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2011

Coupled Graphical Models and Their Thresholds

Hassani, S. Hamed, Macris, Nicolas, Urbanke, Ruediger

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The excellent performance of convolutional low-density parity-check codes is the result of the spatial coupling of individual underlying codes across a window of growing size, but much smaller than the length of the individual codes.

Remarkably, the belief-propagation threshold of the coupled ensemble is boosted to the maximum-a-posteriori one of the individual system.
We investigate the generality of this phenomenon beyond coding theory: we couple general graphical models into a one-dimensional chain of large individual systems.
For the later we take the Curie-Weiss, random field Curie-Weiss, $K$-satisfiability, and $Q$-coloring models.

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Built on

J. L. Lebowitz, O. Penrose, ”Rigorous Treatment of the Van Der Waals-Maxwell Theory of the Liquid-Vapor Transition“, in J. Math. Phys
Original
1966
Earlier work this paper cites.
A. J. Felstrom, K. S. Zizangirov,“Time-varying periodic convolutional codes with low density parity check matrix” in IEEE Trans. inform. Theory
1999
Earlier work this paper cites.
K. Engdahl, K. S. Zizangirov, “On the theory of low density convolutional codes I”, in Problemy Peredachi Informatsii
1999
Earlier work this paper cites.
M. Lentmaier, D. V. Truhachev, K. S. Zizangirov, ”To the theory of low-density convolutional codes ii“, in Probl. Inf. Transm
2001
Earlier work this paper cites.

Similar

R. Mulet, A. Pagnani, M. Weigt, R. Zecchina, ”Coloring random graphs“, in Phys. rev. Lett
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M. Mézard, G. Parisi, ”The cavity method at zero temperature“, in J. Stat. Phys
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R. M Tanner, D. Sridhara, A. Sridhrara, T. E. Fuja, D. J. Costello, ”Ldpc block and convolutional codes based on circulant matrices“, in IEEE Trans. inform. Theory
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Cited alongside, same era.

Then

S. Mertens, M. Mézard, R. Zecchina, ”Threshold values of random K-SAT from the cavity method“, in Rand. Struct. and Algorithms
2006
Later among the works it cites.
M. Lentmaier, G. P. Fettweis, K. S. Zizangirov, D. J. Costello, ”Approaching capacity with asymptotically regular ldpc codes“, in Information theory and Applications
2009
Later among the works it cites.
S. Kudekar, T. Richardson, R. Urbanke, ”Threshold saturation via spatial coupling: why convolutional LDPC ensembles perform so well over the BEC“, Proc. ISIT
Original
2010
Later among the works it cites.

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