ABS+ Polar Codes: Exploiting More Linear Transforms on Adjacent Bits
ABS+ Polar Codes: Exploiting More Linear Transforms on Adjacent Bits
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DOI：
10.1109/tit.2023.3331522
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发表时间：
2022-09
影响因子：
2.5
通讯作者：
Guodong Li;Min Ye;Sihuang Hu
中科院分区：
文献类型：
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作者：
Guodong Li;Min Ye;Sihuang Hu
ABS极性码是最近提出的，通过在每一层极坐标变换之后交换某些相邻比特对来加速极化。在本文中，我们观察到在每个极变换层之后对某些相邻比特对应用ArıKan变换$(U_{i}，U_{i+1})\mapsto(U_{i}+U_{i+1}，U_{i+1})$会导致更快的极化。有鉴于此，我们提出了ABS+极性码，它除了在ABS极性码中进行交换变换外，还结合了ArıKan变换。为了有效地构造和译码ABS+极性码，我们通过不同层次的极变换推导出了相邻比特联合分布之间的一种新的递归关系。仿真结果表明，在译码时间不变的情况下，CRC辅助的ABS+极坐标译码算法比ABS极坐标译码算法提高了$0.1\mathop{\mathom{db}}\noLimits$-$0.25\mathop{\mathom{db}}\noLimits$。此外，当ABS+极坐标译码都使用列表大小为32的CRC辅助SCL译码时，ABS+极坐标编码比标准极坐标译码提高了$0.2\mathop{\mathm{db}}\NoLimits$-$0.45\mathop{\mathm{db}}\noLimits$。本文中所有算法的实现都可以在https://github.com/PlumJelly/ABS-Polar上获得
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 Arıkan 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 Arıkan 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 $0.1 \mathop {\mathrm {dB}}\nolimits $ – $0.25 \mathop {\mathrm {dB}}\nolimits $ while maintaining the same decoding time. Moreover, ABS+ polar codes improve upon standard polar codes by $0.2 \mathop {\mathrm {dB}}\nolimits $ – $0.45 \mathop {\mathrm {dB}}\nolimits $ 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