空间耦合异向编织分析
Analysis of Spatially-Coupled Counter Braids
摘要：
计数器辫（CB）是Lu等人在2007年提出的一种新型计数器架构，用于高速链路上的每流测量。CB实现与流大小分布的熵下限相匹配的渐近压缩率（在最优解码下）。最近提出了空间耦合CB（SC-CB）。在这项工作中，我们进一步分析了单层CB和SC-CB使用等价的二分图表示的CB。在这个等价的表示，我们表明，潜在的和面积阈值是相等的。我们还表明，在扩展的信念传播（BP）的外部信息传递曲线（定义的等效图），计算预期的残留CB图时，剥离解码器相当于BP解码器停止，精确地等于零的面积阈值。这一点，结合模拟和渐近分析的麦克斯韦解码器，导致猜想的面积阈值实际上是等于麦克斯韦解码阈值，因此最大后验概率（MAP）解码阈值的下限。最后，我们提出了一些数值结果，并给出了一些洞察到SC-CB的BP解码阈值的明显差距的MAP解码阈值的简化的下限。
英文摘要：
A counter braid (CB) is a novel counter architecture introduced by Lu et al. in 2007 for per-flow measurements on high-speed links. CBs achieve an asymptotic compression rate (under optimal decoding) that matches the entropy lower bound of the flow size distribution. Spatially-coupled CBs (SC-CBs) have recently been proposed. In this work, we further analyze single-layer CBs and SC-CBs using an equivalent bipartite graph representation of CBs. On this equivalent representation, we show that the potential and area thresholds are equal. We also show that the area under the extended belief propagation (BP) extrinsic information transfer curve (defined for the equivalent graph), computed for the expected residual CB graph when a peeling decoder equivalent to the BP decoder stops, is equal to zero precisely at the area threshold. This, combined with simulations and an asymptotic analysis of the Maxwell decoder, leads to the conjecture that the area threshold is in fact equal to the Maxwell decoding threshold and hence a lower bound on the maximum a posteriori (MAP) decoding threshold. Finally, we present some numerical results and give some insight into the apparent gap of the BP decoding threshold of SC-CBs to the conjectured lower bound on the MAP decoding threshold.
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