ABS+ 极化码：在相邻比特上利用更多线性变换
ABS+ Polar Codes: Exploiting More Linear Transforms on Adjacent Bits
AI总结：
本文提出ABS+极化码，在ABS极化码的交换变换基础上引入Arikan变换以加速极化，并通过新的递归关系实现高效构造与译码，相比ABS极化码和标准极化码分别获得0.1-0.25dB和0.2-0.45dB的性能提升。
摘要：
ABS 极化码最近被提出，通过在每层极化变换后交换某些相邻比特对来加速极化过程。本文观察到，在每层极化变换后，对某些相邻比特对应用 Arikan 变换 $(U_i, U_{i+1}) \mapsto (U_{i}+U_{i+1}, U_{i+1})$ 会导致更快的极化。基于此，我们提出了 ABS+ 极化码，它在 ABS 极化码的交换变换之外还引入了 Arikan 变换。为了高效地构造和译码 ABS+ 极化码，我们推导了相邻比特在不同极化变换层之间的联合分布的新的递归关系。在广泛参数范围内的仿真结果表明，ABS+ 极化码的 CRC 辅助 SCL 译码器相比 ABS 极化码的译码器有 0.1dB--0.25dB 的性能提升，同时保持相同的译码时间。此外，当两者都使用列表大小为 32 的 CRC 辅助 SCL 译码器时，ABS+ 极化码相比标准极化码有 0.2dB--0.45dB 的性能提升。本文所有算法的实现可在 https://github.com/PlumJelly/ABS-Polar 获取。
英文摘要：
ABS polar codes were recently proposed to speed up polarization by swapping certain pairs of adjacent bits after each layer of polar transform. In this paper, we observe that applying the Arikan transform $(U_i, U_{i+1}) \mapsto (U_{i}+U_{i+1}, U_{i+1})$ on certain pairs of adjacent bits after each polar transform layer leads to even faster polarization. In light of this, we propose ABS+ polar codes which incorporate the Arikan transform in addition to the swapping transform in ABS polar codes. In order to efficiently construct and decode ABS+ polar codes, we derive a new recursive relation between the joint distributions of adjacent bits through different layers of polar transforms. Simulation results over a wide range of parameters show that the CRC-aided SCL decoder of ABS+ polar codes improves upon that of ABS polar codes by 0.1dB--0.25dB while maintaining the same decoding time. Moreover, ABS+ polar codes improve upon standard polar codes by 0.2dB--0.45dB when they both use the CRC-aided SCL decoder with list size $32$. The implementations of all the algorithms in this paper are available at https://github.com/PlumJelly/ABS-Polar
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