For serially or parallel concatenated communication systems, spatial coupling techniques enable to improve the threshold of these systems under iterative decoding using belief propagation (BP). For the case of low-density parity-check (LDPC) codes, it has been shown that, under some asymptotic assumptions, spatially coupled ensembles have BP thresholds that approach the bitwise maximum a posteriori (MAP) threshold of the related uncoupled ensemble. This phenomenon is often referred to as threshold saturation, and it has sometimes very important consequences. For example, in the case of regular LDPC code ensembles, spatial coupling enables to achieve asymptotically the capacity for any class of binary memoryless symmetric channels. Since then, this threshold saturation has been conjectured or proved for several other types of concatenations. In this work, we consider a serially concatenated scheme which is the serial concatenation of a simple outer convolutional code and a continuous phase modulator (CPM) separated by an interleaver. Then, we propose a method to do the spatial coupling of several replicas of this serially concatenated scheme, aiming to improve the asymptotic convergence threshold. First, exploiting the specific structure of the proposed system, an original procedure is proposed in order to terminate the spatially coupled turbo-coded CPM scheme. In particular, the proposed procedure aims to ensure the continuity of the transmitted signal among spatially coupled replicas, enabling to keep one of the core characteristics and advantages of coded CPM schemes. Then, based on an asymptotic analysis, we show that the proposed scheme has very competitive thresholds when compared to carefully designed spatially coupled LDPC codes. Furthermore, it is shown how we can accelerate the convergence rate of the designed systems by optimizing the connection distributions in the coupling matrices. Finally, by investigating on different continuous phase modulation schemes, we corroborate the conjecture stating that spatially coupled turbo-coded CPM schemes saturate to a lower bound very close to the threshold given by the extrinsic information transfer (EXIT) area theorem.

对于串行或并行级联的通信系统，空间耦合技术能够在使用置信传播（BP）进行迭代解码的情况下提高这些系统的阈值。对于低密度奇偶校验（LDPC）码的情况，已经表明，在某些渐近假设下，空间耦合合奏的BP阈值接近相关非耦合合奏的按位最大后验（MAP）阈值。这种现象通常称为阈值饱和，有时会产生非常重要的后果。例如，在常规LDPC码集合的情况下，空间耦合使得能够渐近地实现任何类别的二进制无记忆对称信道的容量。从那时起，该阈值饱和度已被推测或证明用于其他几种类型的串联。在这项工作中，我们考虑一个串行级联方案，该方案是一个简单的外部卷积码和一个由交织器分开的连续相位调制器（CPM）的串行级联。然后，我们提出了一种方法来对这种级联方案的多个副本进行空间耦合，旨在提高渐近收敛阈值。首先，利用拟议系统的特定结构，为了终止空间耦合的turbo编码的CPM方案，提出了原始过程。特别地，所提出的过程旨在确保空间耦合的副本之间的发送信号的连续性，从而能够保持编码的CPM方案的核心特征和优势之一。然后，基于渐近分析，我们表明，与精心设计的空间耦合LDPC码相比，该方案具有非常有竞争力的阈值。此外，它显示了如何通过优化耦合矩阵中的连接分布来加快设计系统的收敛速度。最后，通过研究不同的连续相位调制方案，