A Puncturing Algorithm of Polar Code Based on Gaussian Approximation
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摘要: 现有的极化码打孔算法均未考虑信道构造过程对算法性能的影响，针对这一问题，该文提出一种基于高斯近似的极化码打孔算法(GAPPC)。首先将高斯近似作为极化码构造算法，分析高斯近似与打孔算法的关系，以降低信道构造输出值为目标，引入高斯修正因子，推导出改进的高斯近似函数。然后将改进的高斯近似函数引入信道构造，对极化子信道进行排序获得信道可靠性排序集合。最后依据信道容量关系确定映射规则，选出打孔比特集合和冻结比特集合，完成打孔极化码的构建。实验结果显示，在不同的码长和码率下，误帧率和误码率均获得显著降低。Abstract: The influence of channel construction process on the algorithm performance is not considered in the existing polar code puncturing algorithms. To solve this problem, a Puncturing algorithm of Polar Code based on Gaussian Approximation (GAPPC) is proposed. Firstly, using Gaussian approximation for channel construction of polar code and analyzing the relationship between Gaussian approximation and puncturing algorithm, the modified Gaussian approximation function is derived to reduce the output value of channel construction with introduced Gaussian correction factors. Then the ordered channel reliability set is obtained by ordering the polarization subchannels under the channel construction with the modified Gaussian approximation function. Finally, the mapping rule is determined according to the relationship of channel capacity, and the puncturing bit set and frozen bit set are selected so that the puncturing polar code is completed. Experimental results show that the frame error rate and bit error rate are significantly reduced under different code lengths and bit rates.
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Key words:
- Polar code /
- Rate-compatible /
- Puncturing /
- Gaussian Approximation(GA)
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表 1 GAPPC算法
输入：极化码的码长$N$，打孔后码长$M$，信息比特长度$K$，打孔比特长度$P = N - M$ (1) 使用对N长的极化码进行MGA构造，获得子信道可靠性升序集合${R_{\rm{MGA}}}$ (2) 选出无能力比特位置集合$\mathcal{Q} = \left\{ {1,2,\cdots,P} \right\}$，应用改进信道映射在编码结构中找出打孔比特位置集合$\mathcal{P}$ (3) 在${R_{\rm{MGA}}}$中除去无能力比特位置找出可靠性最低的$M - K$比特，设为剩余冻结比特集合${\mathcal{Q}^C}$ (4) 依据${\mathcal{Q}^C}$和$\mathcal{Q}$得出冻结比特集合${A^C}$和信息比特集合$A$ 
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表 2 4种算法的计算复杂度对比
打孔算法 (256, 186, 93) (512, 400, 100) (1024, 860, 512) (2048,1900,1024) LCP 2049 4609 10241 22529 WQP 2118 4720 10404 22676 BD 2049 4609 10241 22529 GAPPC 2608 5616 11880 24156
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