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首页> 外文期刊>IEEE Transactions on Information Theory >Spatial Coupling as a Proof Technique and Three Applications
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Spatial Coupling as a Proof Technique and Three Applications

机译：空间耦合作为证明技术及三种应用

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The aim of this paper is to show that spatial coupling can be viewed not only as a means to build better graphical models, but also as a tool to better understand uncoupled models. The starting point is the observation that some asymptotic properties of graphical models are easier to prove in the case of spatial coupling. In such cases, one can then use the so-called interpolation method to transfer known results for the spatially coupled case to the uncoupled one. Our main use of this framework is for Low-density parity check (LDPC) codes, where we use interpolation to show that the average entropy of the codeword conditioned on the observation is asymptotically the same for spatially coupled as for uncoupled ensembles. We give three applications of this result for a large class of LDPC ensembles. The first one is a proof of the so-called Maxwell construction stating that the MAP threshold is equal to the area threshold of the BP GEXIT curve. The second is a proof of the equality between the BP and MAP GEXIT curves above the MAP threshold. The third application is the intimately related fact that the replica symmetric formula for the conditional entropy in the infinite block length limit is exact.
机译：本文的目的是表明，空间耦合不仅可以被视为构建更好的图形模型的手段，而且可以被视为更好地理解未耦合模型的工具。起点是观察到，在空间耦合的情况下，图形模型的某些渐近性质更容易证明。在这种情况下，然后可以使用所谓的插值方法将空间耦合情况下的已知结果传递给非耦合情况。这个框架的主要用途是用于低密度奇偶校验（LDPC）码，在此我们使用插值法来表明，以条件为条件的码字的平均熵在空间耦合和未耦合合奏上渐近相同。对于大型LDPC集成，我们给出了此结果的三个应用。第一个证明是所谓的麦克斯韦构造，证明MAP阈值等于BP GEXIT曲线的面积阈值。第二个是高于MAP阈值的BP和MAP GEXIT曲线之间相等性的证明。第三个应用是密切相关的事实，即无限块长度限制中的条件熵的副本对称公式是精确的。

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