Integer low-density lattices based on construction A

2012 IEEE Information Theory Workshop, ITW 2012

Volumn , Issue , 2012, Pages 422-426

  Di Pietro, Nicola ^a,b   Boutros, Joseph J ^c   Zemor, Gilles ^b   Brunel, Loic ^a  

^a Mitsubishi Electric R and D Centre Europe   (France)

^b UNIVERSITÉ BORDEAUX 1   (France)

^c TEXAS A AND M UNIVERSITY AT QATAR   (Qatar)

Author keywords

[No Author keywords available]

Indexed keywords

CAPACITY LIMIT; CLASSICAL THEORY; EUCLIDEAN; HIGH DIMENSIONS; INTEGER LATTICE; LATTICE CONSTRUCTION; LOW DENSITY; MESSAGE PASSING ALGORITHM; NON-BINARY LDPC CODES;

INFORMATION THEORY; ITERATIVE DECODING;

LATTICE THEORY;

EID: 84873135811     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ITW.2012.6404707     Document Type: Conference Paper

References (21)

1. L. R. Bahl, J. Cocke, F. Jelinek and J. Raviv, "Optimal decoding for linear codes for minimizing symbol error rate," IEEE Trans. on Inf. Theory, vol. 20, no. 2, pp. 284-287, March 1974.
2. I. J. Baik and S. Y. Chung, "Irregular low-density parity-check lattices," in Proc. of IEEE Intern. Symp. of Inf. Theory 2008, pp. 2479-2483, July 2008.
3. L. Brunel and J. J. Boutros, "Lattice decoding for joint detection in direct-sequence CDMA systems," IEEE Trans. on Inf. Theory, vol. 49, no. 4, pp. 1030-1037, April 2003.
4. J. H. Conway and N. J. Sloane, Sphere packings, lattices and groups, third edition, Springer-Verlag, 1999.
5. U. Erez and R. Zamir, "Achieving 1/2 log(1 + SNR) on the AWGN Channel with Lattice Enconding and Decoding," IEEE Trans. on Inf. Theory, vol. 50, no. 10, pp. 2293-2314, Oct. 2004.
6. U. Erez, S. Litsyn and R. Zamir, "Lattices which are good for (almost) everything," IEEE Trans. on Inf. Theory, vol. 51, no. 10, pp. 3401-3416, Oct. 2005.
7. P. Gaborit and G. Zémor, "On the construction of dense lattices with a given automorphisms group," Ann. de l'Institut Fourier, vol. 57, no. 4, pp. 1051-1062, 2007.
8. R. G. Gallager. Low-density parity-check codes, PhD thesis, Massachus-sets Institute of Technology Press, 1963.
9. C. R. P. Hartmann and L. D. Rudolph, "An optimum symbol-by-symbol decoding rule for linear codes," IEEE Trans. on Inf. Theory, vol. 22, no. 5, pp. 514-517, Sept. 1976.
10. X.-Y. Hu, E. Eleftheriou and D. M. Arnold, "Regular and irregular progressive edge-growth tanner graphs," IEEE Trans. on Inf. Theory, vol. 51, no. 1, pp. 386-398, Jan. 2005.
11. H. Imai and S. Hirakawa, "A new multilevel coding method using error-correcting codes," IEEE Trans. on Information Theory, vol. 23, no. 3, pp. 371-377, May 1977.
12. F. Kschischang, B. Frey and H.-A. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 498-519, Feb. 2001.
13. H.-A. Loeliger, "Averaging bounds for lattices and linear codes," IEEE Trans. on Inf. Theory, vol. 43, no. 6, pp. 1767-1773, Nov. 1997.
14. G. Poltyrev, "On coding without restrictions for the AWGN channel," IEEE Transactions on Information Theory, vol. 40, no. 2, pp. 409-417, March 1994.
15. C. Poulliat, M. Fossorier, and D. Declercq, "Design of non binary LDPC codes using their binary image: algebraic properties," Proc. of IEEE Intern. Symp. of Inf. Theory 2006, pp. 93-97, July 2006.
16. T. Richardson and R. Urbanke, Modern coding theory, Cambridge University Press, 2008.
17. M.-R. Sadeghi, A. H. Banihashemi and D. Panario, "Low-density parity-check lattices: construction and decoding analysis," IEEE Trans. on Inf. Theory, vol. 52, no. 10, pp. 4481-4495, Oct. 2006.
18. A. Sakzad, M.-R. Sadeghi and D. Panario, "Turbo lattices: construction and performance analysis," available on arxiv.org, 2011.
19. N. Sommer, M. Feder and O. Shalvi, "Low-density lattice codes," IEEE Trans. on Inf. Theory, vol. 54, no. 4, pp. 1561-1585, April 2008.
20. E. Viterbo and J. J. Boutros, "A universal lattice code decoder for fading channels," IEEE Trans. on Inf. Theory, vol. 45, no. 5, pp. 1639-1642, July 1999.
21. U. Wachsmann, R.F.H. Fischer, and J.B. Huber, "Multilevel codes: theoretical concepts and practical design rules," IEEE Trans. Inform. Theory, vol. 45, no. 5, pp. 1361-1391, July 1999.