LDPC码和Polar码级联系统的发展综述
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摘要
低密度奇偶校验码(Low Density Parity Check codes,LDPC codes)和极化码(Polar codes),是国际移动通信标准化组织3GPP在5G(5th-Generation)增强移动宽带场景的信道编码技术方案中,分别作为数据信道和控制信道的编码方案.LDPC码编码复杂度较高、硬件资源需求较大以及存在错误平层,而极化码具有线性编码复杂度以及瀑布式下降曲线,基于二者的级联系统可以大大改善彼此的缺点.首先我们研究分析了现有的级联系统,其次详细介绍了级联系统的实现方法,最后就级联系统研究中现存问题进行了分析,并探讨了其未来发展趋势.
Low-Density Parity-Check codes and Polar codes are the encoding schemes of data channels and control channels respectively adopted by the International Mobile Telecommunications Standardization Organization 3 GPP in the 5 GEnhanced Mobile Broadband(eMBB)channel coding scheme.LDPC codes have the shortcomings of high encoding complexity,large hardware resource requirements and error floor.Polar codes have linear coding complexity and own waterfall descent curves.Concatenation systems based on these can greatly improve each other's weaknesses.First of all,we studied and analyzed the existing concatenation system.We then analyzed the concatenation system implementation method and the existing problems.Finally,we discussed its future development trend.
Low-Density Parity-Check codes and Polar codes are the encoding schemes of data channels and control channels respectively adopted by the International Mobile Telecommunications Standardization Organization 3 GPP in the 5 GEnhanced Mobile Broadband(eMBB)channel coding scheme.LDPC codes have the shortcomings of high encoding complexity,large hardware resource requirements and error floor.Polar codes have linear coding complexity and own waterfall descent curves.Concatenation systems based on these can greatly improve each other's weaknesses.First of all,we studied and analyzed the existing concatenation system.We then analyzed the concatenation system implementation method and the existing problems.Finally,we discussed its future development trend.
引文
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[2]SHANNON C E.A mathematical theory of communication[J].Bell Labs Technical Journal,1948,27(4):379-423.
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[4]BERROU C.Near Shannon limit error-correcting coding and decoding:turbo-codes[C]//Proceedings of ICC’93-IEEE International Conference on Communications.Geneva,Switzerland:IEEE,1993:1064-1070
[5]ARIKAN E.Channel Polarization:A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels[J].IEEE Transactions on Information Theory,2009,55(7):3051-3073.
[6]MACKAY D J C,WILSON S T,DAVEY M C.Comparison of constructions of irregular Gallager codes[J].IEEE Transactions on Communications,1999,47(10):1449-1454.
[7]聂阳.LDPC码编码算法与实现[D].武汉:武汉邮电科学研究院,2008.NIE Y.Implementation and Algorithm of LDPC Codes Encoding[D].Wuhan:Wuhan Institute of Posts and Telecommunications,2008.
[8]RICHARDSON T J,URBANKE R L.Efficient encoding of low-density parity-check codes[J].IEEE Transactions on Information Theory,2002,47(2):638-656.
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[10]CHEN J,DHOLAKIA A,ELEFTHERIOU E,et al.Reduced-complexity decoding of LDPC codes[J].IEEE Transactions on Communications,2005,53(8):1288-1299.
[11]CHEN J,FOSSORIER M P C.Near optimum universal belief propagation-based decoding of low-density parity check codes[J].IEEE Transactions on Communications,2002,50(3):406-414.
[12]WU Z,SU K,GUO L.A modified min sum decoding algorithm based on LMMSE for LDPC codes[J].AEU-International Journal of Electronics and Communications,2014,68(10):994-999.
[13]MANSOUR M.A turbo-decoding message-passing algorithm for sparse parity-check matrix codes[J].IEEE Transactions on Signal Processing,2006,54(11):4376-4392.
[14]ZHAO S,SHI P,WANG B.Designs of Bhattacharyya parameter in the construction of polar codes[C]//2011 7th International Conference on Wireless Communications,Networking and Mobile Computing.Wuhan:IEEE,2011:1-4.
[15]MORI R,TANAKA T.Performance of polar codes with the construction using density evolution[J].IEEE Communications Letters,2009,13(7):519-521.
[16]TAL I,VARDY A.List decoding of polar codes[J].IEEE Transactions on Information Theory,2015,61(5):2213-2226.
[17]ALAMDAR-YAZDI A,KSCHISCHANG F R.A simplified successive-cancellation decoder for polar codes[J].IEEE Communications Letters,2011,15(12):1378-1380.
[18]ZHANG Q,LIU A,PAN X.An enhanced probabilistic computation method for the weight distribution of polar codes[J].IEEE Communications Letters,2017,21(12):2565-2565.
[19]YUAN B,PARHI K.Architectures for polar BP decoders using folding[C]//Circuits and Systems(ISCAS),2014IEEE International Symposium on.Melbourne VIC:IEEE,2014:205-208.
[20]FORNEY G D J.Concatenated Codes[M].Cambridge:Massachusetts Institute of Technology Press,1966:7-142.
[21]BLOKH E L,ZYABLOY V.Coding of generalized concatenated codes[J].Problemy Peredachi Informatsii,1974,10(10):45-50.
[22]BAKSHI M,JAGGI S,EFFROS M.Concatenated Polar codes[C]//2010IEEE International Symposium on Information Theory.Austin,USA:IEEE,2010:918-922.
[23]ESLAMI A,PISHRO-NIK H.A practical approach to polar codes[C]//2011IEEE International Symposium on Information Theory.St.Petersburg,Russia:IEEE,2011:16-20.
[24]MURATA T,OCHIAI H.On design of CRC codes for polar codes with successive cancellation list decoding[C]//2017IEEE International Symposium on Information Theory.Aachen,Germany:IEEE,2017:1868-1872.
[25]ZHANG Q,LIU A,PAN X,et al.CRC code design for list decoding of polar codes[J].IEEE Communications Letters,2017,21(6):1229-1232.
[26]江涛,王涛,屈代明,等.极化码与奇偶校验码的级联编码:面向5G及未来移动通信的编码方案[J].数据采集与处理,2017,32(3):463-468.JIANG T,WANG T,QU D M,et al.Concatenated coding of polar codes and parity-check codes:Coding scheme for 5Gand future mobile communications[J].Journal of Data Acquisition and Processing,2017,32(3):463-468.
[27]向旬.基于级联的Polar码译码性能改善[D].西安:西安电子科技大学,2014.XIANG X.Decoding Performance Improvement of Polar Codes Based on Concatenated Scheme[D].Xi’an:Xidian University,2014.
[28]姚冬冬.基于BCH码和系统极化码级联方案的译码性能及改进[D].安徽:安徽大学,2015.YAO D D.The Improvement of the Decoding Performance of the Concatenation of BCH Codes and Systematic Polar Codes[D].Anhui:Anhui University,2015.
[2]SHANNON C E.A mathematical theory of communication[J].Bell Labs Technical Journal,1948,27(4):379-423.
[3]GALLAGER R G.Low-density parity-check codes[J].IRE Transactions on Information Theory,1962,8(1):21-28.
[4]BERROU C.Near Shannon limit error-correcting coding and decoding:turbo-codes[C]//Proceedings of ICC’93-IEEE International Conference on Communications.Geneva,Switzerland:IEEE,1993:1064-1070
[5]ARIKAN E.Channel Polarization:A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels[J].IEEE Transactions on Information Theory,2009,55(7):3051-3073.
[6]MACKAY D J C,WILSON S T,DAVEY M C.Comparison of constructions of irregular Gallager codes[J].IEEE Transactions on Communications,1999,47(10):1449-1454.
[7]聂阳.LDPC码编码算法与实现[D].武汉:武汉邮电科学研究院,2008.NIE Y.Implementation and Algorithm of LDPC Codes Encoding[D].Wuhan:Wuhan Institute of Posts and Telecommunications,2008.
[8]RICHARDSON T J,URBANKE R L.Efficient encoding of low-density parity-check codes[J].IEEE Transactions on Information Theory,2002,47(2):638-656.
[9]FOSSORIER M P C,MIHALJEVIC M,IMAI H.Reduced complexity iterative decoding of low-density parity check codes based on belief propagation[J].IEEE Transactions on Communications,1999,47(5):673-680.
[10]CHEN J,DHOLAKIA A,ELEFTHERIOU E,et al.Reduced-complexity decoding of LDPC codes[J].IEEE Transactions on Communications,2005,53(8):1288-1299.
[11]CHEN J,FOSSORIER M P C.Near optimum universal belief propagation-based decoding of low-density parity check codes[J].IEEE Transactions on Communications,2002,50(3):406-414.
[12]WU Z,SU K,GUO L.A modified min sum decoding algorithm based on LMMSE for LDPC codes[J].AEU-International Journal of Electronics and Communications,2014,68(10):994-999.
[13]MANSOUR M.A turbo-decoding message-passing algorithm for sparse parity-check matrix codes[J].IEEE Transactions on Signal Processing,2006,54(11):4376-4392.
[14]ZHAO S,SHI P,WANG B.Designs of Bhattacharyya parameter in the construction of polar codes[C]//2011 7th International Conference on Wireless Communications,Networking and Mobile Computing.Wuhan:IEEE,2011:1-4.
[15]MORI R,TANAKA T.Performance of polar codes with the construction using density evolution[J].IEEE Communications Letters,2009,13(7):519-521.
[16]TAL I,VARDY A.List decoding of polar codes[J].IEEE Transactions on Information Theory,2015,61(5):2213-2226.
[17]ALAMDAR-YAZDI A,KSCHISCHANG F R.A simplified successive-cancellation decoder for polar codes[J].IEEE Communications Letters,2011,15(12):1378-1380.
[18]ZHANG Q,LIU A,PAN X.An enhanced probabilistic computation method for the weight distribution of polar codes[J].IEEE Communications Letters,2017,21(12):2565-2565.
[19]YUAN B,PARHI K.Architectures for polar BP decoders using folding[C]//Circuits and Systems(ISCAS),2014IEEE International Symposium on.Melbourne VIC:IEEE,2014:205-208.
[20]FORNEY G D J.Concatenated Codes[M].Cambridge:Massachusetts Institute of Technology Press,1966:7-142.
[21]BLOKH E L,ZYABLOY V.Coding of generalized concatenated codes[J].Problemy Peredachi Informatsii,1974,10(10):45-50.
[22]BAKSHI M,JAGGI S,EFFROS M.Concatenated Polar codes[C]//2010IEEE International Symposium on Information Theory.Austin,USA:IEEE,2010:918-922.
[23]ESLAMI A,PISHRO-NIK H.A practical approach to polar codes[C]//2011IEEE International Symposium on Information Theory.St.Petersburg,Russia:IEEE,2011:16-20.
[24]MURATA T,OCHIAI H.On design of CRC codes for polar codes with successive cancellation list decoding[C]//2017IEEE International Symposium on Information Theory.Aachen,Germany:IEEE,2017:1868-1872.
[25]ZHANG Q,LIU A,PAN X,et al.CRC code design for list decoding of polar codes[J].IEEE Communications Letters,2017,21(6):1229-1232.
[26]江涛,王涛,屈代明,等.极化码与奇偶校验码的级联编码:面向5G及未来移动通信的编码方案[J].数据采集与处理,2017,32(3):463-468.JIANG T,WANG T,QU D M,et al.Concatenated coding of polar codes and parity-check codes:Coding scheme for 5Gand future mobile communications[J].Journal of Data Acquisition and Processing,2017,32(3):463-468.
[27]向旬.基于级联的Polar码译码性能改善[D].西安:西安电子科技大学,2014.XIANG X.Decoding Performance Improvement of Polar Codes Based on Concatenated Scheme[D].Xi’an:Xidian University,2014.
[28]姚冬冬.基于BCH码和系统极化码级联方案的译码性能及改进[D].安徽:安徽大学,2015.YAO D D.The Improvement of the Decoding Performance of the Concatenation of BCH Codes and Systematic Polar Codes[D].Anhui:Anhui University,2015.