通信学报 ›› 2020, Vol. 41 ›› Issue (3): 112-119.doi: 10.11959/j.issn.1000-436x.2020021

• 学术论文 • 上一篇    下一篇

基于Zadoff-Chu矩阵的最优码本构造方法

李玉博1,2,刘胜毅1,2,张景景1,2,贾冬艳3   

  1. 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
  • 修回日期:2019-12-07 出版日期:2020-03-25 发布日期:2020-03-31
  • 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
  • 基金资助:
    国家自然科学基金资助项目(61501395)

Construction method of optimal codebook based on Zadoff-Chu matrix

Yubo LI1,2,Shengyi LIU1,2,Jingjing ZHANG1,2,Dongyan JIA3   

  1. 1 School of Information Science &Engineering,Yanshan University,Qinhuangdao 066004,China
    2 Hebei Key Laboratory of Information Transmission and Signal Processing,Qinhuangdao 066004,China
    3 School of Mathematics and Information Science &Technology,Hebei Normal University of Science &Technology,Qinhuangdao 066004,China
  • Revised:2019-12-07 Online:2020-03-25 Published:2020-03-31
  • Supported by:
    The National Natural Science Foundation of China(61501395)

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。

关键词: 码本, 差集, 几乎差集, Welch界, Levenstein界

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.

Key words: codebook, difference set, almost difference set, Welch bound, Levenstein bound

中图分类号: 

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