This work proposes a tractable estimation of the maximum a posteriori (MAP) threshold of various families of sparse-graph code ensembles, by using an approximation for the extended belief propagation generalized extrinsic information transfer (EBP-GEXIT) function, first proposed by Measson et al. We consider the transmission over non-binary complex-input additive white Gaussian noise channel and extend the existing results to obtain an expression for the GEXIT function. We estimate the MAP threshold by applying the Maxwell construction to the obtained approximate EBP-GEXIT charts for various families of low-density parity-check (LDPC), generalized LDPC, doubly generalized LDPC, and serially concatenated turbo codes (SC-TC). When codewords of SC-TC are modulated using Gray mapping, we also explore where the spatially-coupled belief propagation (BP) threshold is located with respect to the previously computed MAP threshold. Numerical results indicate that the BP threshold of the spatially-coupled SC-TC does saturate to the MAP threshold obtained via EBP-GEXIT chart.
翻译:这项工作提出对多种稀释代码组合的各家族的事后(MAP)最大阈值进行可移植的估计,方法是使用由Measson等人首先提议的扩展的信仰传播通用外源信息传输(EBP-GEXIT)功能近似值,对扩大的信仰传播通用外源信息传输(EBP-GEXIT)功能进行估算。我们考虑对非二进制复合合成添加添加物白高斯噪音频道的传输,扩大现有结果,以获得GEXIT功能的表达方式。我们通过对低密度等值家庭(LDPC)、通用LDPC、双倍通用LDPC和串联式涡轮代码(SC-TC)的近似值来对MAP-G-GEX的近值进行估算。当SC-TC的编码词使用灰色绘图进行调控时,我们还探索空间相混合的信仰传播阈值(BBP)与先前计算的MAP MAP阈值的位置。数值结果表明,由空间相混合的SC-TC SC-TC的BBBT-G-EX阈值通过E获得的海图向MAP 。