Minimal syndrome formers for group codes

IEEE Transactions on Information Theory

Volumn 45, Issue 1, 1999, Pages 3-31

  Fagnani, Fabio ^a,b   Zampieri, Sandro ^a,b  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Behavioral approach; Convolutional codes over groups; Dynamical systems; Encoders; Inverters; Observability granules; Observer form realization; State space representations; Syndrome formers; Systems over groups

Indexed keywords

CONVOLUTIONAL CODES; DYNAMICS; ENCODING (SYMBOLS); INFORMATION THEORY; OBSERVABILITY; STATE SPACE METHODS;

GROUP CODES;

CODES (SYMBOLS);

EID: 0032679719     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.746769     Document Type: Article

References (24)

1. J. L. Massey and M. Sain, "Codes, automata, and continuous systems: Explicit interconnections," IEEE Trans. Automat. Contr., vol. AC-12, pp. 644-650, 1967.
2. "Inverses of linear sequential circuits," IEEE Trans. Comput., vol. C-17, pp. 330-337, 1968.
3. G. D. Forney, Jr., "Convolutional codes I: Algebraic structure," IEEE Trans. Inform. Theory, vol. IT16, pp. 720-738, 1970.
4. "Structural analysis of convolutional codes via dual codes," IEEE Trans. Inform. Theory, vol. IT19, pp. 512-518, 1973.
5. 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.
6. H.-A. Loeliger and T. Mittelholzer, "Convolutional codes over groups," IEEE Trans. Inform. Theory, vol. 42, pp. 1660-1686, 1996.
7. J. Rosenthal, J. Schumacher, and E. York, "Convolutional codes over groups," IEEE Trans. Inform. Theory, vol. 42, pp. 1881-1891, 1996.
8. J. C. Willems, "Models for dynamics," Dynamics Reported, vol. 2, pp. 171-269, 1988.
9. G. Ungerboeck, "Channel coding with multilevel phase signals," IEEE Trans. Inform. Theory, vol. IT25, pp. 55-67, 1982.
10. G. D. Forney, Jr., "Geometrically uniform codes," IEEE Trans. Inform. Theory, vol. 37, pp. 1241-1260, 1991.
11. H. Loeliger, G. D. Forney, Jr., T. Mittelholzer, and M. D. Trott, "Minimality and observability of group systems," Linear Alg. itsApplic., vol. 205-206, pp. 937-963, 1994.
12. A. Vardy and F. R. Kschischang, "Proof of a conjecture of McEliace regarding the expansion index of the minimal trellis," IEEE Trans. Inform. Theory, vol. 42, pp. 2027-2033, 1996.
13. G. D. Forney, Jr., and M. D. Trott, "The dynamics of group codes: dual group codes and systems," unpublished manuscript, 1994.
14. "Controllability, observability, and duality in behavioral group systems," in Proc. IEEE Conf. Decision and Control (New Orleans, LA, 1995), pp. 3259-3264.
15. F. Fagnani and S. Zampieri, "Dynamical systems and convolutional codes over finite Abelian groups," IEEE Trans. Inform. Theory, vol. 42, pp. 1892-1912, 1996.
16. J. C. Willems, "Minimal realization in state space form from input/output data," NATO Summer School, Toulose, France, 1972.
17. M. Arbib, "Decomposition theory for automata and biological systems," in System Structure, A. Morse, Ed. New York: IEEE Contr. Syst. Soc., 1971, pp. 1-56.
18. R. Kaiman, P. Falb, and M. Arbib, Topics in Mathematical System Theory. New York: McGraw-Hill, 1969.
19. D. Lind and B. Marcus, Symbolic Dynamics and Coding. Cambridge, U.K.: Cambridge Univ. Press, 1995.
20. G. D. Forney, Jr., B. Marcus, N. Sindhushayana, and M. D. Trott, "Multilingual dictionary: System theory, coding theory, symbolic dynamics and automata theory," in Proc. Symp. Applied Mathematics, 1995, vol. 50, pp. 109-137
21. F. Fagnani, "Some results on the classification of expansive automor-phisms of compact Abelian groups," Ergodic Theory Dyn. Syst., vol. 16, pp. 45-50, 1996
22. B. Kitchens, "Expansive dynamics on zero-dimensional groups," Er-godic Theory Dyn. Syst., vol. 7, pp. 249-261, 1987.
23. B. Kitchens and K. Schmidt, "Automorphisms of compact groups," Ergodic Theory Dyn. Syst., vol. 9, pp. 691-735, 1989.
24. N. Sindhushayana, B. Marcus, and M. D. Trott, "Homogeneous shifts," IM A J. Math. Contr. Inform., vol. 14, pp. 255-287, 1997.