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Spatially Coupled Hybrid Concatenated Codes

机译:空间耦合混合级联代码

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The main purpose of this paper is to make the study of spatially coupled turbo-like codes (SC-TCs) more complete by investigating the impact of spatial coupling on the thresholds of hybrid concatenated codes (HCCs). In our previous studies, we introduced some classes of SC-TCs and considered their density evolution (DE) analysis. The obtained results indicated that for a fixed coupling memory, braided convolutional codes (BCCs) have the best belief propagation (BP) thresholds among the considered classes. Besides having excellent BP thresholds, BCCs have good distance properties and their minimum distance grows linearly with block length. Similarities between BCCs and HCCs make HCCs good competitors for BCCs. This has motivated us to investigate the impact of spatial coupling on HCCs. In this paper, we introduce two spatially coupled ensembles of HCCs, referred to as Type-I SC-HCCs and Type-II SC-HCCs. Then, we derive the exact density evolution (DE) equations for the uncoupled and the coupled ensembles for the binary erasure channel (BEC). Finally, considering different component encoders, we compute the thresholds of the SC-HCC ensembles and compare them with the thresholds of BCCs for a range of different rates.
机译:本文的主要目的是通过研究空间耦合对混合级联代码(HCC)阈值的影响,使对空间耦合的类Turbo码(SC-TC)的研究更加完整。在我们以前的研究中,我们介绍了一些SC-TC类,并考虑了它们的密度演化(DE)分析。获得的结果表明,对于固定的耦合内存,在考虑的类别中,编织卷积码(BCC)具有最佳的置信传播(BP)阈值。除了具有出色的BP阈值外,BCC还具有良好的距离特性,并且其最小距离随块长度线性增长。 BCC和HCC之间的相似性使HCC成为BCC的良好竞争者。这促使我们研究空间耦合对HCC的影响。在本文中,我们介绍了HCC的两个空间耦合集合,分别称为I型SC-HCC和II型SC-HCC。然后,我们导出了二进制擦除通道(BEC)的未耦合和耦合集合的精确密度演化(DE)方程。最后,考虑不同的分量编码器,我们计算SC-HCC集成的阈值,并将它们与BCC的阈值进行比较,以得出一系列不同的速率。

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