ABS+极地代码:在相邻的位子上利用更多的线性变换 (ABS+ Polar Codes: Exploiting More Linear Transforms on Adjacent Bits)

from arxiv, The implementations of all the algorithms in this paper are available at https://github.com/PlumJelly/ABS-Polar. arXiv admin note: text overlap with arXiv:2202.04454

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

翻译：最近有人提议ABS极地代码,以便在每层极变后互换某些相邻的相片,以加速两极分化。在本文中,我们观察到应用Arikan变换$(U_i,U ⁇ i+1})\mapsto(U ⁇ í ⁇ U ⁇ i+1},U ⁇ i+1})对每极变换层后,某些相邻的相邻部分(U ⁇ í ⁇ u ⁇ i ⁇ i+1})来加速两极分化。有鉴于此,我们提议ABS+极地代码,除了交换ABS极变换码外,还包含Arikan变换码。为了高效地构建和解码ABS+极代码,我们发现通过不同层变换换的相邻部分联合分布之间的新循环关系。一系列参数的模拟结果显示, ABS&极值的 CRC SCL 解码比AB 的解码改进了0. 1dJ- 0.25 dB, 同时保持相同的解码时间。此外, ABS+极值的代码在标准极值代码上改进了0.20B-P-OB_0.45B/CAL 使用这个可用的 SC- SAAL CD- dL 。当它们使用这个可用的时, SAL 时, 在 SAL 的 SAL SAD 的的的和 SAD SAL SAL 的 SAD 的的。