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Volumn 39, Issue 5, 1993, Pages 1491-1513

The Dynamics of Group Codes: State Spaces, Trellis Diagrams, and Canonical Encoders

Author keywords

codes over groups; group codes; group systems; Linear codes; linear systems; systems over groups

Indexed keywords

CODES (SYMBOLS); NUMERICAL ANALYSIS;

EID: 0027668052     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.259635     Document Type: Article
Times cited : (161)

References (36)
  • 1
    • 0000204470 scopus 로고
    • Codes, automata, and continuous systems: Explicit interconnections
    • Dec.
    • J. L. Massey and M. K. Sain, “Codes, automata, and continuous systems: Explicit interconnections,” IEEE Trans. Automat. Contr., vol. AC-12, pp. 644–650, Dec. 1967.
    • (1967) IEEE Trans. Automat. Contr , vol.AC-12 , pp. 644-650
    • Massey, J.L.1    Sain, M.K.2
  • 2
    • 84938011883 scopus 로고
    • Inverses of linear sequential circuits
    • Apr.
    • J.L. Massey and M.K. Sain, “Inverses of linear sequential circuits,” IEEE Trans. Comput., vol. C-17, pp. 330–337, Apr. 1968.
    • (1968) IEEE Trans. Comput. , vol.C-17 , pp. 330-337
    • Massey, J.L.1    Sain, M.K.2
  • 3
    • 0014869779 scopus 로고
    • Convolutional codes I: Algebraic structure
    • correction, vol. IT-17, p. 360, Nov. 1971
    • G. D. Forney, Jr., “Convolutional codes I: Algebraic structure,” IEEE Trans. Inform. Theory, vol. IT-16, pp. 720–738, 1970; correction, vol. IT-17, p. 360, Nov. 1971.
    • (1970) IEEE Trans. Inform. Theory , vol.IT-16 , pp. 720-738
    • Forney, G.D.1
  • 4
    • 0015650723 scopus 로고
    • Structural analysis of convolutional codes via dual codes
    • July
    • ——, “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, G.D.1
  • 5
    • 0016508669 scopus 로고
    • Minimal bases of rational vector spaces, with applications to multivariable linear systems
    • May
    • ——, “Minimal bases of rational vector spaces, with applications to multivariable linear systems,” SIAM J. Contr., vol. 13, pp. 493–520, May 1975.
    • (1975) SIAM J. Contr , vol.13 , pp. 493-520
    • Forney, G.D.1
  • 6
    • 0018544086 scopus 로고
    • On the structure of convolutional and cyclic convolutional codes
    • Nov.
    • C. Roos, “On the structure of convolutional and cyclic convolutional codes,” IEEE Trans. Inform. Theory, vol. IT-25, pp. 676–683, Nov. 1979.
    • (1979) IEEE Trans. Inform. Theory , vol.IT-25 , pp. 676-683
    • Roos, C.1
  • 8
    • 0041378659 scopus 로고
    • Algebraic structure of convolutional codes, and algebraic system theory
    • A. C. Antoulas, Ed. Berlin: Springer-Verlag
    • G. D. Forney, Jr., “Algebraic structure of convolutional codes, and algebraic system theory,” in Mathematical System Theory, A. C. Antoulas, Ed. Berlin: Springer-Verlag, 1991, pp. 527–557.
    • (1991) Mathematical System Theory , pp. 527-557
    • Forney, G.D.1
  • 9
    • 0017922440 scopus 로고
    • Efficient maximum likelihood decoding of linear block codes using a trellis
    • Jan.
    • J. K. Wolf, “Efficient maximum likelihood decoding of linear block codes using a trellis,” IEEE Trans. Inform. Theory, vol. IT-24, pp. 76–80, Jan. 1978.
    • (1978) IEEE Trans. Inform. Theory , vol.IT-24 , pp. 76-80
    • Wolf, J.K.1
  • 11
    • 84941860379 scopus 로고
    • Coset codes—Part II: Binary lattices and related codes
    • Sept.
    • G.D. Forney, Jr., “Coset codes—Part II: Binary lattices and related codes,” IEEE Trans. Inform. Theory, vol. 34, pp. 1152–1187, Sept. 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1152-1187
    • Forney, G.D.1
  • 12
    • 0027596646 scopus 로고
    • On complexity of trellis structure of linear block codes
    • T. Kasami, T. Takata, T. Fujiwara, and S. Lin, “On complexity of trellis structure of linear block codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 1057–1064, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1057-1064
    • Kasami, T.1    Takata, T.2    Fujiwara, T.3    Lin, S.4
  • 13
    • 80054814722 scopus 로고
    • Group codes for the Gaussian channel
    • D. Slepian, “Group codes for the Gaussian channel,” Bell Syst. Tech. J., vol. 47, pp. 575–602, 1968.
    • (1968) Bell Syst. Tech. J , vol.47 , pp. 575-602
    • Slepian, D.1
  • 14
    • 0023313295 scopus 로고
    • New trellis codes based on lattices and cosets
    • Jan.
    • A. R. Calderbank and N. J. A. Sloane, “New trellis codes based on lattices and cosets,” IEEE Trans. Inform. Theory, vol. IT-33, pp. 177–195, Jan. 1987.
    • (1987) IEEE Trans. Inform. Theory , vol.IT-33 , pp. 177-195
    • Calderbank, A.R.1    Sloane, N.J.A.2
  • 15
    • 84945713988 scopus 로고
    • Coset codes—Part I: Introduction and geometrical classification
    • Sept.
    • G.D. Forney, Jr., “Coset codes—Part I: Introduction and geometrical classification,” IEEE Trans. Inform. Theory, vol. 34, pp. 1123–1151, Sept. 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1123-1151
    • Forney, G.D.1
  • 16
    • 0026220377 scopus 로고
    • Geometrically uniform codes
    • Sept.
    • ——, “Geometrically uniform codes,” IEEE Trans. Inform. Theory, vol. 37, pp. 1241–1260, Sept. 1991.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1241-1260
    • Forney, G.D.1
  • 17
    • 0001043964 scopus 로고
    • Signal sets matched to groups
    • Nov.
    • H.-A. Loeliger, “Signal sets matched to groups,” IEEE Trans. Inform. Theory, vol. 37, pp. 1675–1682, Nov. 1991.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1675-1682
    • Loeliger, H.-A.1
  • 18
    • 0018708933 scopus 로고
    • System theoretic models for the analysis of physical systems
    • J.C. Willems, “System theoretic models for the analysis of physical systems,” Richerche di Automatica, vol. 10, pp. 71–106, 1979.
    • (1979) Richerche di Automatica , vol.10 , pp. 71-106
    • Willems, J.C.1
  • 19
    • 0022775849 scopus 로고
    • From time series to linear systems, Parts I, II, and III
    • vol. 23, pp. 87–115, 1987
    • ——, “From time series to linear systems, Parts I, II, and III,” Automatica, vol. 22, pp. 561–580 and 675–694, 1986; vol. 23, pp. 87–115, 1987.
    • (1986) Automatica , vol.22
    • Willems, J.C.1
  • 20
    • 0000695559 scopus 로고
    • Models for dynamics
    • U. Kirchgraber and H. O. Walther, Eds. New York: John Wiley
    • ——, “Models for dynamics,” in Dynamics Reported, vol. 2, U. Kirchgraber and H. O. Walther, Eds. New York: John Wiley, 1989.
    • (1989) Dynamics Reported , vol.2
    • Willems, J.C.1
  • 21
    • 0026119885 scopus 로고
    • Paradigms and puzzles in the theory of dynamical systems
    • Mar.
    • ——, “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
  • 22
    • 0015384639 scopus 로고
    • Finite group homomorphic sequential systems
    • R. W. Brockett and A. S. Willsky, “Finite group homomorphic sequential systems,” IEEE Trans. Automat. Contr., vol. AC-17, pp. 483–490, 1972.
    • (1972) IEEE Trans. Automat. Contr , vol.AC-17 , pp. 483-490
    • Brockett, R.W.1    Willsky, A.S.2
  • 23
    • 77957006878 scopus 로고
    • Algebraic systems, trellis codes, and rotational 'invariance
    • New York: Academic
    • H.J. Chizeck and M.D. Trott, “Algebraic systems, trellis codes, and rotational invariance,” in Advances in Electronics and Electron Physics. New York: Academic, 1990, vol. 79, pp. 1–71.
    • (1990) Advances in Electronics and Electron Physics , vol.79 , pp. 1-71
    • Chizeck, H.J.1    Trott, M.D.2
  • 24
    • 84974289002 scopus 로고
    • Expansive dynamics on zero-dimensional groups
    • B. P. Kitchens, “Expansive dynamics on zero-dimensional groups,” Ergodic Theory Dynam. Syst., vol. 7, pp. 249–261, 1987.
    • (1987) Ergodic Theory Dynam. Syst. , vol.7 , pp. 249-261
    • Kitchens, B.P.1
  • 26
    • 0039049186 scopus 로고
    • Convolutional codes over groups
    • submitted to IEEE Trans. Inform. Theory, Apr.
    • H.-A. Loeliger and T. Mittelholzer, “Convolutional codes over groups,” submitted to IEEE Trans. Inform. Theory, Apr. 1992.
    • (1992)
    • Loeliger, H.-A.1    Mittelholzer, T.2
  • 31
    • 84968519149 scopus 로고
    • A note on minimal covers for sofic systems
    • Nov.
    • M. Boyle, B. P. Kitchens and B. H. Marcus, “A note on minimal covers for sofic systems,” Proc. AMS, vol. 95, pp. 403–411, Nov. 1985.
    • (1985) Proc. AMS , vol.95 , pp. 403-411
    • Boyle, M.1    Kitchens, B.P.2    Marcus, B.H.3
  • 32
    • 0011009018 scopus 로고
    • The algebraic structure of trellis codes
    • Ph.D. dissertation, Dept, of Elect. Eng., Stanford Univ., Stanford CA, Aug.
    • M. D. Trott, “The algebraic structure of trellis codes,” Ph.D. dissertation, Dept, of Elect. Eng., Stanford Univ., Stanford CA, Aug. 1992.
    • (1992)
    • Trott, M.D.1
  • 34
    • 84941437145 scopus 로고
    • State spaces, trellis diagrams and minimal encoders for linear codes over groups
    • Budapest, Hungary, June
    • G.D. Forney, Jr. and M.D. Trott, “State spaces, trellis diagrams and minimal encoders for linear codes over groups,” in Proc. IEEE Int. Symp. Inform. Theory, Budapest, Hungary, June 24–28, 1991, p. 45.
    • (1991) Proc. IEEE Int. Symp. Inform. Theory , pp. 24-28
    • Forney, G.D.1    Trott, M.D.2
  • 36
    • 0026953515 scopus 로고
    • On the Hamming distance properties of group codes
    • Nov.
    • G. D. Forney, Jr., “On the Hamming distance properties of group codes,” IEEE Trans. Inform. Theory, vol. 38, pp. 1797–1801, Nov. 1992.
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 1797-1801
    • Forney, G.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.