Applications of the lindeberg principle in communications and statistical learning

IEEE Transactions on Information Theory

Volumn 57, Issue 4, 2011, Pages 2440-2450

  Korada, Satish Babu ^a   Montanari, Andrea ^a  

^a Stanford University   (United States)

Author keywords

Code division multiple access (CDMA); LASSO; Lindeberg principle; multiple input multiple output (MIMO); random matrices; SK model; sparse dense equivalence; universality

Indexed keywords

LASSO; LINDEBERG PRINCIPLE; MULTIPLE-INPUT MULTIPLE-OUTPUT (MIMO); RANDOM MATRICES; SK-MODEL; SPARSE-DENSE EQUIVALENCE; UNIVERSALITY;

COMMUNICATION; INFORMATION THEORY; MIMO SYSTEMS;

CODE DIVISION MULTIPLE ACCESS;

EID: 79952856401     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2112231     Document Type: Article

References (27)

1. S. Chatterjee, "A generalization of the Lindeberg principle," Ann. Probabil., vol. 34, no. 6, pp. 2061-2076, 2006.
2. V. A. Marčenko and L. A. Pastur, "Distribution of eigenvalues for some sets of random matrices," Math. USSR Sb., vol. 1, pp. 457-483, 1967.
3. J. Cardy, Scaling and Renormalization in Statistical Physics. Cambridge, U.K.: Cambridge Univ. Press, 1996.
4. E. Telatar, "Capacity of multi-antenna Gaussian channels," Euro. Trans. Telecommun., vol. 10, no. 6, pp. 585-595, 1999. (Pubitemid 129568930)
5. S. B. Korada and N. Macris, "Tight bounds on the capacity of binary input random CDMA systems," IEEE Trans. Inf. Theory, 2008, to be published.
6. D. L. Donoho and J. Tanner, "Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing," Phil. Trans. R. Soc. A 13, pp. 4273-4293, Nov. 2009.
7. D. L. Donoho and J. Tanner, "Counting faces of randomly-projected polytopes when the projection radically lowers dimension," J. Amer. Math. Soc., vol. 22, no. 1, pp. 1-53, 2009.
8. H. Kesten, "Symmetric random walks on groups," Trans. Amer. Math. Soc., vol. 92, pp. 336-354, 1959.
9. B. D. McKay, "The expected eigenvalue distribution of a large regular graph," Linear Algebra Appl., vol. 40, pp. 203-216, 1981.
10. A. M. Sayeed and V. Raghavan, "Maximizing MIMO capacity in sparse multipath with reconfigurable antenna arrays," IEEE J. Sel. Topics Signal Process., vol. 1, no. 1, pp. 156-166, 2007. (Pubitemid 46805297)
11. S. Verdú, Multiuser Detection. Cambridge, U.K.: Cambridge Univ. Press, 1998.
12. A. J. Grant and P. D. Alexander, "Randomly selected spreading sequences for coded CDMA," in Proc. 4th Int. Spread Spectrum Tech. Appl., Mainz, Germany, Sep. 1996, pp. 54-57.
13. A. Montanari and D. Tse, "Analysis of belief propagation for nonlinear problems: The example of CDMA (or : How to prove Tanaka's formula)," in Proc. IEEE Inf. Theory Workshop, Punta del Este, Uruguay, Mar. 13-Mar. 17, 2006.
14. T. Tanaka, "A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors," IEEE Trans. Inf. Theory, vol. 48, pp. 2888-2910, 2002. (Pubitemid 35327603)
15. R. Tibshirani, "Regression shrinkage and selection via the LASSO," J. Roy. Statist. Soc. B, vol. 58, pp. 267-288, 1996.
16. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM Rev., vol. 43, pp. 129-159, 2001. (Pubitemid 32406896)
17. G. W. Anderson, A. Guionnet, and O. Zeitouni, An Introduction to Random Matrices. Cambridge, U.K.: Cambridge Univ. Press, 2009.
18. A. M. Tulino, A. Lozano, and S. Verdú, "Capacity-achieving input covariance for correlated multi-antenna channels," in Proc. 41st Ann. Allerton Conf. Commun., Contr. Comput., Monticello, IL, Oct. 2003.
19. M. Mézard and A. Montanari, Information, Physics, and Computation. Oxford, U.K.: Oxford Univ. Press, 2009.
20. P. Carmona and Y. Hu, "Universality in Sherrington-Kirkpatrick's spin glass model," Ann. l'Institut Henri Poincare (B) Prob. Stat., vol. 42, pp. 215-222, 2006. (Pubitemid 43149972)
21. M. Talagrand, Spin Glasses: A Challenge for Mathematicians: Cavity and Mean Field Models. New York: Springer, 2003.
22. F. Guerra and F. L. Toninelli, "The high temperature region of the Viana-Bray diluted spin glass model," J. Stat. Phys., vol. 115, pp. 531-555, 2004. (Pubitemid 39015503)
23. M. Talagrand, "Gaussian averages, Bernoulli averages, and Gibbs' measures," Random Structures and Algorithms, vol. 21, pp. 197-204, 2002. (Pubitemid 37340769)
24. F. L. Toninelli, "Rigorous results for mean field spin glasses: Thermodynamic limit and sum rules for the free energy," Ph.D. dissertation, Scuola Normale Superiore, Pisa, Italy, 2002.
25. Y. Seginer, "The expected norm of random matrices," Combinator., Probabil., Comput., vol. 9, pp. 149-166.
26. S. Chatterjee,A Simple Invariance Theorem [Online].Available: http:// arxiv.org/abs/math/0508213v1 2005, unpublished. vol.
27. Z. Bai and J. W. Silverstein, Spectral Analysis of Large Dimensional Random Matrices. New York: Springer, 2009.