Algebraic approach to reduce the number of delay elements in the realization of multidimensional convolutional code

Midwest Symposium on Circuits and Systems

Volumn 2, Issue , 2004, Pages

  Charoenlarpnopparut, C ^a   Tantaratana, S ^a  

^a THAMMASAT UNIVERSITY   (Thailand)

Author keywords

Canonical realization; Channel coding; Generator matrix; Gr bner basis; M D convolutional code; Unimodular

Indexed keywords

ALGORITHMS; DIGITAL COMMUNICATION SYSTEMS; ENCODING (SYMBOLS); ITERATIVE METHODS; MATRIX ALGEBRA; POLYNOMIALS;

CANONICAL REALIZATION; CHANNEL CODING; GENERATOR MATRIX; GRÖBNER BASIS; M-D CONVOLUTIONAL CODES; UNIMODULAR;

CODES (SYMBOLS);

EID: 11144281886     PISSN: 15483746     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (17)

1. W.W. Adams and P. Loustaunau, "An Introduction to Gröbner Bases,": Graduate Studies in Mathematics, vol.3, American Mathematical Society, 1994.
2. K.J. Boo and N.K. Bose, "Multispectral image restoration with multisensors," IEEE Trans on Geosciencc and Remote Sensing, vol. 335B, 1997, pp. 1367-1409.
3. B. Buchberger, "Gröbner Bases: An algorithmic method in polynomial ideal theory," in Multidimensional System Theory (N.K. Bose, ed.), Reidel, Dordrecht, 1985, pp. 184-232.
4. C. Charoenlarpnopparut and N.K. Bose, "Multidimensional filter bank design using Groebner bases," IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 46, no. 12, December 1999, pp. 1475-1486.
5. C. Charoenlarpnopparut and N.K. Bose, "Groebner Bases For Problem Solving in Multidimensional Systems," Multidimensional Systems and Signal Processing, vol. 12, no. 3-4, 2001, pp. 365-376.
6. C. Charoenlarpnopparut, S. Wongsura, and A. Davies, "Direct realization of a 2-D convolutional encoder with fewer number of delay elements." Proceedings of the Third International Symposium on Communications and Information Technology (ISCIT 2003), 3-5 September 2003, Songkhla, Thailand, Vol. I, pp. 258-262.
7. C. Charoenlarpnopparut and S. Tantaratana, "Multidimensional convolutional code: Progresses and bottlenecks," Proceedings of the 2003 IEEE International Symposium on Circuits and Systems (ISCAS 2003), 25-28 May 2003, Bangkok, Thailand, pp. III-686 to III-689.
8. C. Charoenlarpnopparut and S. Tantaratana, "Application of Gröbner Bases on the Algebraic Structure of Multidimensional Convolutional Code," submitted for publication.
9. nd edition, Springer-Verlag, New York, 1996.
10. E. Fornasini and M.E. Valcher, "Algebraic aspect of 2D convolutional codes," IEEE Trans. Inform. Theory, vol. IT-40, No. 4, 1994, pp.1068-1082.
11. G.D. Forney, Jr, "Convolutional codes I: Algebraic structure," IEEE Trans. Info. Theory, vol. IT-16, Nov. 1970, pp. 720-738.
12. G.-M. Greuel, G. Pfister, and H. Schönemann. SINGULAR 2.0. A Computer Algebra System for Polynomial Computations. Centre for Computer Algebra, University of Kaiserslautern (2001). http://www.singular.uni-kl.de.
13. R. Johannesson and Z. Wan, "A linear algebra appoach to minimal convolutional encoders," IEEE Trans. Information Theory, vol. 39), no. 4, Jul. 1993, pp. 1219-1233.
14. R. Johannesson and K.S. Zigangirov, "Fundamentals of Convolutional Coding,", IEEE Press, New York, USA, 1998. ISBN:0-7803-3483-3.
15. S. Mahapakulchai, "MAP source-controlled channel decoding for image transmission using CPFSK and ring convolutional codes," Ph.D. Dissertation, Pennsylvania State University, PA, USA, 2004.
16. M.E. Valcher and E. Fornasini, "On 2-D finite support convolutional codes: An algebraic approach," Multidimensional Systems and Signal Processing," Vol. 5, No. 3, July 1994, pp. 231-243.
17. P.A. Wiener,"Multidimensional Cunvolutional Codes," Ph.D. Dissertation, University of Notre Dame. IN, USA, 1998.