电子学报 ›› 2017, Vol. 45 ›› Issue (4): 855-862.DOI: 10.3969/j.issn.0372-2112.2017.04.013

• 学术论文 • 上一篇    下一篇

一种基于模运算和扩展欧几里得定理的喷泉码

朱文杰1,2, 易本顺1,2, 甘良才1, 姚渭箐1,2   

  1. 1. 武汉大学电子信息学院, 湖北武汉 430072;
    2. 武汉大学深圳研究院, 广东深圳 518000
  • 收稿日期:2015-05-12 修回日期:2016-05-22 出版日期:2017-04-25 发布日期:2017-04-25
  • 作者简介:朱文杰 男,1984年出生于湖北孝昌县,武汉大学博士研究生,研究方向为无线通信,信道编码.E-mail:wenjie8408@163.com;易本顺 男,1965出生于湖北武汉,武汉大学教授,博士生导师,主要研究方向为多媒体通信,无线网络.E-mail:yibs@whu.edu.cn
  • 基金资助:

    国家自然科学基金(No.61371125,No.61072041);深圳市基础研究项目(No.JCYJ20150630153917254)

Novel Fountain Codes Based on Modulo and Extended Euclidean

ZHU Wen-jie1,2, YI Ben-shun1,2, GAN Liang-cai1, YAO Wei-qing1,2   

  1. 1. School of Electronic Information, Wuhan University, Wuhan, Hubei 430072, China;
    2. Shenzhen Institute of Wuhan University, Shenzhen, Guangdong 518000, China
  • Received:2015-05-12 Revised:2016-05-22 Online:2017-04-25 Published:2017-04-25

摘要:

针对中国剩余定理在模运算喷泉码译码过程中的固有不足,本文提出一种全新的基于扩展欧几里德定理的译码算法.该算法采用合并线性同余方程组,避免分解因子非互质情况下求解乘率因子失败的问题.模运算喷泉码将信息数据编码为自然数分解因子和相对应的模余数的数据包,接收方只要获取一定数目的编码数据包就能成功解码.基于扩展欧几里得定理的译码算法扩展了模运算喷泉码的分解因子范围,提高了编译码效率.本文通过理论分析和数值仿真证实了这种编译码算法的可行性.

关键词: 喷泉码, 中国剩余定理, 扩展欧几里德定理, 余数变换码, 线性同余方程

Abstract:

Aiming at the intrinsic problems of Chinese Remainder Theorem in fountain decoding process with modular arithmetic,this paper proposes a decoding algorithm based on extended Euclidean theorem.The linear congruence equations are merged in the extended Euclidean decoding algorithm,which avoids the failure of solving the rate factor when the decomposition factors are non-coprime.In the modular arithmetic fountain encoding process,the original packet is continuously decomposed by the factor,which is randomly selected from the natural number,into the encoded packets consisting of the residues and the factors.When a certain amount of packets are received,it can be achieved to decode successfully.The codec efficiency has been improved as the algorithm has extended the range of the modular arithmetic factor.Through theoretical analysis and numerical simulation,the effectiveness of this decoding algorithm of modular arithmetic fountain code has been proved.

Key words: fountain codes, Chinese remainder theorem, extended Euclidean, remainder transform codes, linear congruence equations

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