A new class of spatially-coupled turbo-like codes (SC-TCs), dubbed generalized spatially coupled parallel concatenated codes (GSC-PCCs), is introduced. These codes are constructed by applying spatial coupling on parallel concatenated codes (PCCs) with a fraction of information bits repeated qq times. GSC-PCCs can be seen as a generalization of the original spatially-coupled parallel concatenated codes proposed by Moloudi et al., 2017. To characterize the asymptotic performance of GSC-PCCs, we derive the corresponding density evolution equations and compute their decoding thresholds. The threshold saturation effect is observed and proven. Most importantly, we rigorously prove that the rate- RR GSC-PCC ensemble with 2-state convolutional component codes achieves at least a fraction 1−RR+q1-\frac {R}{R+q} of the capacity of the binary erasure channel (BEC) for repetition factor q≥2q\geq 2 and this multiplicative gap vanishes as qq tends to infinity. To the best of our knowledge, this is the first class of SC-TCs that are proven to be capacity-achieving. Further, the connection between the strength of the component codes, the decoding thresholds of GSC-PCCs, and the repetition factor is established. The superiority of the proposed codes with finite blocklength is exemplified by comparing their error performance with that of existing SC-TCs via computer simulations.

中文翻译：

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具有部分重复的广义空间耦合并行级联码


引入了一类新型空间耦合涡轮式码（SC-TC），称为广义空间耦合并行级联码（GSC-PCC）。这些代码是通过对并行级联代码 (PCC) 应用空间耦合来构造的，其中一小部分信息比特重复 qq 次。 GSC-PCC 可以看作是 Moloudi 等人于 2017 年提出的原始空间耦合并行级联码的推广。为了表征 GSC-PCC 的渐近性能，我们推导了相应的密度演化方程并计算了其解码阈值。观察并证明了阈值饱和效应。最重要的是，我们严格证明具有 2 状态卷积分量码的速率 RR GSC-PCC 系综至少实现了二进制擦除容量的一小部分 1−RR+q1-\frac {R}{R+q}重复因子 q≥2q\geq 2 的通道（BEC），并且当 qq 趋于无穷大时，该乘法间隙消失。据我们所知，这是第一类被证明能够实现能力的 SC-TC。进一步地，建立了分量码的强度、GSC-PCC的解码阈值和重复因子之间的联系。通过计算机模拟将其错误性能与现有 SC-TC 的错误性能进行比较，证明了所提出的有限块长度代码的优越性。