Some structural properties of convolutional codes over rings

IEEE Transactions on Information Theory

Volumn 44, Issue 2, 1998, Pages 839-845

  Johannesson, Rolf ^a   Wan, Zhe Xian ^a   Wittenmark, Emma ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

Convolutional codes over rings; Direct sum decomposition of rings; Proper convolutional codes; Systematic convolutional codes

Indexed keywords

ENCODING (SYMBOLS); EQUIVALENCE CLASSES; INVERSE PROBLEMS; MATRIX ALGEBRA; PHASE MODULATION; POLYNOMIALS; TRANSDUCERS; TRANSFER FUNCTIONS;

GENERATOR MATRICES; RING CODES;

CONVOLUTIONAL CODES;

EID: 0032023713     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.661532     Document Type: Article

References (19)

1. J. L. Massey and T. Mittelholzer, "Convolutional codes over rings," in Proc. 4th Joint Swedish-Soviet Int. Workshop Information Theory (Gotland, Sweden, Aug. 27-Sept. 1, 1989), pp. 14-18.
2. _, "Systematicity and rotational invariance of convolutional codes over rings," in Proc. 2nd Int. Workshop Algebraic and Combinatorial Coding Theory (Leningrad, USSR, Sept. 16-22, 1990), pp. 154-158.
3. T. Mittelholzer, "Minimal encoders for convolutional codes over rings," in Communications Theory and Applications. HW Comm. Ltd., 1993, pp. 30-36.
4. G. D. Forney, Jr., "Convolutional codes I: Algebraic structure," IEEE Trans. Inform. Theory, vol. IT-16, pp. 720-738, 1970.
5. R. Johannesson and Z.-x. Wan, "A linear algebra approach to minimal convolutional encoders," IEEE Trans. Inform. Theory, vol. 39, pp. 1219-1233, 1993.
6. J. L. Massey, "Coding theory," in Handbook of Applied Mathematics, W. Ledermann, Ed., vol. V, pt. B, Combinatorics and Geometry, W. Ledermann and S. Vajda, Eds. Chichester and New York: Wiley, 1985, ch. 16.
7. T. Mittelholzer, "Convolutional codes over rings and the two chain conditions," in Proc. IEEE Int. Symp. Information Theory (Ulm, Germany, June 29-July 4, 1997), p. 285.
8. H.-A. Loeliger, G. D. Forney, Jr., T. Mittelholzer, and M. D. Trott, "Minimality and observability of group systems," Linear Algebra and Its Applications, vol. 205-206, pp. 937-963, July 1994.
9. G. D. Forney Jr., private communication, Aug. 21, 1997.
10. G. D. Forney, Jr., and M. D. Trott, "The dynamics of group codes: State spaces, trellis diagrams and canonical encoders," IEEE Trans. Inform. Theory, vol. 39, pp. 1491-1513, 1993.
11. E. Wittenmark and Z.-x. Wan, "Convolutional codes from a dynamical system point of view," in Proc. 1994 IEEE Int. Symp. Information Theory (Trondheim, Norway, June 27-July 1, 1994), p. 160.
12. C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes (1)," in Proc., IEEE Int. Conf. Communications (Geneva, Switzerland, May 1993), pp. 1064-1070.
13. H. Osthoff, J. B. Anderson, R. Johannesson, and C.-f. Lin, "Systematic feed-forward convolutional encoders are better than other encoders with an M-algorithm decoder," this issue, pp. 831-838.
14. I. Ingemarsson, "Commutative group codes for the Gaussian channel," IEEE Trans. Inform. Theory, vol. IT-19, pp. 215-219, 1973.
15. C.-J. Chen, T.-Y. Chen and H.-A. Loeliger, "Construction of linear ring codes for 6-PSK," IEEE Trans. Inform. Theory, vol. 40, pp. 563-566, 1994.
16. G. Caire and E. Biglieri, "Linear block codes over cyclic groups," IEEE Trans. Inform. Theory, vol. 41, pp. 1246-1256, 1995.
17. H.-A. Loeliger and T. Mittelholzer, "Convolutional codes over groups," IEEE Trans. Inform. Theory, vol. 42, pp. 1660-1686, 1996.
18. V. V. Vazirani, H. Saran, and B. S. Rajan, "An efficient algorithm for constructing minimal trellises for codes over finite Abelian groups," IEEE Trans. Inform. Theory, vol. 42, pp. 1839-1854, 1996.
19. F. Fagnini and S. Zampieri, "Dynamical systems and convolutional codes over finite abelian groups," IEEE Trans. Inform. Theory, vol. 42, pp. 1892-1912, 1996.