Distance bounds for an ensemble of LDPC convolutional codes

IEEE Transactions on Information Theory

Volumn 53, Issue 12, 2007, Pages 4537-4555

  Sridharan, Arvind ^a,b   Truhachev, Dmitri ^c   Lentmaier, Michael ^a,d   Costello Jr , Daniel J ^a   Zigangirov, Kamil Sh ^a,e  

^a University of Notre Dame   (United States)

^b SEAGATE TECHNOLOGY   (United States)

^c UNIVERSITY OF ALBERTA   (Canada)

^d GERMAN AEROSPACE CENTER DLR   (Germany)

^e INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS   (Russian Federation)

Author keywords

Free distance lower bounds; LDPC convolutional codes; Low density parity check (LDPC) codes; Minimum distance lower bounds

Indexed keywords

BLOCK LENGTHS; CODE SEGMENTS; CONSTRAINT LENGTHS; DISTANCE BOUNDS; FINITE LENGTHS; FREE DISTANCE LOWER BOUNDS; LDPC CONVOLUTIONAL CODES; LOW DENSITY PARITY CHECKS; LOW-DENSITY PARITY-CHECK (LDPC) CODES; MINIMUM DISTANCES; MINIMUM-DISTANCE LOWER BOUNDS;

BLOCK CODES; CONTROL THEORY; CONVOLUTION; TURBO CODES;

CONVOLUTIONAL CODES;

EID: 49049101282     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2007.909113     Document Type: Article

References (19)

1. R. G. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963.
2. R. M. Tanner, "Error-Correcting Coding System," U.S. Patent 4,295,218, 1981.
3. A. J. Feltström and K. Sh. Zigangirov, "Time-varying periodic convolutional codes with low-density parity-check matrix," IEEE Trans. Inf. Theory, vol. 45, no. 6, pp. 2181-2190, Sep. 1999.
4. K. Engdahl and K. Sh. Zigangirov, "On the theory of low density convolutional codes I," Probl. Inf. Transm. (Probl. Pered. Inform.) vol. 35, no. 4, pp. 295-310, Oct./Dec. 1999.
5. R. M. Tanner, D. Sridhara, A. Sridharan, T. E. Fuja, and D. J. Costello, Jr, "LDPC block and convolutional codes based on circulant matrices," IEEE Trans. Inf. Theory, vol. 50, 12, pp. 2966-2984, Dec. 2004.
6. D. J. Costello, Jr, A. E. Pusane, S. Bates, and K. Sh. Zigangirov, "A comparison between LDPC block and convolutional codes," in Proc. Information Theory and Application Workshop, San Diego, CA, Feb. 2006.
7. S. Bates, Z. Chen, and X. Dong, "Low-density parity check convolutional codes for ethernet networks," in Proc. IEEE Pacific Rim Conf. Communications, Computers and Signal Processing, Victoria, BC, Canada, Aug. 2005, pp. 85-88.
8. A. E. Pusane, A. J. Feltström, A. Sridharan, M. Lentmaier, K. Sh. Zigangirov, and D. J. Costello, Jr, "Implementation aspects of LDPC convolutional codes," IEEE Trans. Commun., to be published.
9. A. Sridharan, M. Lentmaier, D. J. Costello, Jr, and K. Sh. Zigangirov, "Convergence analysis of a class of LDPC convolutional codes for the erasure channel," in Proc. 42nd Allerton Conf. Communication, Control, and Computing, Monticello, IL, Oct. 2004, pp. 953-962.
10. M. Lentmaier, A. Sridharan, D. J. Costello, Jr, and K. Sh. Zigangirov, "Terminated LDPC convolutional codes with thresholds close to capacity," in Proc. IEEE Intl. Sympo. Information Theory, Adelaide, Australia, Sep. 2005, pp. 1372-1376.
11. D. J. C. MacKay and M. C. Davey, "Evaluation of Gallager codes for short block length and high rate applications," in Codes, Systems and Graphical Model, B. Marcus and J. Rosenthal, Eds. New York: Springer-Verlag, 2001, vol. 123, IMA Volumes in Mathematics and its Applications, ch. 5, pp. 113-130.
12. A. Sridharan, M. Lentmaier, D. V. Truhachev, D. J. Costello, Jr, and K. Sh. Zigangirov, "On the minimum distance of low-density parity-check codes with parity-check matrices constructed from permutation matrices," Probl. Inf. Transm. (Probl. Pered. Inform.), vol. 41, no. 1, pp. 33-44, 2005.
13. E. N. Gilbert, "A comparison of signalling alphabets," Bell Syst. Tech. J., vol. 31, pp. 504-522, 1952.
14. R. R. Varsharmov, "Estimates of the number of signals in error correcting codes," Doklady Akad. Nauk S.S.R, vol. 117, no. 5, pp. 739-741, 1957.
15. D. J. Costello, Jr, "Free distance bounds for convolutional codes," IEEE Trans. Inf. Theory, vol. IT-20, no. 3, pp. 356-365, May 1974.
16. K. Engdahl, M. Lentmaier, and K. Sh. Zigangirov, "On the theory of low-density convolutional codes," in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 13th International Symposium, AAECC-13 (Lecture Notes in Computer Science), M. P. C. Fossorier, H. Imai, S. Lin, and A. Poli, Eds. Berlin, Germany: Springer-Verlag, Nov. 1999, vol. 1719, pp. 77-86.
17. R. Johannesson and K. Sh. Zigangirov, Fundamentals of Convolutional Coding. Piscataway, NJ: IEEE Press, 1999.
18. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics. Reading, MA: Addison-Wesley, 1989.
19. R. M. Fano, Transmission of Information, A Statistical Theory of Communications. New York: MIT Press/Wiley, 1961.