Adjacent-Bits-Swapped Polar Codes: A New Code Construction to Speed up Polarization
Adjacent-Bits-Swapped Polar Codes: A New Code Construction to Speed up Polarization
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相邻位交换极性码：一种加速极化的新码结构
DOI：
10.1109/tit.2022.3228862
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发表时间：
2022
影响因子：
2.5
通讯作者：
Sihuang Hu
中科院分区：
文献类型：
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作者：
Guodong Li;Min Ye;Sihuang Hu
具有码长<inline-formula><tex-math notation="LaTeX">$n=2^{m}$的</tex-math></inline-formula>极化码的构造涉及<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula>层的极化变换。在本文中，我们观察到，在每一层极坐标变换之后，可以交换某些相邻位对以加速极化过程。更准确地说，如果在连续解码器下，前一位比其下一位更可靠，则切换这两个相邻位的解码顺序将使可靠位更加可靠，并且噪声位更加噪声。基于这一观察，我们提出了一个新的家庭的代码称为相邻位交换（ABS）极化码。在ABS极化码的构造中，我们在每个极化变换层之后添加置换层。为了选择在置换层中交换哪些相邻比特对，我们依赖于一种新的极坐标变换，该变换将两个独立的通道与4进制输入相结合。这种新的极化变换允许我们通过不同层的极化变换来跟踪每对相邻比特的演变，并且它在ABS极化码的连续消除列表（SCL）解码器中也起着至关重要的作用。广泛的仿真结果表明，ABS极化码始终优于标准极化码<inline-formula><tex-math notation="LaTeX">的0.15\mathop {\mathrm {dB}}\nolimits $</tex-math></inline-formula>-<inline-formula><tex-math notation="LaTeX">0.3\mathrm {dB}\nolimits $时</tex-math></inline-formula>，我们使用CRC辅助SCL解码器与列表大小为32的两个代码。本文中所有算法的实现都可以在<monospace><uri>https://github.com/PlumJelly/ABS-Polar</uri></monospace>上获得
The construction of polar codes with code length <inline-formula> <tex-math notation="LaTeX">$n=2^{m}$ </tex-math></inline-formula> involves <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> layers of polar transforms. In this paper, we observe that after each layer of polar transforms, one can swap certain pairs of adjacent bits to accelerate the polarization process. More precisely, if the previous bit is more reliable than its next bit under the successive decoder, then switching the decoding order of these two adjacent bits will make the reliable bit even more reliable and the noisy bit even noisier. Based on this observation, we propose a new family of codes called the Adjacent-Bits-Swapped (ABS) polar codes. We add a permutation layer after each polar transform layer in the construction of the ABS polar codes. In order to choose which pairs of adjacent bits to swap in the permutation layers, we rely on a new polar transform that combines two independent channels with 4-ary inputs. This new polar transform allows us to track the evolution of every pair of adjacent bits through different layers of polar transforms, and it also plays an essential role in the successive cancellation list (SCL) decoder for the ABS polar codes. Extensive simulation results show that ABS polar codes consistently outperform standard polar codes by <inline-formula> <tex-math notation="LaTeX">$0.15 \mathop {\mathrm {dB}}\nolimits $ </tex-math></inline-formula>—<inline-formula> <tex-math notation="LaTeX">$0.3 \mathop {\mathrm {dB}}\nolimits $ </tex-math></inline-formula> when we use CRC-aided SCL decoder with list size 32 for both codes. The implementations of all the algorithms in this paper are available at <monospace><uri>https://github.com/PlumJelly/ABS-Polar</uri></monospace>
BEC 和 BSC 通道上 Reed-Muller 码的近乎最优缩放
DOI：
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发表时间：
2018
期刊：
2018 IEEE Int. Symp. Inf. Theory (ISIT
影响因子：
--
作者：
Hassani, Hamed;Kudekar, Shrinivas;Ordentlich, Or;Polyanskiy, Yury;Urbanke, Rudiger
通讯作者：
Urbanke, Rudiger
使用冗余代码约束解码 Reed Muller 代码
DOI：
10.1109/isit44484.2020.9174087
发表时间：
2020
期刊：
2020 IEEE International Symposium on Information Theory (ISIT
影响因子：
--
作者：
Lian, Mengke;Hager, Christian;Pfister, Henry D.
通讯作者：
Pfister, Henry D.
DOI：
--
发表时间：
2022
期刊：
and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022
影响因子：
--
作者：
Duursma, I. M.;Gabrys, R.;Guruswami, Venkatesan;Lin, T. and
通讯作者：
Lin, T. and