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Volumn 50, Issue 12, 2004, Pages 2935-2965

The dynamics of group codes: Dual abelian group codes and systems

Author keywords

Behavioral systems; Controllability; Duality; Group codes; Group systems; Linear systems; Observability

Indexed keywords

CONTROLLABILITY; LINEAR SYSTEMS; MATRIX ALGEBRA; OBSERVABILITY; STATE SPACE METHODS;

EID: 10644220416     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.838340     Document Type: Article
Times cited : (24)

References (50)
  • 4
    • 0026237598 scopus 로고
    • "Controllability and observability indices for linear time-invariant systems: A new approach"
    • F. Fagnani, "Controllability and observability indices for linear time-invariant systems: A new approach," Syst. Contr. Lett., vol. 17, pp. 243-250, 1991.
    • (1991) Syst. Contr. Lett. , vol.17 , pp. 243-250
    • Fagnani, F.1
  • 5
    • 0030544185 scopus 로고    scopus 로고
    • "Some results on the classification of expansive automorphisms of compact abelian groups"
    • F. Fagnani, "Some results on the classification of expansive automorphisms of compact abelian groups," Ergod. Theory Dyn. Syst. vol. 16, pp. 45-50, 1996.
    • (1996) Ergod. Theory Dyn. Syst. , vol.16 , pp. 45-50
    • Fagnani, F.1
  • 6
    • 0031562875 scopus 로고    scopus 로고
    • "Shifts on compact and discrete Lie groups: Algebraic-topological invariants and classification problems"
    • F. Fagnani, "Shifts on compact and discrete Lie groups: Algebraic-topological invariants and classification problems," Adv. Math., vol. 127, pp. 283-306, 1997.
    • (1997) Adv. Math. , vol.127 , pp. 283-306
    • Fagnani, F.1
  • 8
    • 0030284120 scopus 로고    scopus 로고
    • "Dynamical systems and convolutional codes over finite abelian groups"
    • Nov
    • F. Fagnani and S. Zampieri, "Dynamical systems and convolutional codes over finite abelian groups," IEEE Trans. Inform. Theory, vol. 42, pp. 1892-1912, Nov. 1996.
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 1892-1912
    • Fagnani, F.1    Zampieri, S.2
  • 9
    • 21744458666 scopus 로고    scopus 로고
    • "Classification problems for shifts on modules over a principal ideal domain
    • F. Fagnani and S. Zampieri, "Classification problems for shifts on modules over a principal ideal domain,, Trans. AMS, vol. 349, pp. 1993-2006, 1997.
    • (1997) Trans. AMS , vol.349 , pp. 1993-2006
    • Fagnani, F.1    Zampieri, S.2
  • 10
    • 0032679719 scopus 로고    scopus 로고
    • "Minimal syndrome formers for group codes"
    • Jan
    • F. Fagnani and Zampieri, "Minimal syndrome formers for group codes," IEEE Trans. Inform. Theory, vol. 45, pp. 3-31, Jan. 1999.
    • (1999) IEEE Trans. Inform. Theory , vol.45 , pp. 3-31
    • Fagnani, F.1    Zampieri, S.2
  • 11
    • 0028462695 scopus 로고
    • "Algebraic aspects of 2D convolutional codes"
    • July
    • E. Fornasini and M. E. Valcher, "Algebraic aspects of 2D convolutional codes," IEEE Trans. Inform. Theory, vol. 40, pp. 1068-1082, July 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1068-1082
    • Fornasini, E.1    Valcher, M.E.2
  • 12
    • 0032026017 scopus 로고    scopus 로고
    • "Multidimensional systems with finite support behaviors: Signal structure, generation and detection"
    • E. Fornasini and M. E. Valcher, "Multidimensional systems with finite support behaviors: Signal structure, generation and detection," SIAM J. Contr. Opt., vol. 36, pp. 760-779, 1998.
    • (1998) SIAM J. Contr. Opt. , vol.36 , pp. 760-779
    • Fornasini, E.1    Valcher, M.E.2
  • 13
    • 0015650723 scopus 로고
    • "Structural analysis of convolutional codes via dual codes"
    • July
    • G. D. Forney, Jr., "Structural analysis of convolutional codes via dual codes," IEEE Trans. Inform. Theory, vol. IT-19, pp. 512-518, July 1973.
    • (1973) IEEE Trans. Inform. Theory , vol.IT-19 , pp. 512-518
    • Forney Jr., G.D.1
  • 14
    • 0035246123 scopus 로고    scopus 로고
    • "Codes on graphs: Normal realizations"
    • Feb
    • G. D. Forney, Jr., "Codes on graphs: Normal realizations," IEEE Trans. Inform. Theory, vol. 47, pp. 520-548, Feb. 2001.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 520-548
    • Forney Jr., G.D.1
  • 15
    • 0027668052 scopus 로고
    • "The dynamics of group codes: State spaces, trellis diagrams and canonical encoders"
    • Sept
    • 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, Sept. 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1491-1513
    • Forney Jr., G.D.1    Trott, M.D.2
  • 16
    • 0027210212 scopus 로고
    • "The dynamics of group codes: Syndromes, normal codes and observers"
    • San Antonio, TX, Jan
    • G. D. Forney, Jr. and M. D. Trott, "The dynamics of group codes: Syndromes, normal codes and observers," in Proc. 1993 Intl. Symp. Information Theory, San Antonio, TX, Jan. 1993, p. 177.
    • (1993) Proc. 1993 Intl. Symp. Information Theory , pp. 177
    • Forney Jr., G.D.1    Trott, M.D.2
  • 18
    • 0029514297 scopus 로고
    • "Controllability, observability and duality in behavioral group systems"
    • New Orleans, LA, Dec
    • G. D. Forney, Jr. and M. D. Trott, "Controllability, observability and duality in behavioral group systems," in Proc. 34th Conf. Decision and Control, vol. 3, New Orleans, LA, Dec. 1995, pp. 3259-3264.
    • (1995) Proc. 34th Conf. Decision and Control , vol.3 , pp. 3259-3264
    • Forney Jr., G.D.1    Trott, M.D.2
  • 19
    • 0000364847 scopus 로고
    • "Multilingual dictionary: System theory, coding theory, symbolic dynamics and automata theory"
    • G. D. Forney, Jr., B. Marcus, N. T. Sindhushayana, and M. D. Trott, "Multilingual dictionary: System theory, coding theory, symbolic dynamics and automata theory," in Proc. Symp. Applied Mathematics vol. 50, 1995, pp. 109-137.
    • (1995) Proc. Symp. Applied Mathematics , vol.50 , pp. 109-137
    • Forney Jr., G.D.1    Marcus, B.2    Sindhushayana, N.T.3    Trott, M.D.4
  • 21
    • 0003792312 scopus 로고
    • Englewood Cliffs, NJ: Prentice-Hall
    • T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
    • (1980) Linear Systems
    • Kailath, T.1
  • 22
    • 0000142226 scopus 로고
    • "Extension of the Pontrjagin duality I: Infinite products"
    • S. Kaplan, "Extension of the Pontrjagin duality I: Infinite products," Duke Math. J., vol. 15, pp. 649-658, 1948.
    • (1948) Duke Math. J. , vol.15 , pp. 649-658
    • Kaplan, S.1
  • 23
    • 84974289002 scopus 로고
    • "Expansive dynamics on zero-dimensional groups"
    • B. Kitchens, "Expansive dynamics on zero-dimensional groups," Ergod. Theory Dyn. Syst., vol. 7, pp. 249-261, 1987.
    • (1987) Ergod. Theory Dyn. Syst. , vol.7 , pp. 249-261
    • Kitchens, B.1
  • 24
  • 30
    • 0011004784 scopus 로고
    • "The breakdown of automorphisms of compact topological groups"
    • New York: Academic, Adv. Math. Suppl. Stud
    • G. Miles and R. K. Thomas, "The breakdown of automorphisms of compact topological groups," in Studies in Probability and Ergodic Theory New York: Academic, 1978, vol. 2, Adv. Math. Suppl. Stud., pp. 207-218.
    • (1978) Studies in Probability and Ergodic Theory , vol.2 , pp. 207-218
    • Miles, G.1    Thomas, R.K.2
  • 32
    • 4244091951 scopus 로고    scopus 로고
    • "Matroids representable over modules, electrical network topology and behavioral systems theory"
    • Indian Inst. Technol.-Bombay, Elec. Eng. Dept. Res. Rep
    • H. Narayanan, "Matroids representable over modules, electrical network topology and behavioral systems theory," Indian Inst. Technol.-Bombay, Elec. Eng. Dept. Res. Rep., 2000.
    • (2000)
    • Narayanan, H.1
  • 33
    • 0007689276 scopus 로고    scopus 로고
    • "On the duality between controllability and observability in behavioral systems theory"
    • Bangalore, July
    • H. Narayanan, "On the duality between controllability and observability in behavioral systems theory," in Proc. CCSP 2000, Bangalore, July 2000, pp. 183-186.
    • (2000) Proc. CCSP 2000 , pp. 183-186
    • Narayanan, H.1
  • 34
    • 0000067766 scopus 로고
    • "k-groups and duality"
    • Oct
    • N. Noble, "k-groups and duality," Trans. AMS, vol. 151, pp. 551-561, Oct. 1970.
    • (1970) Trans. AMS , vol.151 , pp. 551-561
    • Noble, N.1
  • 35
    • 0004160647 scopus 로고
    • Princeton, NJ: Princeton Univ. Press
    • L. Pontryagin, Topological Groups. Princeton, NJ: Princeton Univ. Press, 1946.
    • (1946) Topological Groups
    • Pontryagin, L.1
  • 36
    • 0026135748 scopus 로고
    • "Controllability of 2D systems"
    • Apr
    • P. Rocha and J. C. Willems, "Controllability of 2D systems," IEEE Trans. Automat. Contr., vol. 36, pp. 413-423, Apr. 1991.
    • (1991) IEEE Trans. Automat. Contr. , vol.36 , pp. 413-423
    • Rocha, P.1    Willems, J.C.2
  • 40
    • 0003391815 scopus 로고
    • Boston, MA: Allyn and Bacon, Translated by S. Moran
    • H. Schubert, Topology. Boston, MA: Allyn and Bacon, 1968. Translated by S. Moran.
    • (1968) Topology
    • Schubert, H.1
  • 41
    • 0001240275 scopus 로고
    • "Automorphisms of compact abelian groups and affine varieties"
    • K. Schmidt, "Automorphisms of compact abelian groups and affine varieties," in Proc. London Math. Soc., vol. 61, 1990, pp. 480-496.
    • (1990) Proc. London Math. Soc. , vol.61 , pp. 480-496
    • Schmidt, K.1
  • 42
    • 0001307640 scopus 로고    scopus 로고
    • "A truly behavioral approach to the H∞ control problem"
    • J. W. Polderman and H. Trentelman, Eds. Groningen, The Netherlands: Univ. Groningen Press
    • H. Trentelman, "A truly behavioral approach to the H∞ control problem," in The Mathematics of Systems and Control: From Intelligent Control to Behavioral Systems, J. W. Polderman and H. Trentelman, Eds. Groningen, The Netherlands: Univ. Groningen Press, 1999, pp. 177-190.
    • (1999) The Mathematics of Systems and Control: From Intelligent Control to Behavioral Systems , pp. 177-190
    • Trentelman, H.1
  • 43
    • 0011009018 scopus 로고
    • "The algebraic structure of trellis codes"
    • Ph.D. dissertation, Stanford Univ., Dept. Elec. Eng., Stanford, CA
    • M. D. Trott, "The algebraic structure of trellis codes," Ph.D. dissertation, Stanford Univ., Dept. Elec. Eng., Stanford, CA, 1992.
    • (1992)
    • Trott, M.D.1
  • 44
    • 0028465405 scopus 로고
    • "On 2D finite-support convolutional codes: An algebraic approach"
    • M. E. Valcher and E. Fornasini, "On 2D finite-support convolutional codes: An algebraic approach," Multid. Syst. Sig. Proc., vol. 5, pp. 231-243, 1994.
    • (1994) Multid. Syst. Sig. Proc. , vol.5 , pp. 231-243
    • Valcher, M.E.1    Fornasini, E.2
  • 45
    • 0039069271 scopus 로고
    • "A characterization of Pontryagin duality"
    • R. Venkataraman, "A characterization of Pontryagin duality," Math. Z., vol. 149, pp. 109-119, 1976.
    • (1976) Math. Z. , vol.149 , pp. 109-119
    • Venkataraman, R.1
  • 46
    • 0022775849 scopus 로고
    • "From time series to linear systems, Parts I-III"
    • J. C. Willems, "From time series to linear systems, Parts I-III," Automatica, vol. 22, pp. 561-580, 1986.
    • (1986) Automatica , vol.22 , pp. 561-580
    • Willems, J.C.1
  • 47
    • 0000695559 scopus 로고
    • "Models for dynamics"
    • J. C. Willems, "Models for dynamics," Dynamics Reported, vol. 2, pp. 171-269, 1989.
    • (1989) Dynamics Reported , vol.2 , pp. 171-269
    • Willems, J.C.1
  • 48
    • 0026119885 scopus 로고
    • "Paradigms and puzzles in the theory of dynamical systems"
    • Mar
    • J. C. Willems, "Paradigms and puzzles in the theory of dynamical systems," IEEE Trans. Automat. Contr., vol. 36, pp. 259-294, Mar. 1991.
    • (1991) IEEE Trans. Automat. Contr. , vol.36 , pp. 259-294
    • Willems, J.C.1
  • 49
    • 0031100338 scopus 로고    scopus 로고
    • "On interconnections, control and feedback"
    • Mar
    • J. C. Willems, "On interconnections, control and feedback," IEEE Trans. Automat. Contr., vol. 42, pp. 326-339, Mar. 1997.
    • (1997) IEEE Trans. Automat. Contr. , vol.42 , pp. 326-339
    • Willems, J.C.1
  • 50
    • 0029736005 scopus 로고    scopus 로고
    • "Linear systems over Noetherian rings in the behavioral approach"
    • S. Zampieri and S. Mitter, "Linear systems over Noetherian rings in the behavioral approach," J. Math. Syst. Estim. Contr., vol. 6, pp. 235-238, 1996.
    • (1996) J. Math. Syst. Estim. Contr. , vol.6 , pp. 235-238
    • Zampieri, S.1    Mitter, S.2


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