Computer Science – Information Theory
Scientific paper
2011-05-04
Computer Science
Information Theory
In proceedings of ITW 2010
Scientific paper
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. We always find, based on analytical as well as numerical calculations, that the message passing thresholds of the coupled systems come very close to the static ones of the individual models. The remarkable properties of convolutional low-density parity-check codes are a manifestation of this very general phenomenon.
Hassani Steven H.
Macris Nicolas
Urbanke Ruediger
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