Trellis complexity versus the coding gain of lattices I

IEEE Transactions on Information Theory

Volumn 42, Issue 6 PART 1, 1996, Pages 1796-1807

  Tarokh, Vahid ^a,b   Blake, Lan F ^c  

^a UNIVERSITY OF WATERLOO   (Canada)

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

^c AT AND T LABS RESEARCH   (United States)

Author keywords

Coding gain; Lattices; Maximum likelihood decoding; Trellis complexity

Indexed keywords

DECODING; ENCODING (SYMBOLS); MATHEMATICAL MODELS; SET THEORY; TRELLIS CODES;

CODING GAIN; MAXIMUM LIKELIHOOD DECODING; TRELLIS COMPLEXITY;

COMPUTATIONAL COMPLEXITY;

EID: 0030289445     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.556675     Document Type: Article

References (26)

1. L. Bahl, J. Cocke, F. Jelinek, and J. Raviv, Optimal decoding of linear codes for minimizing symbol error rates, IEEE Trans, Inform. Theory, vol. IT-20, pp. 284-287, 1974.
2. J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups. New York: Springer-Verlag, 1993.
3. M. V. Eyuboglu and G. D. Forney, Lattices and trellis quantization with lattice and trellis-bounded code-books, IEEE Trans. Inform. Theory, vol. 39, pp. 46-59, 1993.
4. G. D. Forney, Coset codes-Part II: Binary lattices and related codes, IEEE Trans. Inform. Theory, vol. 34, pp. 1152-1187, 1988.
5. -, Trellises old and new, in Communications and Cryptography: Two Sides of One Tapestry, R. E. Blahut et al, Eds. Dordrecht, The Netherlands: Kluwer, 1994.
6. Density/length profiles and trellis complexity of lattices, IEEE Trans. Inform. Theory, vol. 40, pp. 1753-1772, 1995.
7. Dimension/length profiles and trellis complexity of linear block codes, IEEE Trans. Inform. Theory, vol. 40, pp. 1741-1752, 1995.
8. G. D. Forney, Jr., R. G. Gallager, G. R. Lang, F. M. Longstaff, and S. U. Qureshi, Efficient modulation for band-limited channels, IEEE J. Sel. Areas Commun., vol. SAC-2, pp. 632-647, 1984.
9. G. D. Forney 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.
10. J. E. Hopcroft and J. D. Ullman, Introduction To Automata Theory, Languages, and Computation. Reading, MA: Addison-Wesley, 1979.
11. Y. Kitaoka, Scalar extensions of quadratic lattices II, Nagoya Math. J., vol. 67, pp. 159-164, 1977.
12. Tensor products of positive definite quadratic forms III, Nagoya Math. J., vol. 70, pp. 173-181, 1978.
13. Tensor products of positive definite quadratic forms V, Nagoya Math. J., vol. 82, pp. 99-111, 1981.
14. Tensor products of positive definite quadratic forms VII, Nagoya Math. J., vol. 96, pp. 133-137, 1984.
15. A. D. Kot and C. Leung, On the construction and dimensionality of linear block code trellises, in Proc. 1993 IEEE Int. Symp. on Information Theory.
16. A. Lafourcade and A. Vardy, Asymptotically good codes have infinite trellis complexity, IEEE Trans. Inform. Theory, vol. 41, pp. 555-559, 1995.
17. R. J. McEliece, The Viterbi decoding complexity of linear block codes, presented at the IEEE Int. Symp. on Information Theory, Trondheim, Norway, June 1994.
18. On the BCJR trellis for linear block codes,"/EEE Trans. Inform. Theory, vol. 42, no. 4, pp. 1072-1092, July 1996.
19. D. J. Muder, Minimal trellises for block codes, IEEE Trans. Inform. Theory, vol. 34, pp. 1049-1053, 1988.
20. W. H. Ruckle, Modem Analysis. PWS-Kent Pub. Co.y, 1991.
21. W. Rudin, Principles of Mathematical Analysis. New York: McGraw-Hill, 1953
22. Real and Complex Analysis. New York: McGraw-Hill, 1966.
23. V. Tarokh, Trellis complexity versus the coding gain of lattice-based communication systems, Ph.D. dissertation, Univ. of Waterloo, Waterloo, Waterloo, Ont., Canada, 1995.
24. V. Tarokh and I. F. Blake, Trellis complexity versus the coding gain of lattices II, this issue, pp. 1808-1816.
25. V. Tarokh, A. Vardy, and K. Zeger, Sequential decoding of lattice codes, preprint.
26. J. K. Wolf, Efficient maximum-likelihood decoding of linear block codes, IEEE Trans. Inform. Theory, vol. IT-24, pp. 76-80, 1978.