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We establish the existence of wave-like solutions to spatially coupled graphical models which, in the large size limit, can be characterized by a one-dimensional real-valued state.
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A. Yedla, H. Pfister, and K. Narayanan, “Universality for the noisy slepian-wolf problem via spatial coupling,” in Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on , 31 2011-aug. 5 2011, pp. 2567 –2571
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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
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Y. Wu and S. Verdu, “Rényi information dimension: Fundamental limits of almost lossless analog compression,” Information Theory, IEEE Transactions on , vol. 56, no. 8, pp. 3721–3748, 2010
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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, no. 2, pp. 803–834, Feb. 2011
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C. Schlegel and D. Truhachev, “Multiple access demodulation in the lifted signal graph with spatial coupling,” in Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on , 31 2011-aug. 5 2011, pp. 2989 –2993
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F. Krzakala, M. Mézard, F. Sausset, Y. Sun, and L. Zdeborova, “Statistical physics-based reconstruction in compressed sensing,” Physical Review X , vol. 2:021005, May 2012
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A. Giurgiu, N. Macris, and R. Urbanke, “How to prove the maxwell conjecture via spatial coupling – a proof of concept,” Proc. of the IEEE Int. Symposium on Inform. Theory , July 2012
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K. Takeuchi, T. Tanaka, and T. Kawabata, “A phenomenological study on threshold improvement via spatial coupling,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences , vol. 95, no. 5, pp. 974–977, May 2012
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S. Kudekar, T. Richardson, and R. Urbanke, “Spatially coupled ensembles universally achieve capacity under belief propagation,” Information Theory, IEEE Transactions on , vol. 59, no. 12, pp. 7761–7813, Dec 2013
2013
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D. Truhachev, “Universal multiple access via spatially coupling data transmission,” in Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on , July 2013, pp. 1884–1888
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2014
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