Decoding by sampling: A randomized lattice algorithm for bounded distance decoding

IEEE Transactions on Information Theory

Volumn 57, Issue 9, 2011, Pages 5933-5945

  Liu, Shuiyin ^a   Ling, Cong ^a   Stehlé, Damien ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITÉ DE LYON   (France)

Author keywords

Bounded distance decoding; lattice decoding; lattice reduction; randomized algorithms

Indexed keywords

BOUNDED DISTANCE DECODING; EFFICIENT IMPLEMENTATION; ERROR PERFORMANCE; GAUSSIAN-LIKE DISTRIBUTIONS; LATTICE ALGORITHMS; LATTICE DECODING; LATTICE POINTS; LATTICE REDUCTION; NUMBER OF SAMPLES; ORIGINAL ALGORITHMS; POLYNOMIAL COMPLEXITY; RANDOM ROUNDING; RANDOMIZED ALGORITHMS; REDUCED COMPLEXITY; SAMPLING TECHNIQUE; SIMULATION RESULT; SPHERE DECODING; SUCCESSIVE INTERFERENCE CANCELATIONS; TECHNICAL CONTRIBUTION;

ALGORITHMS; MAXIMUM LIKELIHOOD; SAMPLING; SPHERES;

DECODING;

EID: 80052349133     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2162180     Document Type: Article

References (37)

1. R. Kannan, "Minkowski's convex body theorem and integer programming", Math. Oper. Res., vol. 12, 415-440, Aug. 1987.
2. G. Hanrot and D. Stehlé, "Improved analysis of Kannan's shortest vector algorithm", in Proc. Crypto 2007, Santa Barbara, CA, Aug. 2007.
3. D. Micciancio and P. Voulgaris, "A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations", in Proc. STOC'10, Cambridge, MA, Jun. 2010.
4. M. O. Damen, H. E. Gamal, and G. Caire, "On maximum likelihood detection and the search for the closest lattice point", IEEE Trans. Inf. Theory, vol. 49, 2389-2402, Oct. 2003.
5. E. Viterbo and J. Boutros, "A universal lattice code decoder for fading channels", IEEE Trans. Inf. Theory, vol. 45, 1639-1642, Jul. 1999.
6. E. Agrell, T. Eriksson, A. Vardy, and K. Zeger, "Closest point search in lattices", IEEE Trans. Inf. Theory, vol. 48, 2201-2214, Aug. 2002.
7. J. Jaldén and B. Ottersen, "On the complexity of sphere decoding in digital communications", IEEE Trans. Signal Process., vol. 53, 1474-1484, Apr. 2005.
8. F. Oggier, G. Rekaya, J.-C. Belfiore, and E. Viterbo, "Perfect space time block codes", IEEE Trans. Inf. Theory, vol. 52, 3885-3902, Sep. 2006.
9. E. Biglieri, Y. Hong, and E. Viterbo, "On fast-decodable space-time block codes", IEEE Trans. Inf. Theory, vol. 55, 524-530, Feb. 2009.
10. L. Babai, "On Lovász' lattice reduction and the nearest lattice point problem", Combinatorica, vol. 6, no. 1, pp. 1-13, 1986.
11. H. Yao and G. W. Wornell, "Lattice-reduction-aided detectors for MIMO communication systems", in Proc. Globecom'02, Taipei, China, Nov. 2002, pp. 17-21.
12. C. Windpassinger and R. F. H. Fischer, "Low-complexity near-maximum-likelihood detection and precoding for MIMO systems using lattice reduction", in Proc. IEEE Inf. Theory Workshop, Paris, France, Mar. 2003, pp. 345-348.
13. M. Taherzadeh, A. Mobasher, and A. K. Khandani, "LLL reduction achieves the receive diversity in MIMO decoding", IEEE Trans. Inf. Theory, vol. 53, 4801-4805, Dec. 2007.
14. X. Ma and W. Zhang, "Performance analysis for V-BLAST systems with lattice-reduction aided linear equalization", IEEE Trans. Commun., vol. 56, 309-318, Feb. 2008.
15. C. Ling, "On the proximity factors oflattice reduction-aided decoding", IEEE Trans. Signal Process., vol. 59, no. 6, 2795-2808, Jun. 2011.
16. J. Jaldén and P. Elia, "DMT optimality of LR-aided linear decoders for a general class of channels, lattice designs, and system models", IEEE Trans. Inf. Theory, vol. 56, 4765-4780, Oct. 2010.
17. D. Wübben, R. Böhnke, V. Kühn, and K. D. Kammeyer, "Near-maximum-likelihood detection of MIMO systems using MMSE-based lattice reduction", in Proc. IEEE Int. Conf. Commun. (ICC'04), Paris, France, Jun. 2004, pp. 798-802.
18. P. Klein, "Finding the closest lattice vector when it's unusually close", in Proc. ACM-SIAM Symp. Discr. Algorithms, 2000, pp. 937-941.
19. G. R.-B. Othman, L. Luzzi, and J.-C. Belfiore, "Algebraic reduction for the golden code", in Proc. IEEE Int. Conf. Commun. (ICC'09), Dresden, Germany, Jun. 2009.
20. L. Luzzi, G. R.-B. Othman, and J.-C. Belfiore, "Augmented lattice reduction for MIMO decoding", IEEE Trans. Wireless Commun., vol. 9, 2853-2859, Sep. 2010.
21. D. W. Waters and J. R. Barry, "The chase family of detection algorithms for multiple-input multiple-output channels", IEEE Trans. Signal Process., vol. 56, 739-747, Feb. 2008.
22. C. Windpassinger, L. H.-J. Lampe, and R. F. H. Fischer, "From lattice-reduction-aided detection towards maximum-likelihood detection in MIMO systems", in Proc. Int. Conf. Wireless Opt. Commun., Banff, Canada, Jul. 2003.
23. K. Su and F. R. Kschischang, "Coset-based lattice detection for MIMO systems", in Proc. Int. Symp. Inf. Theory (ISIT'07), Jun. 2007, pp. 1941-1945.
24. J. Choi and H. X. Nguyen, "SIC based detection with list and lattice reduction for MIMO channels", IEEE Trans. Veh. Technol., vol. 58, 3786-3790, Sep. 2009.
25. T. Shimokawa and T. Fujino, "Iterative lattice reduction aided MMSE list detection in MIMO system", in Proc. Int. Conf. Adv. Technol. Commun. ATC'08, Oct. 2008, pp. 50-54.
26. H. Najafi, M. E. D. Jafari, and M. O. Damen, "On adaptive lattice reduction over correlated fading channels", IEEE Trans. Commun., vol. 59, 2011.
27. P. Q. Nguyen and T. Vidick, "Sieve algorithms for the shortest vector problem are practical", J. Math. Cryptol, vol. 2, no. 2, 2008.
28. C. Gentry, C. Peikert, and V. Vaikuntanathan, "Trapdoors for hard lattices and new cryptographic constructions", in Proc. 40th Ann. ACM Symp. Theory of Comput., Victoria, Canada, 2008, pp. 197-206.
29. P. M. Gruber and C. G. Lekkerkerker, Geometry of Numbers. Amsterdam, Netherlands: Elsevier, 1987.
30. J. W. S. Cassels, An Introduction to the Geometry of Numbers. Berlin, Germany: Springer-Verlag, 1971.
31. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U. K.: Cambridge University Press, 1985.
32. L. Devroye, Non-Uniform Random Variate Generation. New York: Springer-Verlag, 1986, pp. 117-117.
33. D. Micciancio and S. Goldwasser, Complexity of Lattice Problems: A Cryptographic Perspective. Boston, MA: Kluwer Academic, 2002.
34. Y. H. Gan, C. Ling, and W. H. Mow, "Complex lattice reduction algorithm for low-complexity full-diversity MIMO detection", IEEE Trans. Signal Process., vol. 57, 2701-2710, Jul. 2009.
35. B. M. Hochwald and S. ten Brink, "Achieving near-capacity on a multiple-antenna channel", IEEE Trans. Commun., vol. 51, 389-399, Mar. 2003.
36. C. Ling and N. Howgrave-Graham, "Effective LLL reduction for lattice decoding", in Proc. Int. Symp. Inf. Theory (ISIT'07), Nice, France, Jun. 2007.
37. J.-C. Belfiore, G. Rekaya, and E. Viterbo, "The Golden code: A 2 X 2 full-rate space-time code with nonvanishing determinants", IEEE Trans. Inf. Theory, vol. 51, 1432-1436, Apr. 2005.