The effect of spatial coupling on compressive sensing

2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010

Volumn , Issue , 2010, Pages 347-353

  Kudekar, Shrinivas ^a   Pfister, Henry D ^b  

^a CENTER FOR NONLINEAR STUDIES   (United States)

^b Texas A and M University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BELIEF PROPAGATION; BLOCK LENGTHS; COMPRESSED SENSING; COUPLED CODE; GENERAL CLASS; LDPC CODES; MAXIMUM A POSTERIORI DECODING; MAXIMUM VALUES; MEMORYLESS; RECONSTRUCTION ALGORITHMS; SHANNON CAPACITY; SPATIAL COUPLINGS; THRESHOLD ANALYSIS;

ALGORITHMS; CODING ERRORS; DECODING;

SIGNAL RECONSTRUCTION;

EID: 79952426734     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ALLERTON.2010.5706927     Document Type: Conference Paper

References (47)

1. S. Kudekar, T. Richardson, and R. Urbanke, "Threshold saturation via spatial coupling: Why convolutional LDPC ensembles perform so well over the BEC," 2010, e-print: http://arxiv.org/abs/1001.1826.
2. A. J. Felström and K. S. Zigangirov, "Time-varying periodic convolutional codes with low-density parity-check matrix," IEEE Trans. Inform. Theory, vol. 45, no. 5, pp. 2181-2190, Sept. 1999.
3. K. Engdahl and K. S. Zigangirov, "On the theory of low density convolutional codes I," Problemy Peredachi Informatsii, vol. 35, no. 4, pp. 295-310, 1999.
4. K. Engdahl, M. Lentmaier, and K. S. Zigangirov, "On the theory of low-density convolutional codes," in AAECC-13: Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. London, UK: Springer-Verlag, 1999, pp. 77-86.
5. M. Lentmaier, D. V. Truhachev, and K. S. Zigangirov, "To the theory of low-density convolutional codes. II," Probl. Inf. Transm., vol. 37, no. 4, pp. 288-306, 2001.
6. R. M. Tanner, D. Sridhara, A. Sridharan, T. E. Fuja, and D. J. Costello, Jr., "LDPC block and convolutional codes based on circulant matrices," IEEE Trans. Inform. Theory, vol. 50, no. 12, pp. 2966-2984, Dec. 2004.
7. A. Sridharan, M. Lentmaier, D. J. Costello, Jr., and K. S. Zigangirov, "Convergence analysis of a class of LDPC convolutional codes for the erasure channel," in Proc. of the Allerton Conf. on Commun., Control, and Computing, Monticello, IL, USA, Oct. 2004.
8. M. Lentmaier, A. Sridharan, K. S. Zigangirov, and D. J. Costello, Jr., "Terminated LDPC convolutional codes with thresholds close to capacity," in Proc. of the IEEE Int. Symposium on Inform. Theory, Adelaide, Australia, Sept. 2005.
9. -, "Iterative decoding threshold analysis for LDPC convolutional codes," IEEE Trans. Info. Theory, Oct. 2010.
10. D. G. M. Mitchell, A. E. Pusane, K. S. Zigangirov, and D. J. Costello, Jr., "Asymptotically good LDPC convolutional codes based on protographs," in Proc. of the IEEE Int. Symposium on Inform. Theory, Toronto, CA, July 2008, pp. 1030-1034.
11. M. Lentmaier, G. P. Fettweis, K. S. Zigangirov, and D. J. Costello, Jr., "Approaching capacity with asymptotically regular LDPC codes," in Information Theory and Applications, San Diego, USA, Feb. 8-Feb. 13, 2009, pp. 173-177.
12. R. Smarandache, A. Pusane, P. Vontobel, and D. J. Costello, Jr., "Pseudo-codewords in LDPC convolutional codes," in Proc. of the IEEE Int. Symposium on Inform. Theory, Seattle,WA, USA, July 2006, pp. 1364-1368.
13. -, "Pseudocodeword performance analysis for LDPC convolutional codes," IEEE Trans. Inform. Theory, vol. 55, no. 6, pp. 2577-2598, June 2009.
14. M. Papaleo, A. Iyengar, P. Siegel, J. Wolf, and G. Corazza, "Windowed erasure decoding of LDPC convolutional codes," in Proc. of the IEEE Inform. Theory Workshop, Cairo, Egypt, Jan. 2010, pp. 78-82.
15. M. Lentmaier and G. P. Fettweis, "On the thresholds of generalized LDPC convolutional codes based on protographs," in Proc. of the IEEE Int. Symposium on Inform. Theory, Austin, USA, 2010.
16. S. Kudekar, C. Méasson, T. Richardson, and R. Urbanke, "Threshold saturation on BMS channels via spatial coupling," Sept. 2010, 6th International Symposium on Turbo Codes and Iterative Information Processing.
17. M. Lentmaier, D. G. M. Mitchell, G. P. Fettweis, and D. J. Costello, Jr., "Asymptotically good LDPC convolutional codes with AWGN channel thresholds close to the Shannon limit," Sept. 2010, 6th International Symposium on Turbo Codes and Iterative Information Processing.
18. S. Chen, D. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comp., vol. 20, no. 1, pp. 33-61, 1998.
19. I. Gorodnitsky and B. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," Signal Processing, IEEE Transactions on, vol. 45, no. 3, pp. 600-616, 2002.
20. S. Cotter, B. Rao, K. Engan, and K. Kreutz-Delgado, "Sparse solutions to linear inverse problems with multiple measurement vectors," IEEE Trans. Signal Processing, vol. 53, no. 7, pp. 2477-2488, 2005.
21. D. L. Donoho, "Compressed sensing," IEEE Trans. Inform. Theory, vol. 52, no. 4, pp. 1289-1306, 2006.
22. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inform. Theory, vol. 52, no. 2, pp. 489-509, 2006.
23. A. Gilbert, S. Muthukrishnan, and M. Strauss, "Approximation of functions over redundant dictionaries using coherence." SODA, 2003.
24. G. Cormode and S. Muthukrishnan, "An improved data stream summary: the count-min sketch and its applications," Journal of Algorithms, vol. 55, no. 1, p. 75, 2005.
25. A. C. Gilbert, M. J. Strauss, J. A. Tropp, and R. Vershynin, "One sketch for all: Fast algorithms for compressed sensing," in in Proceedings of the ACM Symposium on the Theory of Computing (STOC 2007), 2007.
26. A. Cohen, W. Dahmen, and R. DeVore, "Compressed sensing and best k-term approximation," RWTH-Aachen IGPM, Tech. Rep., July 2006.
27. W. Johnson and J. Lindenstrauss, "Extensions of lipschitz maps into hilbert space," Contemp. Math., vol. 26, pp. 189-206, 1984.
28. E. D. Gluskin, "Norms of random matrices and widths of finite-dimensional sets," Math. USSR Sbornik, vol. 48, pp. 173-182, 1984.
29. S. Sarvotham, D. Baron, and R. G. Baraniuk, "Sudocodes-fast measurement and reconstruction of sparse signals," pp. 2804-2808, July 2006.
30. W. Xu and B. Hassibi, "Efficient compressive sensing with deterministic guarantees using expander graphs," in Proc. IEEE Inform. Theory Workshop, Lake Tahoe, CA, Sept. 2007, pp. 414-419.
31. F. Zhang and H. D. Pfister, "Compressed sensing and linear codes over real numbers," in Proc. 3rd Annual Workshop on Inform. Theory and its Appl., San Diego, CA, Feb. 2008.
32. S. Sarvotham, D. Baron, and R. Baraniuk, "Compressed sensing reconstruction via belief propagation," Rice University, Tech. Rep. ECE-06-01, July 2006.
33. W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," 2008. [Online]. Available: http://arxiv.org/abs/ 0803.0811
34. D. Donoho, A. Maleki, and A. Montanari, "Message-passing algorithms for compressed sensing: I. motivation and construction," in Proc. IEEE Inform. Theory Workshop, Cairo, Egypt, Jan. 2010.
35. -, "Message-passing algorithms for compressed sensing," Proc. Natl. Acad. Sci. USA, vol. 106, no. 45, pp. 18 914-18 919, 2009.
36. -, "Online supplement to message-passing algorithms for compressed sensing," Proc. Natl. Acad. Sci. USA, vol. 106, no. 45, 2009, [Online]. DOI: 10.1073/pnas.0909892106.
37. F. Zhang and H. D. Pfister, "On the iterative decoding of high rate LDPC codes with applications in compressed sensing," in Proc. 47th Annual Allerton Conf. on Commun., Control, and Comp., Monticello, IL, Sept. 2008.
38. R. Berinde, A. Gilbert, P. Indyk, H. Karloff, and M. Strauss, "Combining geometry and combinatorics: A unified approach to sparse signal recovery," 2008, pp. 798-805.
39. D. Baron, S. Sarvotham, and R. Baraniuk, "Bayesian compressive sensing via belief propagation," IEEE Trans. Signal Processing, vol. 58, no. 1, pp. 269-280, 2010.
40. M. Bayati and A. Montanari, "The dynamics of message passing on dense graphs, with applications to compressed sensing," 2010, [Online]. Available: http://arxiv.org/abs/1001.3448.
41. T. Richardson, M. A. Shokrollahi, and R. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, Feb. 2001.
42. F. Zhang and H. D. Pfister, "On the iterative decoding of high rate LDPC codes with applications in compressed sensing," 2009, submitted to IEEE Trans. on Inform. Theory also available in Arxiv preprint cs.IT/0903.2232.
43. M. Luby and M. Mitzenmacher, "Verification-based decoding for packet-based low-density parity-check codes," IEEE Trans. Inform. Theory, vol. 51, no. 1, pp. 120-127, 2005.
44. F. Zhang and H. D. Pfister, "List-message passing achieves capacity on the q-ary symmetric channel for large q," 2008, submitted to IEEE Trans. on Inform. Theory also available in Arxiv preprint cs.IT/0806.3243.
45. T. Richardson and R. Urbanke, Modern Coding Theory. Cambridge University Press, 2008.
46. D. Donoho, "High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension," Discrete and Computational Geometry, vol. 35, no. 4, pp. 617-652, 2006.
47. S. H. Hassani, N. Macris, and R. Urbanke, "Coupled graphical models and their thresholds," in Proc. of the IEEE Inform. Theory Workshop, Dublin, Ireland, Sept. 2010.