A Linear Algebra Approach to Minimal Convolutional Encoders

IEEE Transactions on Information Theory

Volumn 39, Issue 4, 1993, Pages 1219-1233

  Wan, Zhe Xian ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

CODES (SYMBOLS); CONSTRAINT THEORY; ENCODING (SYMBOLS); INVERSE PROBLEMS; LINEAR ALGEBRA; MATRIX ALGEBRA; SIGNAL ENCODING; THEOREM PROVING;

BASIC ENCODING MATRIX; CONVOLUTIONAL CODE; MINIMAL BASIC ENCODING MATRIX; MINIMAL ENCODER; MINIMAL ENCODING MATRIX;

INFORMATION THEORY;

EID: 0027634632     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.243440     Document Type: Article

References (14)

1. G. D. Forney, Jr., “Convolutional codes I: Algebraic structure,” IEEE Trans. Inform. Theory, vol. IT-16, pp. 720–738, 1970.
2. G. D. Forney, Jr., “Correction to ‘Convolutional ‘codes I: Algebraic structure,” IEEE Trans. Inform. Theory, vol. IT-17, pp. 360, 1971.
3. G. D. Forney, Jr., “Structural analyses of convolutional codes via dual codes,” IEEE Trans. Inform. Theory, vol. IT-19, pp. 512–518, 1973
4. J. L. Massey and M. K. Sain, “Inverses of linear sequential circuits,” IEEE Trans. Comput., vol, C-17, pp. 330–337, 1968.
5. N. Jacobson, Basic Algebra I. San Fransisco, CA: Freeman, 1974.
6. T. Kailath, Linear systems. Englewood Cliffs, NJ: Prentice Hall, 1980.
7. 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. 527–558.
8. H.-A. Loeliger and T. Mittelholzer, “Convolutional codes over groups,” submitted to IEEE Trans. Inform. Theory, 1992.
9. G. D. Forney, Jr., Private communication, Aug. 1991.
10. A. J. Viterbi and J. K. Omura, Principles of Digital Communication and Coding New York: McGraw-Hill, 1979.
11. D. J. Costello, Jr., “Construction of convolutional codes for sequential decoding,” Rep. EE-692, Univ. of Notre Dame, Notre Dame, IN, Aug. 1969.
12. G. D. Forney, Jr. and M. D. Trott, “The dynamics of linear codes over groups: state spaces, trellis diagrams and canonical encoders,” submitted to IEEE Trans. Inform. Theory, 1992.
13. C. Roos, “On the structure of convolutional and cyclic convolutional codes,” IEEE Trans. vol. IT-25, 676–683, 1979.
14. P. Piret, Convolutional Codes: An Algebraic Approach. Cambridge, MA: MIT Press, 1988.