基于3×3高维核矩阵的终止极化码研究

doi:10.3969/j.issn.0255-8297.2021.06.009

应用科学学报 ›› 2021, Vol. 39 ›› Issue (6): 983-994.doi: 10.3969/j.issn.0255-8297.2021.06.009

基于3×3高维核矩阵的终止极化码研究

文豪, 曹阳

重庆理工大学电气与电子工程学院, 重庆 400054

收稿日期:2020-10-23 发布日期:2021-12-04
通信作者: 曹阳,教授,研究方向为光通信。E-mail:1325106406@qq.com E-mail:1325106406@qq.com
基金资助:
重庆市教委基金（No.KJ120827）；重庆市教委科学技术项目（No.KJ1500934，No.KJ1709205）；重庆市研究生科研创新项目（No.CYS18311）；重庆市基础与前沿研究计划项目（No.cstc2015jcyjA40051）资助

Research on Relaxed Polar Code Based on 3×3 High Dimensional Kernel Matrix

WEN Hao, CAO Yang

School of Electrical and Electronic Engineering, Chongqing University of Technology, Chongqing 400054, China

Received:2020-10-23 Published:2021-12-04

摘要/Abstract

摘要： 针对高维核矩阵构造的极化码中为提升纠错性能而造成的复杂度增加的问题,提出了基于3×3高维核矩阵终止极化码的构造方案。首先筛选出极化率最高的核矩阵G₅₃₁构造终止极化码,并在二进制擦除信道上证明了在不影响纠错性能的前提下终止极化码能够降低编译码计算复杂度,同时推导出终止极化码的复杂度降低比的上下界。仿真表明,终止极化码复杂度降低比与二进制擦除信道(binary erasure channel,BEC)的擦除概率有关,在擦除概率为0.5左右时,复杂度降低比最小,且目标误帧率(frame error rate,FER)越高,复杂度降低比越大,在目标误帧率为10^-5时,最高可实现71.43%的复杂度降低比。

关键词: 3×3核矩阵, 终止极化码, 完全极化码, 目标误帧率, 复杂度降低比

Abstract: Aiming at the problem of high complexity in the polarization code constructed by the high-dimensional kernel matrix to improve the error correction performance, a construction scheme based on the 3×3 high-dimensional kernel matrix terminating the polarization code is proposed. Firstly, the kernel matrix G₅₃₁ with the highest polarization rate is selected to construct a termination polarization code, and it is theoretically proved on the binary erasure channel that the termination polarization code can reduce the computational complexity of encoding and decoding without affecting the error correction performance, and derive the upper and lower bounds of the complexity reduction ratio (CRC) of terminating polarization codes at the same time. Simulation shows that the complexity reduction ratio of the termination polarization code is related to the BEC (binary erasure channel) erasure probability. When the erasure probability is about 0.5, the complexity reduction ratio reaches the smallest, and the higher the target frame error rate (FER), the greater the complexity reduction ratio. When the FER is 10^-5, the highest complexity reduction rate of 71.43% can be achieved.

Key words: 3×3 kernel matrix, relaxed polar codes, full polar codes, target frame error rate, complexity reduction ratio (CRC)

中图分类号:

TN911.22

文豪, 曹阳. 基于3×3高维核矩阵的终止极化码研究[J]. 应用科学学报, 2021, 39(6): 983-994.

WEN Hao, CAO Yang. Research on Relaxed Polar Code Based on 3×3 High Dimensional Kernel Matrix[J]. Journal of Applied Sciences, 2021, 39(6): 983-994.

参考文献

[1] Arikan E. Channel polarization:a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels[J]. IEEE Transactions on Information Theory, 2009, 55(7):3051-3073.
[2] Korada S B, Sasoglu E, Urbanke R. Polar codes:characterization of exponent, bounds, and constructions[J]. IEEE Transactions on Information Theory, 2009, 56(12):6253-6264.
[3] Jin S, Liu J, Wang Z. Improved BP decoder for polar codes based on a modified kernel matrix[J]. Electronics Letters, 2016, 52(24):1982-1984.
[4] Liu Z, Kai N, Chao D, et al. Performance analysis of polar codes based on 3×3 kernel matrix[C]//International Conference on Communications & Networking in China. IEEE, 2016:382-386.
[5] Korada S B, Sasoglu E. A class of transformations that polarize symmetric binary-input memoryless channels[J]. Proceedings of the 2009 IEEE International Conference on Symposium on Information Theory, 2009, 3:1478-1482.
[6] Liang Z, Zhang Z, Wang X. Polar code with block-length N=3n[C]//International Conference on Wireless Communications & Signal Processing. IEEE, 2012:1-6.
[7] Mori R, Tanaka T. Channel polarization on q-ary discrete memoryless channels by arbitrary kernels[C]//2010 IEEE International Symposium on Information Theory. IEEE, 2010:894-898.
[8] Mori R, Tanaka T. Non-binary polar codes using Reed-Solomon codes and algebraic geometry codes[C]//2010 IEEE Information Theory Workshop. Dublin, 2010:1-5.
[9] Serbetci B, Pusane A E. On the selection of generator matrices for polar coded communication systems[C]//Signal Processing & Communications Applications Conference. IEEE, 2012:1-4.
[10] Mori R, Tanaka T. Performance of polar codes with the construction using density evolution[J]. IEEE Communications Letters, 2009, 13(7):519-521.
[11] Wu D, Li Y, Sun Y. Construction and block error rate analysis of polar codes over AWGN channel based on Gaussian approximation[J]. IEEE Communications Letters, 2014, 18(7):1099- 1102.
[12] 张施怡, 黄志亮, 周水红, 等. 一种基于蒙特卡洛的快速极化码构造方法[J]. 计算机工程, 2019, 45(9):76-81. Zhang S Y, Huang Z L, Zhou S H, et al. A Monte Carlo-based fast polarization code construction method[J]. Computer Engineering, 2019, 45(9):76-81. (in Chinese)
[13] 曹阳, 李岳, 李小红. 无线光通信中极化码构造方法研究[J]. 光学学报, 2020, 40(21):1-14. Cao Y, Li Y, Li X H. Research on polarization code construction method in wireless optical communication[J]. Acta Optica Sinica, 2020, 40(21):1-14. (in Chinese)
[14] El-Khamy M, Mahdavifar H, Feygin G, et al. Relaxed channel polarization for reduced complexity polar coding[C]//2015 IEEE Wireless Communications and Networking Conference (WCNC), 2015:207-212.
[15] El-Khamy M, Mahdavifar H, Feygin G, et al. Relaxed polar codes[J]. IEEE Transactions on Information Theory, 2017, 63(4):1986-2000.
[16] Cao Y, Zhang H, Tu Q. Decoding performance analysis of good-channel relaxed polar codes with 3×3 kernel matrix[J]. IET Communications, 2019, 13(8):1131-1139.

基于3×3高维核矩阵的终止极化码研究

Research on Relaxed Polar Code Based on 3×3 High Dimensional Kernel Matrix

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	吴韵清, 吴鹏, 陈北京, 鞠兴旺, 高野. 基于残差全卷积网络的图像拼接定位算法[J]. 应用科学学报, 2019, 37(5): 651-662.
[2]	李坤, 吴绍华, 高翔, 张钦宇. 基于凿孔的系统极化码编码协作[J]. 应用科学学报, 2017, 35(2): 139-148.
[3]	张顺外，仰枫帆，唐蕾. 网络编码的LDPC编码协作[J]. 应用科学学报, 2014, 32(3): 251-256.
[4]	巫光福，王琳. 一种短小的高码率LDPC 码设计[J]. 应用科学学报, 2013, 31(6): 559-563.
[5]	古强1，许小东1，蒋轶2，戴旭初1. 适合传输三路数据流的最小距离MIMO 预编码[J]. 应用科学学报, 2013, 31(2): 135-141.
[6]	宋磊1，李立华1，高向川2，裴郁杉1，王化磊1. 不精确帧同步对幅值相位线性插值影响的分析[J]. 应用科学学报, 2012, 30(5): 441-447.
[7]	庞宝茂1;2，史浩山1，何光华3. 多元LDPC随机译码的似然概率快速生成算法[J]. 应用科学学报, 2012, 30(3): 234-238.
[8]	肖旻，黎勇，王琳. 码率自适应LDPC码删余算法[J]. 应用科学学报, 2011, 29(4): 385-389.
[9]	高献坤，崔岩，傅洪亮. 连续迭代优化SLNR准则的下行多用户MIMO预编码[J]. 应用科学学报, 2011, 29(3): 251-255.
[10]	张小军1，田应洪1，余磊1，冉峰2，赖宗声1. 针对LDPC码的伸缩因子量化方案[J]. 应用科学学报, 2011, 29(1): 33-38.
[11]	范俊1，肖扬2. 可快速编码的准循环LDPC码设计[J]. 应用科学学报, 2010, 28(1): 1-8.
[12]	许拔1，张仲明1，何英亮2，张尔扬1. GF(q)域上LDPC码的改进扩展最小和译码算法[J]. 应用科学学报, 2010, 28(1): 9-13.
[13]	管武董明科项海格. 应用循环移位矩阵设计LDPC码译码器[J]. 应用科学学报, 2009, 27(2): 117-123.
[14]	李晋, 徐晓东, 姜明, 尤肖虎. PCGC码低复杂度译码算法的研究[J]. 应用科学学报, 2005, 23(2): 140-143.
[15]	唐朝京, 刘东华. 基于二次同余映射交织器设计的改进[J]. 应用科学学报, 2002, 20(3): 246-250.