Estimation with random linear mixing, belief propagation and compressed sensing

2010 44th Annual Conference on Information Sciences and Systems, CISS 2010

Volumn , Issue , 2010, Pages

  Rangan, Sundeep ^a  

^a NONE

Author keywords

Belief propagation; Bounded noise; Compressed sensing; Density evolution; Non Gaussian estimation; Sparsity

Indexed keywords

BELIEF PROPAGATION; BOUNDED NOISE; COMPRESSED SENSING; DENSITY EVOLUTION; NON-GAUSSIAN; NON-GAUSSIAN ESTIMATION;

BIOLOGY; ESTIMATION; GAUSSIAN DISTRIBUTION; INFORMATION SCIENCE; SIGNAL RECONSTRUCTION;

BACKPROPAGATION;

EID: 77953688837     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CISS.2010.5464768     Document Type: Conference Paper

References (32)

1. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, CA: Morgan Kaufmann Publ., 1988.
2. M. J. Wainwright and M. I. Jordan, Graphical Models, Exponential Families, and Variational Inference, ser, Foundations and Trends in Machine Learning. Hanover, MA: NOW Publishers, 2008, vol. 1.
3. R. J. McEliece, D. J. C. MacKay, and J.-F. Cheng, "Turbo decoding as an instance of Pearl's 'belief propagation' algorithm," IEEE J. Sel. Areas Comm., vol. 16, no. 2, pp. 140-152, Feb. 1988.
4. D. J. C. MacKay, "Good error-correcting codes based on very sparse matrices," IEEE Trans. Inform. Theory, vol. 45, no. 3, pp. 399-431, Mar. 1999.
5. D. J. C. MacKay and R. M. Neal, "Near shannon limit performance of low density parity check codes," Electron. Letters, vol. 33.
6. M. Yoshida and T. Tanaka, "Analysis of sparsely-spread CDMA via statistical mechanics," in Proc. IEEE Int. Symp. Inform. Th., Seattle, WA, Jun. 2006, pp. 2378-2382.
7. G. Guo and C. C. Wang, "Multiuser detection of sparsely spread CDMA," IEEE J. Sel. Areas Comm., vol. 26, no. 3, p. 421431, Mar. 2008.
8. M. F. N. Sommer and O. Shalvi, "Low-density lattice codes," IEEE Trans. Inform. Theory, vol. 54, no. 4, pp. 1561-1585, Apr. 2008.
9. D. Baron, S. Sarvotham, and R. G. Baraniuk, "Bayesian compressive sensing via belief propagation ," IEEE Trans. Signal Process., vol. 58, no. 1, pp. 269-280, Jan. 2010.
10. D. Guo, D. Baron, and S. Shamai, "A single-letter characterization of optimal noisy compressed sensing," in Proc. 47st Ann. Allerton Conf. on Commun., Control and Comp., Monticello, IL, Sep. 2009.
11. D. L. Donoho, A. Maleki, and A. Montanari, "Message passing algorithms for compressed sensing," arXiv:0907.3574v1 [cs.IT], Jul. 2009.
12. A. Montanari and D. Tse, "Analysis of belief propagation for non-linear problems: The example of CDMA (or: How to prove Tanaka's formula)," arXiv:cs/0602028vl [cs.IT]., Feb. 2006.
13. D. Guo and C-C. Wang, "Asymptotic mean-square optimality of belief propagation for sparse linear systems," in "Proc. lnform. Th. Workshop", Chengdu, China, Oct. 2006, pp. 194-198.
14. -, "Random sparse linear systems observed via arbitrary channels: A decoupling principle," in Proc. IEEE Int. Symp. Inform. Th., Nice, France, Jun. 2007, pp. 946-950.
15. T. Tanaka, "A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors," IEEE Trans. Inform. Theory, vol. 48, no. 11, pp. 2888-2910, Nov. 2002.
16. D. Guo and S. Verdii, "Randomly spread CDMA: Asymptotics via statistical physics," IEEE Trans. Inform. Theory, vol. 51, no. 6, pp. 1983-2010, Jun. 2005.
17. Y. Kabashima, "A CDMA multiuser detection algorithm on the basis of belief propagation," J. Phys. A: Math. Gen, vol. 36.
18. T. Tanaka and M. Okada, "Approximate belief propagation, density evolution, and neurodynamics for CDMA multiuser detection," IEEE Trans. Inform. Theory, vol. 51, no. 2, pp. 700-706, Feb. 2005.
19. J. P. Neirotti and D. Saad, " Improved message passing for inference in densely connected systems," Europhys. Lett., vol. 71, no. 5, p. 866872, Sep. 2005.
20. S.-Y. Chung, T. J. Richardson, and R. L. Urbanke, "Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation," IEEE Trans. Inform. Theory, vol. 47, no. 2, pp. 657-670, Feb. 2001.
21. L. R. Varshney, "Performance of LDPC codes under noisy message-passing decoding," in Proc. Inform. Th. Workshop, Lake Tahoe, CA, Sep. 2007, pp. 178-183.
22. S. Rangan, "Estimation with random linear mixing, belief propagation and compressed sensing," arXiv:1001.2228v1 [cs.IT]., Jan. 2010.
23. M. Bayati and A. Montanari, "The dynamics of message passing on dense graphs, with applications to compressed sensing," arXiv:1001.3448v1 [cs.IT], Jan. 2010.
24. S. Rangan, A. Fletcher, and V. K. Goyal, "Asymptotic analysis of MAP estimation via the replica method and applications to compressed sensing," arXiv:0906.3234v2 [cs.lT]., Aug. 2009.
25. p-norm minimization," arXiv:0907.0914 [cs.IT]., Jun. 2009.
26. D. L. Donoho, "Compressed sensing," IEEE Trans. Inform. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
27. E. J. Candès and T. Tao, "Near-optimal signal recovery from random projections: Universal encoding strategies?" IEEE Trans. Inform. Theory, vol. 52, no. 12, pp. 5406-5425, Dec. 2006.
28. R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Royal Stat. Soc., Ser. B, vol. 58, no. 1, pp. 267-288, 1996.
29. 2 )," IEEE Trans. Signal Process., vol. 42, no. 1, pp. 200-203, Jan. 1994.
30. -, "Lower bound on the mean-squared error in oversampled quantization of periodic signals using vector quantization analysis," IEEE Trans. Inform. Theory, vol. 42, no. 2, pp. 469-479, Mar. 1996.
31. Z. Cvetković, "Source coding with quantized redundant expansions: Accuracy and reconstruction," in Proc. IEEE Data Compression Conf., Snowbird, Utah, Mar. 1999, pp. 344-353.
32. S. Rangan and V. K. Goyal, "Recursive consistent estimation with bounded noise," IEEE Trans. Inform. Theory, vol. 47, no. 1, pp. 457-464, Jan. 2001.