Optimal sectionalization of a trellis

IEEE Transactions on Information Theory

Volumn 42, Issue 3, 1996, Pages 689-703

  Lafourcade, Alec ^a,b   Vardy, Alexander ^a,b  

^a IEEE

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

Dynamics of block codes; Maximum likelihood decoding; Optimal sectionalization; Trellis complexity; Trellis structure

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DECODING; MATRIX ALGEBRA; OPTIMIZATION; POLYNOMIALS;

LINEAR CODES; MAXIMUM LIKELIHOOD DECODING; NONLINEAR CODES; OPTIMAL SECTIONALIZATION; POLYNOMIAL TIME ALGORITHMS; REED-MULLER CODES; TRELLIS COMPLEXITY; TRELLIS STRUCTURE; VITERBI ALGORITHMS;

TRELLIS CODES;

EID: 0030150338     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.490504     Document Type: Article

References (37)

1. O. Amrani, Y. Bc'ery. A. Vardy, F.-W. Sun, and H. C. A. van Tilborg, "The Leech lattice and the Golay code: Bounded-distance decoding and multilevel constructions," IEEE Trans. Inform. Theory, vol. 40, pp. 1030-1043, 1994.
2. [21 L.R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, "Optimal decoding of linear codes for minimizing symbol error rate,'1 IEEE Trans. Inform. Tlieory, vol. IT-20, pp. 284-287, 1974.
3. D.P. Bertsekas and R. G. Gallager, Data Networks, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1991.
4. Y. Be'ery and J. Snyders, "Optimal soft decision block decoders based on fast Hadamard transform," IEEE Trans. Inform. Theory, vol. IT-32, pp. 355-364, 1986.
5. Y. Berger and Y. Be'ery, "Soft trellis-based decoder for linear block codes," IEEE Trans. Inform. Theory, vol. 40, pp. 764-773, 1994.
6. J.H. Conway and N. J. A. Sloane, "Soft decoding techniques for codes and lattices, including the Golay code and the Leech lattice," IEEE Trans. Inform. Theory, vol. IT-32, pp. 41-50, 1986.
7. N. Deo, Graph Theory with Applications in Engineering and Computer Science. Englewood Cliffs, NJ: Prentice-Hall, 1974.
8. R. Dial, F. Glover, D. Karney, and D. Klingman, "A computational analysis of alternative algorithms and labeling techniques for finding shortest path trees," Networks, vol. 9, pp. 215-248, 1979.
9. E.W. Dijkslra, "A note on two problems in connection with graphs," Numer. Math., vol. 1, pp. 269-271, 1959.
10. G.D. Forney, Jr., "Coset codes II: Binar)' lattices and related codes," IEEE Trans. Inform. Theory, vol. IT-34, pp. 1152-1187, 1988.
11. _, "Dimension/length profiles and trellis complexity of linear block codes," IEEE Trims. Inform. Theory, vol. 40. pp. 1741-1752, 1994.
12. 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.
13. T. Fujiwara, T. Kasami, R. Morelos-Zaragoza, and S. Lin, "The state complexity of trellis diagrams for a class of generalized concatenated codes," preprint.
14. G.S. Gallo and S. Pallotino, "Shortest path algorithms," Annals Oper. Res., vol. 7, pp. 3-79, 1988.
15. M R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theorv ofNP-Completeness. New York: Freeman, 1979.
16. T. Kasami, T. Takata, T. Fujiwara, and S. Lin, "Trellis diagram construction for some BCH codes," in IEEE Int. Sytnp. on Information Theory and Applications (Honolulu, HI, 1990).
17. _, "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. 242-243, 1993.
18. _, "On structural complexity of the Z-section minimal trellis diagrams for binary linear block codes," IEICE Trans., vol. E76-A, pp. 1411-1421, 1993.
19. A.B. Kiely, S. Oolmar, R. J. McEliece, L. Hkroot, and W. Lin, "Trellis decoding complexity of linear block codes," IEEE Trans. Inform. Theory, to appear.
20. F.R. Kschischang and V. Sorokine, "On the irellis structure of block codes," IEEE Trans. Inform. Theory, vol. 41, pp. 1924-1937, Nov. 1995.
21. A. Lafourcade and A. Vardy. "Lower bounds on trellis complexity of block codes," IEEE Trans. Inform. Theory, vol. 41, pp. 1938-1954, Nov. 1995.
22. F.J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. New York: North-Holland, 1977.
23. R.J. McEliece, "On the BCJR trellis for linear block codes," preprint.
24. D.I. Müder, "Minimal trellises for block codes," IEEE Trans. Inform. Theory, vol. 34, pp. 1049-1053, 1988.
25. U. Pape, "Implementation and efficiency of Moore-algorithms for the shortest route problem," Math. Programming, vol. 7, pp. 212-222, 1974.
26. E.M. Rcingold, J. Nicvcrgelt, and N. Deo, Combinatorial Algorithms: Theory and Practice. Englewood Cliffs, NJ: Prentice-Hall, 1977.
27. J.B. Shearer, personal comniunicaiion, 1994.
28. 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.
29. A. Vardy, "Dynamical structure of block codes," in IEEE Inform. Theory Workshop on Coding, System Theory, and Symbolic Dynamics (Mansfield, MA, Oct. 1993).
30. _, "The Nordstrom-Robinson code: Representation over GF(4) and efficient decoding," IEEE Trans. Inform. Theory, vol. 40, pp. 1686-1693, 1994.
31. _, "Even more efficient bounded-distance decoding of the hexacode, the Golay code, and the Leech lattice," IEEE Trans. Inform. Théo/y, vol. 41. pp. 1495-1499, Sept. 1995.
32. A. Vardy and Y. Be'ery, "Bit-level soft decision decoding of Reed-Solomon codes," IEEE Trans. Commun., vol. 39, pp. 440-445, 1991.
33. _, "More efficient soft-decision decoding of the Golay codes," IEEE Trans. Inform. Theory, vol. 37, pp. 667-672, 1991.
34. _, "Maximum-likelihood decoding of the Leech lattice," IEEE Trans. Inform. Theory, vol. 39, pp. 1435-1444, 1993.
35. _. "Maximum-likelihood soft decision decoding of BCH codes," 1ELE Trans. Inform. Theory, vol. 4Ü. pp. 546-554, 1994.
36. A.J. Viterbi, "Error bounds for convolutional codes and an asymptot-ically optimum decoding algorithm," IEEE Tram. Inform. Theory, vol. IT-13, pp. 260-269, 1967.
37. J.K. Wolf, "Efficient maximum-likelihood decoding of linear block codes using a trellis," IEEE Trans. Inform. Theoiy, vol. IT-24, pp. 76-80, 1978.