BCH convolutional codes

IEEE Transactions on Information Theory

Volumn 45, Issue 6, 1999, Pages 1833-1844

  Rosenthal, Joachim ^a   York, Eric V ^b,c  

^a EPFL   (Switzerland)

^b UNIVERSITY OF NOTRE DAME   (United States)

^c NATIONAL SECURITY AGENCY   (United States)

Author keywords

Bch codes; Convolutional codes; Cyclotomic sets; Linear systems

Indexed keywords

BLOCK CODES; ERROR CORRECTION; LINEAR SYSTEMS; MATRIX ALGEBRA; SET THEORY; SYSTEM THEORY;

BOSE-CHAUDHURI-HOCQUENGHEM CONVOLUTIONAL CODES; CYCLOTOMIC SETS;

CONVOLUTIONAL CODES;

EID: 0033184598     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.782104     Document Type: Article

References (27)

1. M. Esmaeili, T. A. Gulliver, N. P. Secord, and S. A. Mahmoud, "A link between quasicyclic codes and convolutional codes," IEEE Trans. Inform. Theory, vol. 44, pp. 431-435, Jan. 1998.
2. G. D. Forney, Jr., "Convolutional codes I: Algebraic structure," IEEE Trans. Inform. Theory, vol. IT16, pp. 720-738, Sept. 1970.
3. "Minimal bases of rational vector spaces, with applications to multivariable linear systems," SIAM J. Contr. Optim., vol. 13, no. 3, pp. 493-520, 1975.
4. T. W. Hungerford, Algebra. New York: Springer, 1980.
5. R. Johannesson and Z. Wan, "A linear algebra approach to minimal convolutional encoders," IEEE Trans. Inform. Theory, vol. 39, pp. 1219-1233, July 1993.
6. R. Johannesson and K. Sh. Zigangirov, Fundamentals of Convolutional Coding. New York: IEEE Press, 1999.
7. J. Justesen, "New convolutional code constructions and a class of asymptotically good time-varying codes," IEEE Trans. Inform. Theory, vol. IT19, pp. 220-225, Mar. 1973.
8. "An algebraic construction of rate 1/v convolutional codes," IEEE Trans. Inform. Theory, vol. IT21, pp. 577-580, Jan. 1975.
9. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
10. R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications. Cambridge, London, U.K.: Cambridge Univ. Press, 1994, revised edition.
11. S. Lin and D. Costello, Error Control Coding: Fundamentals and Applications. Englewood Cliffs, NJ, Prentice-Hall, 1983.
12. F. J. Mac Williams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1977.
13. J. L. Massey, D. J. Costello, and J. Justesen, "Polynomial weights and code constructions," IEEE Trans. Inform. Theory, vol. IT19, pp. 101-110, Jan. 1973.
14. J. L. Massey and M. K. Sain, "Codes, automata, and continuous systems: Explicit interconnections," IEEE Trans. Automat. Contr., vol. AC12, no. 6, pp. 644-650, 1967.
15. R. J. McEliece, "The algebraic theory of convolutional codes," in Handbook of Coding Theory, R. Brualdi, W. C. Huffman, and V. Pless, Eds. Amsterdam, The Netherlands: Elsevier, 1998.
16. H. F. Münzner and D. Prätzel-Wolters, "Minimal bases of polynomial modules, structural indices and Brunovsky-transformations," Int. J. Contr., vol. 30, pp. 291-318, 1979.
17. Ph. Piret, Convolutional Codes, an Algebraic Approach. Cambridge, MA: MIT Press, 1988.
18. "A convolutional equivalent to Reed-Solomon codes," Philips J. Res., vol. 43, no. 3-4, pp. 441-458, 1988.
19. V. M. Popov, "Invariant description of linear time-invariant controllable systems," SIAM J. Contr. Optim., vol. 10, pp. 252-264, 1972.
20. M. S. Ravi and J. Rosenthal, "A smooth compactification of the space of transfer functions with fixed McMillan degree," Acta Appl. Math, vol. 34, pp. 329-352, 1994.
21. J. Rosenthal, "An algebraic decoding algorithm for convolutional codes," in Dynamical Systems, Control, Coding, Computer Vision: New Trends, Interfaces, and Interplay, G. Picci and D. S. Gilliam, Eds. Boston-Basel-Berlin: Birkäuser, 1999, pp. 343-360.
22. J. Rosenthal and J. M. Schumacher, "Realization by inspection," IEEE Trans. Automat. Contr., vol. AC42, pp. 1257-1263, Sept. 1997.
23. J. Rosenthal, J. M. Schumacher, and E. V. York, "On behaviors and convolutional codes," IEEE Trans. Inform. Theory, vol. 42, pp. 1881-1891, Nov. 1996.
24. J. Rosenthal and R. Smarandache, "Construction of convolutional codes using methods from linear systems theory," in Proc. 35th Anna. Allerton Conf. Communication, Control, and Computing, 1997, pp. 953-960.
25. "A state space approach for constructing MDS rate 1/ra convolutional codes," in Proc. 1998 IEEE Information Theory Workshop on Information Theory (Killarney, Kerry, Ireland, June 1998), pp. 116-117.
26. R. M. Tanner, "Convolutional codes from quasicyclic codes: A link between the theories of block and convolutional codes," Computer Res. Lab., Tech. Rep., USC-CRL87-21, Nov. 1987.
27. E. V. York, "Algebraic description and construction of error correcting codes, a systems theory point of view," Ph.D. dissertation, Univ. Notre Dame, 1997. [Online]. Available WWW at: http://www.nd.edur rosen/preprints.html.