论文标题
基于熵的阈值证明，用于BEC上的非二进制SC-LDPC合奏
An Entropy-based Proof of Threshold Saturation for Nonbinary SC-LDPC Ensembles on the BEC
论文作者
论文摘要
在本文中，我们关注的是非二进制的空间耦合的低密度平价检查（SC-LEDPC）的集合，定义在GL $ \ left（2^{M} \右）$（GF $ \ weft（2 \ weft）$ $ M $ M $的通用线性$ $ M $）$（2 \ weft（2 \ right）$）上。我们的目的是证明当传输发生在二进制擦除通道（BEC）上时。为此，我们为非二元变量节点（VN）和校验节点（CN）卷积算子建立二元性规则，以适应非二进制密度演化（DE）分析。基于此，我们为未耦合和耦合的递归构建了潜在函数的明确形式。此外，我们表明，这些功能具有与一般二元无内存对称（BMS）通道相似的单调性属性。这导致了S. Kumar等人开发的证明技术，导致了BEC上非二元SC-LDPC集合的阈值饱和定理。
In this paper we are concerned with the asymptotic analysis of nonbinary spatially-coupled low-density parity-check (SC-LDPC) ensembles defined over GL$\left(2^{m}\right)$ (the general linear group of degree $m$ over GF$\left(2\right)$). Our purpose is to prove threshold saturation when the transmission takes place on the binary erasure channel (BEC). To this end, we establish the duality rule for entropy for nonbinary variable-node (VN) and check-node (CN) convolutional operators to accommodate the nonbinary density evolution (DE) analysis. Based on this, we construct the explicit forms of the potential functions for uncoupled and coupled DE recursions. In addition, we show that these functions exhibit similar monotonicity properties as those for binary LDPC and SC-LDPC ensembles over general binary memoryless symmetric (BMS) channels. This leads to the threshold saturation theorem and its converse for nonbinary SC-LDPC ensembles on the BEC, following the proof technique developed by S. Kumar et al.
