Generalized low-density (GLD) lattices

2014 IEEE Information Theory Workshop, ITW 2014

Volumn , Issue , 2014, Pages 15-19

  Boutros, Joseph J ^a   Di Pietro, Nicola ^a   Basha, Nour ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

CHANNEL CODING; COMPUTER PROGRAMMING; DIGITAL COMMUNICATION SYSTEMS; NETWORK CODING; NETWORK LAYERS;

CODED MODULATION; CODING THEORY; DIGITAL COMMUNICATIONS; INTEGER LATTICE; LARGE DIMENSIONS; LOW DENSITY; PHYSICAL LAYER NETWORK CODING (PNC); SPHERE PACKINGS;

LATTICE THEORY;

EID: 84929338332     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ITW.2014.6970783     Document Type: Conference Paper

References (23)

1. J.H. Conway and N.J.A. Sloane. Sphere Packings, Lattices and Groups. Springer-Verlag, New York, 3rd edition, 1999.
2. T. Richardson and R. Urbanke. Modern Coding Theory. Cambridge University Press, New York, 2008.
3. O. Pothier, L. Brunel, and J.J. Boutros, "A low complexity FEC scheme based on the intersection of interleaved block codes," IEEE Veh. Tech. Conf., vol. 1, pp. 274-278, Houston, May 1999.
4. J.J. Boutros, O. Pothier, and G. Zémor, "Generalized low density (Tanner) codes," IEEE Intern. Conf. on Comm. (ICC), vol. 1, pp. 441-445, Vancouver, June 1999.
5. G. Poltyrev, "On coding without restrictions for the AWGN channel," IEEE Trans. on Inf. Theory, vol. 40, no. 2, pp. 409-417, March 1994.
6. H.-A. Loeliger, "Averaging bounds for lattices and linear codes," IEEE Trans. on Inf. Theory, vol. 43, no. 6, pp. 1767-1773, Nov. 1997.
7. U. Erez and R. Zamir, "Achieving 1 2 log(1+SNR) on the AWGN channel with lattice encoding and decoding," IEEE Trans. on Inf. Theory, vol. 50, no. 10, pp. 2293-2314, Oct. 2004.
8. O. Ordentlich and U. Erez, "A simpler proof for the existence of good pairs of nested lattices," 2012. Available at http://arxiv.org/abs/1209.5083.
9. C. Ling and J.-C. Belfiore, "Achieving the AWGN channel capacity with lattice Gaussian coding," IEEE Intern. Symp. on Inf. Theory Proceedings (ISIT), pp. 1416-1420, July 2013.
10. A. Ingber, R. Zamir, and M. Feder, "Finite-dimensional infinite constellations," IEEE Trans. on Inf. Theory, vol. 59, no. 3, pp. 1630-1656, March 2013.
11. P. Gaborit and G. Zémor, "On the construction of dense lattices with a given automorphism group," Annales de l'Institut Fourier, vol. 57, no. 4, pp. 1051-1062, 2007.
12. I.-J. Baik and S.-Y. Chung, "Irregular low-density parity-check lattices," IEEE Intern. Symp. on Inf. Theory (ISIT), pp. 2479-2483, 2008.
13. 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.
14. A. Sakzad, M.-R. Sadeghi, and D. Panario, "Turbo lattices: Construction and error decoding performance," 2012. Available at http://arxiv.org/abs/1108.1873v3.
15. M.-R. Sadeghi and A. Sakzad, "On the performance of 1-level LDPC lattices," Iran Workshop on Comm. and Inf. Theory (IWCIT), pp. 1-5, 2013.
16. Y. Yan, C. Ling, and X. Wu, "Polar lattices: Where Arikan meets Forney," IEEE Intern. Symp. on Inf. Theory (ISIT), pp. 1292-1296, July 2013.
17. N. di Pietro, J.J. Boutros, G. Zémor, and L. Brunel, "Integer low-density lattices based on Construction A," Proc. of the 2012 IEEE Information Theory Workshop, pp. 422-426, Lausanne, Sept. 2012.
18. N. di Pietro, G. Zémor, and J.J. Boutros "New results on Construction A lattices based on very sparse parity-check matrices," Proc. of the 2013 IEEE Intern. Symp. on Inf. Theory (ISIT), pp. 1675-1679, July 2013.
19. N. di Pietro, "On Infinite and Finite Lattice Constellations for the Additive White Gaussian Noise Channel," PhD thesis, Université de Bordeaux, Jan. 2014.
20. G. D. Forney, "Coset codes I: introduction and geometrical classification,", IEEE Trans. on Inf. Theory, vol. 34, no. 5, pp. 1123-1151, 1988.
21. 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.
22. J.J. Boutros, N. Gresset, L. Brunel, and M. Fossorier, "Soft-input softoutput lattice sphere decoder for linear channels," IEEE Glob. Comm. Conf., vol. 3, pp. 1583-1587, Dec. 2003.
23. 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.