How to prove the Maxwell conjecture via spatial coupling - A proof of concept

IEEE International Symposium on Information Theory - Proceedings

Volumn , Issue , 2012, Pages 458-462

  Giurgiu, Andrei ^a   MacRis, Nicolas ^a   Urbanke, Rüdiger ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

CONDITIONAL ENTROPY; COUPLED CODE; INPUT-OUTPUT; INTERPOLATION METHOD; LOW DENSITY PARITY CHECK; LOW-DENSITY PARITY-CHECK (LDPC) CODES; MEMORYLESS; PROOF OF CONCEPT; SPATIAL COUPLINGS; SYMMETRIC CHANNELS;

ENTROPY; INFORMATION THEORY; POISSON DISTRIBUTION;

MAXWELL EQUATIONS;

EID: 84867542202     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2012.6284230     Document Type: Conference Paper

References (16)

1. A. J. Felström and K. S. Zigangirov, "Time-varying periodic convolutional codes with low-density parity-check matrix," IEEE Trans. Inform. Theory, vol. 45, pp. 2181-2190, Sept. 1999.
2. S. Kudekar, T. Richardson, and R. Urbanke, "Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC," IEEE Trans. Inform. Theory, vol. 57, pp. 803-834, Feb. 2011.
3. S. Kudekar, T. Richardson, and R. Urbanke, "Wave-Like Solutions of General One-Dimensional Spatially Coupled Systems." In preparation, Jan. 2012.
4. S. Kudekar and H. D. Pfister, "The effect of spatial coupling on compressive sensing," in Proc. of the Allerton Conf. on Commun., Control, and Computing, (Monticello, IL, USA), 2010.
5. Y. Sato, K. Kasai, and K. Sakaniwa, "Compressed sensing via node-based verification recovery with band sparse matrices." SITA 2011, in Japanese, 2011.
6. F. Krzakala, M. Mézard, F. Sausset, Y. Sun, and L. Zdeborova, "Statistical physics-based reconstruction in compressed sensing," CoRR, vol. abs/1109.4424, 2011.
7. D. Donoho, A. Javanmard, and A. Montanari, "Information- theoretically optimal compressed sensing via spatial coupling and approximate message passing," CoRR, vol. abs/1112.0708, 2011.
8. T. Richardson and R. Urbanke, Modern Coding Theory. Cambridge University Press, 2008.
9. N. Macris, "Sharp bounds on generalized EXIT functions," IEEE Trans. Inform. Theory, vol. 53, no. 7, pp. 2365-2375, 2007.
10. S. B. Korada, S. Kudekar, and N. Macris, "Exact solution for the conditional entropy of Poissonian LDPC codes over the Binary Erasure Channel," in Proceedings of the IEEE Int. Symp. Inf. Theory (ISIT) 2007, pp. 1016-1020, 2007.
11. M. Bayati, D. Gamarnik, and P. Tetali, "Combinatorial approach to the interpolation method and scaling limits in sparse random graphs," in Proceedings of the 42nd ACM Symp. on Theory of Comp., STOC '10, (New York, NY, USA), pp. 105-114, ACM, June 2010.
12. A. Montanari, "The glassy phase of Gallager codes," Eur. Phys. J. B, vol. 23, pp. 121-136, Sept. 2001.
13. S. Kudekar, T. Richardson, and R. Urbanke, "Spatially coupled ensembles universally achieve capacity under belief propagation." E-print arXiv:1201.2999, Jan. 2012.
14. N. Macris, "Griffith-Kelly-Sherman correlation inequalities: a useful tool in the theory of error correcting codes," IEEE Trans. Inform. Theory, vol. 53, pp. 664-683, Feb. 2007.
15. F. Guerra and F. L. Toninelli, "The high temperature region of the Viana-Bray diluted spin glass model," J. Stat. Phys., vol. 115, pp. 501-555, Apr. 2004.
16. S. H. Hassani, N. Macris, and R. L. Urbanke, "Threshold saturation in spatially coupled constraint satisfaction problems." E-print arXiv:1112.6320, Dec. 2011.