Trellis-Oriented Decomposition and Trellis Complexity of Composite-Length Cyclic Codes

IEEE Transactions on Information Theory

Volumn 41, Issue 4, 1995, Pages 1185-1191

  Berger, Yuval ^a   Be'ery, Yair ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

concatenated codes; constacyclic codes; cyclic codes; generalized Hamming weights; product codes; soft decision decoding; Trellis diagrams

Indexed keywords

BLOCK CODES; COMPUTATIONAL COMPLEXITY; DECODING; GRAPH THEORY; OPTIMAL SYSTEMS; STATE SPACE METHODS;

COMPOSITE LENGTH CYCLIC CODES; CONCATENATED CODES; CONSTACYCLIC CODES; GENERALIZED HAMMING WEIGHTS; PRODUCT CODES; SOFT DECISION DECODING; TRELLIS DIAGRAMS;

CODES (SYMBOLS);

EID: 0029341338     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.391268     Document Type: Article

References (24)

1. J. K. Wolf, “Efficient maximum likelihood decoding of linear block codes using a trellis,” IEEE Trans. Inform. Theory, vol. IT-24, pp. 76–80, 1978.
2. G. D. Forney, Jr., “Coset codes—part II: Binary lattices and related codes,” IEEE Trans. Inform. Theory, vol. 34, pp. 1152–1187, 1988.
3. Y. Berger and Y. Be'ery, “Soft trellis-based decoder for linear block codes,” IEEE Trans. Inform. Theory, vol. 40, pp. 764–773, 1994.
4. D. J. Muder, “Minimal trellises for block codes,” IEEE Trans. Inform. Theory, vol. 34, pp. 1049–1053, 1988.
5. Y. Berger and Y. Be'ery, “Bounds on the trellis size of linear block codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 203–209, 1993.
6. 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.
7. T. Kasami, T. Takata, T. Fujiwara, and S. Lin, “On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 242–245, 1993.
8. G. D. Forney, Jr., “Dimension/length profiles and trellis complexity of linear block codes,” preprint, submitted to IEEE Trans. Inform. Theory.
9. T. Fujiwara, T. Kasami, R. Morelos-Zaragoza, and S. Lin, “The state complexity of trellis diagram for a class of generalized concatenated codes,” in 16th Symp. on Information Theory and its Applications (Kanazawa, Japan, Oct. 1993).
10. A. Vardy and Y. Be'ery, “Maximum-likelihood soft-decision decoding of BCH codes,” IEEE Trans. Inform. Theory, vol. 40, pp. 546–554, 1994.
11. J. Snyders and Y. Be'ery, “Maximum likelihood soft decoding of binary block codes and decoders for the Golay codes,” IEEE Trans. Inform. Theory, vol. 35, pp. 963–975, 1989.
12. V. K. Wei, “Generalized Hamming weights for linear codes,” IEEE Trans. Inform. Theory, vol. 37, pp. 1412–1418, Sept. 1991.
13. E. R. Berlekamp, Algebraic Coding Theory. Laguna Hills, CA: Aegean Park Press, 1984.
14. Y. Be'ery and J. Snyders, “A recursive Hadamard transform optimal soft decision decoding algorithm,” SIAM J. Alg. Disc. Math., vol. 8, no. 4, pp. 778–789, 1987.
15. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1977.
16. E. R. Berlekamp and J. Justesen, “Some long cyclic linear binary codes are not so bad,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 351–356, 1974.
17. Y. Be'ery, “Optimal decoding of error correcting codes based on fast transforms,” Ph.D. dissertation, Faculty of Electrical Engineering, Tel-Aviv Univ., Tel-Aviv, Israel, 1985.
18. T. Kasami, “Some lower bounds on the minimum weight of cyclic codes of composite length,” IEEE Trans. Inform. Theory, vol. IT-14, pp. 814–818, 1968.
19. —, “Construction and decomposition of cyclic codes of composite length,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 680–683, 1974.
20. J. M. Jensen, “The concatenated structure of cyclic and abelian codes,” IEEE Trans. Inform. Theory, vol. IT-31, pp. 788–793, 1985.
21. —, “Cyclic concatenated codes with constacyclic outer codes,” IEEE Trans. Inform. Theory, vol. 38, pp. 950–959, 1992.
22. G. Promhouse and S. E. Tavares, “The minimum distance of all binary cyclic codes of odd lengths from 69 to 99,” IEEE Trans. Inform. Theory, vol. IT-24, pp. 438–442, 1978.
23. A. E. Brouwer and T. Verhoeff, “An updated table of minimum-distance bounds for binary linear codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 662–677, 1993.
24. V. K. Wei and K. Yang, “On the generalized Hamming weights of product codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 1709–1713, 1993.