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The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems.
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2009
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2009
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N. Merhav, “Physics of the Shannon limits,” arXiv:0903.1484 [cs.IT]., Mar. 2009
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2009
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M. J. Wainwright, “Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting,” IEEE Trans. Inform. Theory , vol. 55, no. 12, pp. 5728–5741, Dec. 2009
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2010
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S. Rangan, “Estimation with random linear mixing, belief propagation and compressed sensing,” in Proc. Conf. on Inform. Sci. & Sys. , Princeton, NJ, Mar. 2010, pp. 1–6
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N. Merhav, D. Guo, and S. Shamai, “Statistical physics of signal estimation in Gaussian noise: Theory and examples of phase transitions,” IEEE Trans. Inform. Theory , vol. 56, no. 3, pp. 1400–1416, 2010
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M. Akçakaya and V. Tarokh, “Shannon-theoretic limits on noisy compressive sampling,” IEEE Trans. Inform. Theory , vol. 56, no. 1, pp. 492–504, Jan. 2010
2010
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S. Aeron, V. Saligrama, and M. Zhao, “Information theoretic bounds for compressed sensing,” IEEE Trans. Inform. Theory , vol. 56, no. 10, pp. 5111–5130, Oct. 2010
2010
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M. Bayati and A. Montanari, “The dynamics of message passing on dense graphs, with applications to compressed sensing,” IEEE Trans. Inform. Theory , vol. 57, no. 2, pp. 764–785, Feb. 2011
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2011
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G. Caire, S. Shamai, A. Tulino, and S. Verdú, “Support recovery in compressed sensing: Information-theoretic bounds,” in Proc. UCSD Workshop Inform. Theory & Its Applications , La Jolla, CA, Jan. 2011
2011
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V. Saligrama and M. Zhao, “Thresholded basis pursuit: LP algorithm for oder-wise optimal support recovery for sparse and approximately sparse signals from noisy measurements,” IEEE Trans. Inform. Theory , vol. 57, no. 3, pp. 1567–1586, Mar. 2011
2011
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