 71 78 0492.05044 10.1007/BF02579283 671147
26. Lazebnik, F., Ustimenko, V.A., and Woldar, A.J., New Upper Bounds on the Order of Cages, Electron. J. Combin., 1997, vol. 4, no. 2, Art. R13, 11 pp.
27. A. Lubotzky R. Phillips P. Sarnak 1988 Ramanujan Graphs Combinatorica 8 3 261 277 0661.05035 10.1007/BF02126799 963118