偶联LDPC链增长率的近似解
Near concavity of the growth rate for coupled LDPC chains
摘要：
卷积低密度奇偶校验（LDPC）集成具有优异的性能。它们的迭代阈值随着它们的平均度或随机构造中的耦合窗口的大小而增加。在后一种情况下，随着窗口大小的增长，置信传播（BP）阈值达到底层集合的最大后验（MAP）阈值。在这方面的贡献，我们表明，一个类似的现象发生的增长率耦合合奏。粗略地说，我们观察到，随着耦合强度的增长，耦合系综的增长率接近底层系综增长率的凹壳。对于跨窗口随机耦合的系综，随着窗口大小的增加，增长率实际上趋向于底层系综的凹壳。我们的观察得到支持的组合增长率的计算，并从副本方法的增长率。所观察到的辐射是耦合平均场图形模型的一般特征，并且已经存在于耦合居里-外斯模型的水平上。在那里，耦合系统的正则自由能趋向于下一个系统的凹壳。正如我们所解释的，耦合系综的增长率行为完全类似。
英文摘要：
Convolutional Low-Density-Parity-Check (LDPC) ensembles have excellent performance. Their iterative threshold increases with their average degree, or with the size of the coupling window in randomized constructions. In the later case, as the window size grows, the Belief Propagation (BP) threshold attains the maximum-a-posteriori (MAP) threshold of the underlying ensemble. In this contribution we show that a similar phenomenon happens for the growth rate of coupled ensembles. Loosely speaking, we observe that as the coupling strength grows, the growth rate of the coupled ensemble comes close to the concave hull of the underlying ensemble's growth rate. For ensembles randomly coupled across a window the growth rate actually tends to the concave hull of the underlying one as the window size increases. Our observations are supported by the calculations of the combinatorial growth rate, and that of the growth rate derived from the replica method. The observed concavity is a general feature of coupled mean field graphical models and is already present at the level of coupled Curie-Weiss models. There, the canonical free energy of the coupled system tends to the concave hull of the underlying one. As we explain, the behavior of the growth rate of coupled ensembles is exactly analogous.
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