基于Zadoff-Chu矩阵的最优码本构造方法

李玉博; 刘胜毅; 张景景; 贾冬艳

doi:10.11959/j.issn.1000-436x.2020021

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基于Zadoff-Chu矩阵的最优码本构造方法

学术论文 | 更新时间：2024-06-05

- 基于Zadoff-Chu矩阵的最优码本构造方法
- Construction method of optimal codebook based on Zadoff-Chu matrix
- 通信学报 2020年41卷第3期页码：112-119
- 作者机构：
  
  1. 燕山大学信息科学与工程学院，河北秦皇岛 066004
  2. 河北省信息传输与信号处理重点实验室，河北秦皇岛 066004
  3. 河北科技师范学院数学与信息科技学院，河北秦皇岛 066004
- 作者简介：
  
  [ "李玉博（1985– ），男，河北衡水人，博士，燕山大学副教授，主要研究方向为编码理论、序列设计、信息处理等" ]
  [ "刘胜毅（1994– ），男，河北沧州人，燕山大学硕士生，主要研究方向为编码理论、压缩感知" ]
  [ "张景景（1995– ），女，河北石家庄人，燕山大学硕士生，主要研究方向为编码理论、压缩感知" ]
  [ "贾冬艳（1983– ），女，河北衡水人，博士，河北科技师范学院讲师，主要研究方向为推荐系统、智能信息处理" ]
- 基金信息：
  
  国家自然科学基金资助项目(61501395)
- DOI：10.11959/j.issn.1000-436x.2020021
  中图分类号： TN911.2
- 网络出版日期：2020-03，
  
  纸质出版日期：2020-03-25
- 稿件说明：
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李玉博, 刘胜毅, 张景景, 等. 基于Zadoff-Chu矩阵的最优码本构造方法[J]. 通信学报, 2020,41(3):112-119.

Yubo LI, Shengyi LIU, Jingjing ZHANG, et al. Construction method of optimal codebook based on Zadoff-Chu matrix[J]. Journal on communications, 2020, 41(3): 112-119.
李玉博, 刘胜毅, 张景景, 等. 基于Zadoff-Chu矩阵的最优码本构造方法[J]. 通信学报, 2020,41(3):112-119. DOI： 10.11959/j.issn.1000-436x.2020021.

Yubo LI, Shengyi LIU, Jingjing ZHANG, et al. Construction method of optimal codebook based on Zadoff-Chu matrix[J]. Journal on communications, 2020, 41(3): 112-119. DOI： 10.11959/j.issn.1000-436x.2020021.

摘要

具有低相关性质的码本在同步码分多址系统（CDMA）、量子信息理论以及压缩感知领域都有重要应用。为扩展码本数量，放宽了变换矩阵的限制条件。基于Zadoff-Chu矩阵，利用差集、几乎差集以及有限域特征和构造了新的码本，得到的码本依照Welch界限或Levenstein界是最优或几乎最优的。通过实验仿真发现，基于该类码本构造的确定性测量矩阵在压缩感知中具有良好的性能。

Abstract

Codebooks with low-coherence have wide utilization in code division multiple access (CDMA) communications

quantum information theory

compressed sensing and so on.In order to expand the number of codebooks

the restrictions on the transformation matrix were relaxed.Based on the Zadoff-Chu matrix

new codebooks were constructed using the difference set

almost difference set

and finite field character sum.The proposed codebooks were optimal or near optimal according to the Welch bound or Levenstein bound.Through experimental simulation

it is found that the deterministic measurement matrices constructed using these codebooks also have good performance in the process of compressed sensing.

关键词

Keywords

references

DING C S , GOLIN M,KLØVE T . Meeting the Welch and Karystinos-Pados bounds on DS-CDMA binary signature sets [J ] . Design Codes and Cryptography , 2003 , 30 ( 1 ): 73 - 84 .

冯克勤 , 金玲飞 . 量子信息理论中的几个数学问题 [J ] . 中国科学:数学 , 2017 , 47 ( 11 ): 1387 - 1408 .

FENG K Q , JIN L F . Several mathematical problems in quantum information theory [J ] . Scientia Sinica (Mathematics) , 2017 , 47 ( 11 ): 1387 - 1408 .

LI S X , GE G . Deterministic sensing matrices arising from near orthogonal systems [J ] . IEEE Transactions on Information Theory , 2014 , 64 ( 4 ): 2291 - 2302 .

XIA P F , ZHOU S L , GIANNAKIS G B . Achieving the Welch bound with difference sets [J ] . IEEE Transactions on Information Theory , 2005 , 51 ( 5 ): 1900 - 1907 .

DING C S . Complex codebooks from combinatorial designs [J ] . IEEE Transactions on Information Theory , 2006 , 52 ( 9 ): 4229 - 4235 .

DING C S , FENG T . Codebooks from almost difference sets [J ] . Design Codes and Cryptography , 2008 ( 46 ): 113 - 126 .

张爱仙 , 冯克勤 . 一类近似最佳码本的构造 [J ] . 中国科学:信息科学 , 2015 , 45 ( 12 ): 1632 - 1639 .

ZHANG A X , FENG K Q . Construction of a class of codebooks nearly meeting the Welch bound [J ] . Scientia Sinica (Informations) , 2015 , 45 ( 12 ): 1632 - 1639 .

LI C J , YUE Q , HUANG Y W . Two families of nearly optimal codebooks [J ] . Design Codes and Cryptography , 2015 , 75 ( 1 ): 43 - 57 .

ZHANG A X , FENG K Q . Construction of cyclotomic codebooks nearly meeting the Welch bound [J ] . Design Codes and Cryptography , 2012 , 63 ( 2 ): 209 - 224 .

张爱仙 , 何春燕 , 吉喆 . 几类近似达到 Welch 界码本的构造 [J ] . 纯粹数学与应用数学 , 2018 , 34 ( 3 ): 323 - 330 .

ZHANG A X , HE C Y , JI Z . Constructions of some classes of codebooks nearly meeting the Welch bound [J ] . Pure and Applied Mathematics , 2018 , 34 ( 3 ): 323 - 330 .

ZHOU Z C , DING C S , LI N . New families of codebooks achieving the Levenstein bound [J ] . IEEE Transactions on Information Theory , 2014 , 60 ( 11 ): 2507 - 2511 .

QU L J . A new approach to constructing quadratic pseudo-planar functions over F 2 n [J ] . IEEE Transactions on Information Theory , 2016 , 62 ( 11 ): 6644 - 6658 .

HENG Z L , DING C S , YUE Q . New constructions of asymptotically optimal codebooks with multiplicative characters [J ] . IEEE Transactions on Information Theory , 2017 , 63 ( 10 ): 6179 - 6187 .

HENG Z L . Nearly optimal codebooks based on generalized Jacobi sums [J ] . Discrete Applied Mathematics , 2018 ( 250 ): 227 - 240 .

LUO G J , CAO X W . Two constructions of asymptotically optimal codebooks via the hyper Eisenstein sum [J ] . IEEE Transactions on Information Theory , 2018 , 64 ( 10 ): 6498 - 6505 .

LUO G J , CAO X W . Two constructions of asymptotically optimal codebooks [J ] . Cryptography and Communications , 2018 , 11 ( 4 ): 825 - 838 .

XIANG C , DING C S , MESNAGER S . Optimal codebooks from binary codes meeting the Levenstein bound [J ] . IEEE Transactions on Information Theory , 2015 , 61 ( 12 ): 6526 - 6535 .

YU N Y . A construction of codebooks associated with binary sequences [J ] . IEEE Transactions on Information Theory , 2012 , 58 ( 8 ): 5522 - 5533 .

CAO X W , CHOU W S , ZHANG X Y . More constructions of near optimal codebooks associated with binary sequences [J ] . Advances in Mathematics of Communications , 2017 , 11 ( 1 ): 187 - 202 .

HONG S , PARK H , NO J . Near optimal partial Hadamard codebook construction using binary sequences obtained from quadratic residue mapping [J ] . IEEE Transactions on Information Theory , 2014 , 60 ( 6 ): 3698 - 3705 .

WANG X , ZHANG J , GE G . Deterministic convolutional compressed sensing matrices [J ] . Finite Fields and Their Applications , 2016 ( 42 ): 102 - 117 .

BERNDT B , EVANS R , WILLIAMS K . Gauss and Jacobi sums [M ] . New York : WileyPress , 1990 .

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