In this paper, we study a class of spatially coupled turbo codes, namely partially information- and partially parity-coupled turbo codes. This class of codes enjoy several advantages such as flexible code rate adjustment by varying the coupling ratio and the encoding and decoding architectures of the underlying component codes can remain unchanged. For this work, we first provide the construction methods for partially coupled turbo codes with coupling memory $m$ and study the corresponding graph models. We then derive the density evolution equations for the corresponding ensembles on the binary erasure channel to precisely compute their iterative decoding thresholds. Rate-compatible designs and their decoding thresholds are also provided, where the coupling and puncturing ratios are jointly optimized to achieve the largest decoding threshold for a given target code rate. Our results show that for a wide range of code rates, the proposed codes attain close-to-capacity performance and the decoding performance improves with increasing the coupling memory. In particular, the proposed partially parity-coupled turbo codes have thresholds within 0.0002 of the BEC capacity for rates ranging from 1/3 to 9/10, yielding an attractive way for constructing rate-compatible capacity-approaching channel codes.

中文翻译：

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部分信息和部分奇偶耦合的Turbo码的分析和设计

在本文中，我们研究了一类空间耦合的turbo码，即部分信息耦合和部分奇偶耦合的turbo码。此类代码具有多种优势，例如通过更改耦合比率来灵活地进行码率调整，并且底层组件代码的编码和解码体系结构可以保持不变。对于这项工作，我们首先提供带有耦合内存的部分耦合turbo码的构造方法 $ m $ 并研究相应的图形模型。然后，我们导出二进制擦除通道上相应集合的密度演化方程，以精确计算其迭代解码阈值。还提供了速率兼容的设计及其解码阈值，其中耦合和删余比被联合优化，以针对给定的目标码率实现最大的解码阈值。我们的结果表明，对于大范围的码率，所提出的码可达到接近容量的性能，并且随着耦合存储器的增加，解码性能也会提高。特别地，所提出的部分奇偶性耦合的turbo码具有在BEC容量的0.0002内的阈值，以用于1/3至9/10的速率，这为构造速率兼容的容量接近信道码提供了一种有吸引力的方式。