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Research of the BCH Code Decoding Based on the Compressive Sensing Theory(PDF)

Journal of Xiamen University(Natural Science)[ISSN:0438-0479/CN:35-1070/N]

2017 04
Research Field:
Research Articles
Publishing date:


Research of the BCH Code Decoding Based on the Compressive Sensing Theory
Article ID:
JIANG EnhuaLI SuwenDOU DezhaoZHAO Qingping
School of Physics and Electronic Information,Huaibei Normal University,Huaibei 235000,China
compressive sensing basis pursuit BP algorithm BCH code check matrix syndrome
CLC number:
TN 911.7
Document code:

By means of the compressed sensing theory under no noise condition,this paper conducts a study on the decoding method of the BCH code.The check matrix is used as the measurement matrices,and the syndrome is used as the measurement signal.Hence,the compressed sensing model of the reconstructing error pattern is built.By the basis pursuit BP algorithm,the error pattern of the BCH code is reconstructed.Taking the(15,11)BCH code as an example,we have proved that the reconstructing error pattern is correct.According to the receiving code and the reconstructing error pattern,the value of the code word is calculated.On the basis of bit error rate and the code word estimating success rate,the decoding effect of the basis pursuit BP algorithm and the Berlekamp iterative decoding algorithm are analyzed and compared.Taking the BCH short-code and long-code as an example,the simulation experiment is complete,the experiment results prove that the compressed sensing theory and the basis pursuit BP algorithm are feasible and effective in decoding the BCH code.


[1] DONOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[2] CANDES E J,ROMBERG J,TAO T.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J].IEEE Transactions on Information Theory,2004,52(2):489-509.
[3] ELAD M,AHARON M.Image denoising via sparse and redundant representations over learned dictionaries[J].IEEE Transactions on Image Processing,2006,15(12):3736-3745.
[4] BARANIUK R G.A lecture on compressive sensing[J].IEEE Signal Processing Magazine,2007,24(4):118-120,124.
[5] CANDES E J.The restricted isometry property and its implications for compressed sensing[J].Comptes Rendus Mathematique,2008,346(9/10):589-592.
[6] SARVOTHAM S,BARON D,BARANIUK R G.Measurements vs.bits:compressed sensing meets information theory[C]∥44th Allerton Conference Communication,Control,and Computing.Monticello:Allerton Conference on Communication Control & Computing,2006:1-5.
[7] 张景雄,阳柯,郭建中.压缩感知的信息论解译[J].武汉大学学报(信息科学版),2014,39(11):1261-1268.
[8] 董小亮,杨良龙,赵生妹,等.用信道编码构造压缩感知测量矩阵[J].信号处理,2013,29(7):809-815.
[9] 张轶,达新宇,褚振勇.低密度奇偶校验码的压缩感知重构[J].吉林大学学报(工学版),2015,45(3):985-990.
[10] BOYD S,VANDENBERGHE L.Convex optimization[M].Cambridge:Cambridge University Press,2004:609-612.
[11] WRIGHT S J.Primal-dual interior-point methods [M].Philadelphia:SIAM,1997:50-61.
[12] Foucart S,Rauhut H.A mathematical introduction to compressive sensing[M].New York:Springer,2013:61-63.
[13] ELAD,MICHAEL.Sparse and redundant representations:from theory to applications in signal and image processing[M].New York:Springer,2010:26-30.
[14] 曹雪虹,张宗橙.信息论与编码[M].北京:清华大学出版社,2009:135-158.
[15] BERLEKAMP E R.algebraic coding theory [M].New York:McGraw-Hill Book Company,1968:176-199.


收稿日期:2017-02-21 录用日期:2017-04-11
基金项目:国家自然科学基金(41475017,11504121); 安徽省高校自然科学研究重点项目(KJ2016A628,KJ2016A650)
Last Update: 1900-01-01