基于二进制对称信道的极化码研究
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摘要
现有极化码构造方案仅适用于二进制删除信道和加性高斯白噪声信道。为此,研究极化码在二进制对称信道(BSC)的构造方案。分析BSC中的极化码构造方式和编译码算法原理,利用连续删除译码算法对极化码在BSC中的纠错效率进行测试。仿真结果表明,蒙特卡罗法构造的极化码相对于巴氏参数法构造的极化码具有较好的纠错效率。
The exisiting polar code construction scheme is only applicable to Binary Erasure Channel(BEC) and Additive White Gaussian Noise(AWGN) channel.Therefore,the constrution scheme of polar code in Binary Symmetric Channel(BSC) is studied.The construction method of the polar code and the principle of the coding and decoding algorithm in the BSC are analyzed.The error correction efficiency of the polar code constructed in the BSC is tested by the Successive Cancellation(SC) decoding algorithm.Simulation results show that the polar code constructed by Monte Carlo method has better error correction efficiency than the polar code constructed by Bhattacharyya method.
The exisiting polar code construction scheme is only applicable to Binary Erasure Channel(BEC) and Additive White Gaussian Noise(AWGN) channel.Therefore,the constrution scheme of polar code in Binary Symmetric Channel(BSC) is studied.The construction method of the polar code and the principle of the coding and decoding algorithm in the BSC are analyzed.The error correction efficiency of the polar code constructed in the BSC is tested by the Successive Cancellation(SC) decoding algorithm.Simulation results show that the polar code constructed by Monte Carlo method has better error correction efficiency than the polar code constructed by Bhattacharyya method.
引文
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[8] ARIKAN E.A performance comparison of polar codes and Reed-Muller codes[J].IEEE Communications Letters,2008,12(6):447-449.
[9] ZHAO S,SHI P,WANG B.Designs of Bhattacharyya parameter in the construction of polar codes[C]//Proceedings of International Conference on Wireless Communications,Networking and Mobile Computing.Washington D.C.,USA:IEEE Press,2011.
[10] BALATSOUKAS S A,PARIZI M B,BURG A.LLR-based successive cancellation list decoding of polar codes[J].IEEE Transactions on Signal Processing,2013,63(19):5165-5179.
[11] TAL I,VARDY A.List decoding of polar codes[C]//Proceedings of IEEE International Symposium on Information Theory.Washington D.C.,USA:IEEE Press,2011.
[12] NIU K,CHEN K.CRC-aided decoding of polar codes[J].IEEE Communications Letters,2012,16(10):1668-1671.
[13] 刘亚军,李世宝,刘建航,等.一种低时延极化码列表连续删除译码算法[J].计算机工程,2018,44(3):78-81.
[14] ALAMDAR Y A,KSCHISCHANG F R.A simplified successive-cancellation decoder for polar codes[J].IEEE Communications Letters,2011,15(12):1378-1380.
[15] KORADA S B,URBANKE R L.Polar codes are optimal for lossy source coding[J].IEEE Transactions on Information Theory,2010,56(4):1751-1768.
[2] ARIKAN E.Channel polarization:a method for constructing capacity-achieving codes for symmetric binary-input memory less channels[J].IEEE Transactions on Information Theory,2009,55(7):3051-3072.
[3] 杨武周,刘彤.极化码研究现状分析与展望[J].信息通信,2016(4):218-219.
[4] ARIKAN E.Channel combining and splitting for cutoff rate improvement[J].IEEE Transactions on Information Theory,2005,52(2):628-639.
[5] MORI R,TANAKA T.Performance of polar codes with the construction using density evolution[J].IEEE Communica-tions Letters,2009,13(7):519-521.
[6] RICHARDSON T,URBANKE R.Modern coding theory[M].Cambridge,UK:Cambridge University Press,2008.
[7] WU D,LI Y,SUN Y.Construction and block error rate analysis of polar codes over AWGN channel based on Gaussian approximation[J].IEEE Communications Letters,2014,18(7):1099-1102.
[8] ARIKAN E.A performance comparison of polar codes and Reed-Muller codes[J].IEEE Communications Letters,2008,12(6):447-449.
[9] ZHAO S,SHI P,WANG B.Designs of Bhattacharyya parameter in the construction of polar codes[C]//Proceedings of International Conference on Wireless Communications,Networking and Mobile Computing.Washington D.C.,USA:IEEE Press,2011.
[10] BALATSOUKAS S A,PARIZI M B,BURG A.LLR-based successive cancellation list decoding of polar codes[J].IEEE Transactions on Signal Processing,2013,63(19):5165-5179.
[11] TAL I,VARDY A.List decoding of polar codes[C]//Proceedings of IEEE International Symposium on Information Theory.Washington D.C.,USA:IEEE Press,2011.
[12] NIU K,CHEN K.CRC-aided decoding of polar codes[J].IEEE Communications Letters,2012,16(10):1668-1671.
[13] 刘亚军,李世宝,刘建航,等.一种低时延极化码列表连续删除译码算法[J].计算机工程,2018,44(3):78-81.
[14] ALAMDAR Y A,KSCHISCHANG F R.A simplified successive-cancellation decoder for polar codes[J].IEEE Communications Letters,2011,15(12):1378-1380.
[15] KORADA S B,URBANKE R L.Polar codes are optimal for lossy source coding[J].IEEE Transactions on Information Theory,2010,56(4):1751-1768.