西安电子科技大学学报 ›› 2020, Vol. 47 ›› Issue (6): 158-163.doi: 10.19665/j.issn1001-2400.2020.06.022

• 信息与通信工程 & 网络空间安全 • 上一篇    下一篇

广义Helberg码纠插入/删除错误的一个简单证明

马国臣1(),焦晓鹏1,慕建君1,韩辉1,郭军军2   

  1. 1.西安电子科技大学 计算机科学与技术学院,陕西 西安 710071
    2.西安工业大学 计算机学院,陕西 西安 710021
  • 收稿日期:2019-12-24 出版日期:2020-12-20 发布日期:2021-01-06
  • 作者简介:马国臣(1994—),男,西安电子科技大学博士研究生,E-mail: guochenma@163.com
  • 基金资助:
    国家自然科学基金(61971322);国家自然科学基金(61977051);陕西省重点研发计划项目(2018GY-023)

Simple proof the generalized Helberg codes being capable of correcting insertion/deletion errors

MA Guochen1(),JIAO Xiaopeng1,MU Jianjun1,HAN Hui1,GUO Junjun2   

  1. 1. School of Computer Science and Technology, Xidian University, Xi’an 710071, China
    2. School of Computer Science and Engineering, Xi’an Technological University, Xi’an 710021, China
  • Received:2019-12-24 Online:2020-12-20 Published:2021-01-06

摘要:

针对广义Helberg码纠错能力的现有证明方法较为复杂的缺点,提出了广义Helberg码能够纠正多个插入/删除错误的一种简单证明方法。 通过深入分析广义Helberg码的码字与权重之间內积的单调性, 证明了任意两个不同码字与权重之间的內积之差的上下界。 利用所得到的上下界, 简化了广义Helberg码纠错能力的现有证明方法。 所给出的简单证明方法有助于对广义Helberg码的理解和进一步深入研究。

关键词: 纠错码, 插入/删除错误, Helberg码, 广义Helberg码

Abstract:

Since the existing proof method of the error correction capability for generalized Helberg codes is complicated, a simple proof that generalized Helberg codes are capable of correcting multiple insertion/deletion errors is proposed. By making a detailed analysis of the monotonicity of the inner product between the codeword and the weights for the generalized Helberg codes, the upper and lower bounds of the difference of the inner product between any two different codewords and weights are proved. By using the upper and lower bounds, the existing proof method for the error correction capability for generalized Helberg codes is simplified. The proposed simple proof is helpful in understanding generalized Helberg codes and making a further study.

Key words: error-correcting codes, insertion/deletion errors, Helberg codes, generalized Helberg codes

中图分类号: 

  • TN911.22