基于单载波频域均衡系统的LDPC码的性能研究
摘要
以香农定理为基础,信道编码成为了研究领域之一。如何构造接近信道容量的编码方式、如何设计相应的编码方法及译码方法、如何实现信息的可靠传输和有效传输成为了信道编码领域的重要课题。低密度奇偶校验码(简称LDPC码)是信道编码领域的一个重要的研究成果。它具有如下诸多优点：描述简单、较低的译码复杂度、可以并行实现、使用相对灵活、错误平台较低、可以逼近香农极限等。这些优秀的性能使LDPC码成为当前通信领域的热门研究课题之一,同时也是B3G/4G移动通信系统中的关键研究技术。
当前,宽带无线接入技术已经成为必然。在宽带无线通信中,由于多径传输的存在,引起了频率选择性衰落,进而对通信的可靠性造成了严重的影响。采用何种传输技术来有效抵抗多径衰落的影响,针对这类系统的物理层研究成为了研究的热点。单载波频域均衡(SCFDE)系统的出现,给物理层的研究带来了新的方向。SCFDE技术的特点：联合简单的时域反馈均衡、性能上与正交频分复用(OFDM)相似(在高码率的情况下甚至性能更优)、并且没有峰均比大的问题、在相噪和频偏方面也不如OFDM来的敏感、还可以与OFDM技术进行较好的融合等。随着SCFDE技术的发展,它受到了研究者越来越多的关注,并且在宽带无线通信协议IEEE802.16a中SCFDE支术做为建议的物理层传输方案之
本论文首先分析了低密度奇偶校验码的组成原理及结构特点,在此基础上提出了两种基于802.16e标准的编码方法,并着重分析了三种通用的译码算法。通过阅读大量的相关文献,提出了适合于802.16e标准的校验矩阵的译码架构,详细的介绍了译码的整个流程及相关步骤,并在此基础上实现了编解码功能合一的LDPC码结构的仿真。其次研究了单载波频域均衡系统,对发射端及接收端进行了框图分析,搭载整个仿真系统,进行了基于单载波频域均衡系统的LDPC码的性能研究。最后得出了在AWGN信道、1344码长、不同码率、不同调制方式、不同多普勒频率下的仿真结果,并进行分析。
Based on Shannon theorem, channel coding has become one of the research areas. How to construct close to the channel capacity of the encoding method, how to design a corresponding encoding method and decoding method and how to guarantee information transmission reliable and efficient has become the important subject in channel coding areas.Low Density Parity Check (referred to as the LDPC code) is an important field of channel coding research. It has the following many advantages:simple description, the low decoding complexity, parallel implementation, the use of a relatively flexible, low error platform, may be approaching the Shannon limit and so on. These excellent performance make LDPC codes become one of the the current hot research topics in the field of communications, and is also a key research technology in the B3G/4G mobile communication system.
Now,wireless broadBand access technology has become a necessity. In the broadBand wireless communication, due to the presence of multipath transmission, cause frequency selective fading, thereby causing serious influence on the reliability of the communications. What transmission technology to effectively resist the impact of multipath fading, has become a key issue for the study of the physical layer of such systems. The emergence of the single-carrier frequency domain equalization (SCFDE)system, bring a new direction to the study of the physical layer. Technical characteristics of the SCFDE:joint simple time domain feedBack equalizer performance,similar to orthogonal frequency division multiplexing (OFDM)in Performance(even in case of high bit rate performance is more excellent), no PAPR big problem, not sensitive to such OFDM in terms of phase noise and frequency offset, also has better fusion with OFDM technology. With the development of SC-FDE technology, it has been more and more attention in the researchers and SC-FDE technology has been suggested as one of the proposed physical layer transmission schemein in broadBand wireless communication protocol IEEE802.16a.
This paper firstly analyzed the principle and structural characteristics of the composition of low density parity check code, proposed two coding method based on the802.16e standard, and analyzed three universal decoding algorithm. By reading a lot of literature, we proposed a decoding architecture suited to802.16e standard check matrix, detaile introduced entire process of decoding steps, and on this basis achieve code structurethe simulation of unity of LDPC codec functions. Secondly, researched dsingle-carrier frequency domain equalization system,analyzed the block diagram of the transmitter and receiver, equipped with the entire simulation system, researched the performance of the LDPC codes based on single-carrier frequency domain equalization system.In AWGN channel,1344yards long, different rate and different modulation schemes under different Doppler frequency we came to the simulation results and analysised all results.
当前,宽带无线接入技术已经成为必然。在宽带无线通信中,由于多径传输的存在,引起了频率选择性衰落,进而对通信的可靠性造成了严重的影响。采用何种传输技术来有效抵抗多径衰落的影响,针对这类系统的物理层研究成为了研究的热点。单载波频域均衡(SCFDE)系统的出现,给物理层的研究带来了新的方向。SCFDE技术的特点：联合简单的时域反馈均衡、性能上与正交频分复用(OFDM)相似(在高码率的情况下甚至性能更优)、并且没有峰均比大的问题、在相噪和频偏方面也不如OFDM来的敏感、还可以与OFDM技术进行较好的融合等。随着SCFDE技术的发展,它受到了研究者越来越多的关注,并且在宽带无线通信协议IEEE802.16a中SCFDE支术做为建议的物理层传输方案之
本论文首先分析了低密度奇偶校验码的组成原理及结构特点,在此基础上提出了两种基于802.16e标准的编码方法,并着重分析了三种通用的译码算法。通过阅读大量的相关文献,提出了适合于802.16e标准的校验矩阵的译码架构,详细的介绍了译码的整个流程及相关步骤,并在此基础上实现了编解码功能合一的LDPC码结构的仿真。其次研究了单载波频域均衡系统,对发射端及接收端进行了框图分析,搭载整个仿真系统,进行了基于单载波频域均衡系统的LDPC码的性能研究。最后得出了在AWGN信道、1344码长、不同码率、不同调制方式、不同多普勒频率下的仿真结果,并进行分析。
Based on Shannon theorem, channel coding has become one of the research areas. How to construct close to the channel capacity of the encoding method, how to design a corresponding encoding method and decoding method and how to guarantee information transmission reliable and efficient has become the important subject in channel coding areas.Low Density Parity Check (referred to as the LDPC code) is an important field of channel coding research. It has the following many advantages:simple description, the low decoding complexity, parallel implementation, the use of a relatively flexible, low error platform, may be approaching the Shannon limit and so on. These excellent performance make LDPC codes become one of the the current hot research topics in the field of communications, and is also a key research technology in the B3G/4G mobile communication system.
Now,wireless broadBand access technology has become a necessity. In the broadBand wireless communication, due to the presence of multipath transmission, cause frequency selective fading, thereby causing serious influence on the reliability of the communications. What transmission technology to effectively resist the impact of multipath fading, has become a key issue for the study of the physical layer of such systems. The emergence of the single-carrier frequency domain equalization (SCFDE)system, bring a new direction to the study of the physical layer. Technical characteristics of the SCFDE:joint simple time domain feedBack equalizer performance,similar to orthogonal frequency division multiplexing (OFDM)in Performance(even in case of high bit rate performance is more excellent), no PAPR big problem, not sensitive to such OFDM in terms of phase noise and frequency offset, also has better fusion with OFDM technology. With the development of SC-FDE technology, it has been more and more attention in the researchers and SC-FDE technology has been suggested as one of the proposed physical layer transmission schemein in broadBand wireless communication protocol IEEE802.16a.
This paper firstly analyzed the principle and structural characteristics of the composition of low density parity check code, proposed two coding method based on the802.16e standard, and analyzed three universal decoding algorithm. By reading a lot of literature, we proposed a decoding architecture suited to802.16e standard check matrix, detaile introduced entire process of decoding steps, and on this basis achieve code structurethe simulation of unity of LDPC codec functions. Secondly, researched dsingle-carrier frequency domain equalization system,analyzed the block diagram of the transmitter and receiver, equipped with the entire simulation system, researched the performance of the LDPC codes based on single-carrier frequency domain equalization system.In AWGN channel,1344yards long, different rate and different modulation schemes under different Doppler frequency we came to the simulation results and analysised all results.
引文
[1]C E Shannon.A Mathematical Theory of Communication.Bell System Tech. J.,vol.27,pp.379-473 July 1948
[2]The International Forum on Future Mobile Telecommunication & China-EU Post. Conference on Beyond 3G,The High Technology Research and Development Center. of MOST(HTRDC) Future Coordination Committee of 863 Program, (FuTURE),Conference proceedings,Nov.20-22,Beijing,China
[3]http://ieee802.org/16
[4]Falconer D,Ariyavisitakul S L, and Benyamin-Seeyar A, et al.Frequency domain equalization for single-carrier broadBand wireless systems. IEEE Commun. Mag., 2002,33(4):58-66.
[5]Falconer D and Ariyavisitakul S L. BroadBand wireless using single carrier and frequency domain equalization. The 5th International Symposium on Wireless Personal Multimedia Communications, Honolulu, Hawaii,2002,1:27-36.
[6]T. Walzman and M.Schwartz, "Automatic Equalization Using the Discrete FrequencyDomain",IEEETrans.Info.Theory,V01.IT-19,No.1,Jan,1973,Page(s):59-68.
[7]E.R.Ferrara,Jr.,"Frequency-Domain Adaptive Filtering",in Adaptive Filters,C.F.N.Cowan and P.M.Grant,editors,Prentice-Hall,1985.
[8]Falconer,D.; Ariyavisitakul,S.L.; Benyamin-Seeyar,A.;Eidson,B.;"Frequency domain equalization for single-carrier broadBand wireless systems",Communications Magazine, IEEE Volume 40,Issue 4, April 2002, Page(s):58-66.
[9]Tingting Shi, Shidong Zhou, Yan Yao, "Capacity of single carrier systems with frequency-domain equalization", Emerging Technologies:Frontiers of Mobile and Wireless Communication,2004. Proceedings of the IEEE 6th Circuits and Systems Symposium on Volume 2,31 May-2 June 2004 Page(s):429-432 V01.2.
[10]Falconer,D.D.; Ariyavisitakul, S.L.; "BroadBand wireless using single carrier and frequency domain equalization",Wireless Personal Multimedia Communications, 2002. The 5th International Symposium on Volume 1,27-30 Oct.2002 Page(s):27-36 vol.1
[11]Mendicute, M.; Altuna,J.;Atxa,V. and Zabalegui,J.M.; "Performance comparison of OFDM and FDE single-carrier modulation for spatial multiplexing MIMO systems", Signal Processing Advances in Wireless Communications,2004 IEEE 5th Workshop on 11-14 July 2004;Page(s):532-535.
[12]Reirdlardt,s.; Weigel,R.; "Pilot aided timing synchronization for SC-FDE and OFDM:a comparison". Communications and Information Technology,2004.ISCIT 2004. IEEE International Symposium on Volume 1,26-29 oct.2004 Page(s):628-633 v01.1.
[13]Yeesoo Han; Heon Huh; Krogmeier,J.V.; "Comparison of error probability for OFDM and SC-FDE", Signals, Systems and Computers,2003.Conference Record ofthe Thirty-Seventh Asilomar Conference on Volume 1,9-12 Nov.2003 Page(s):497-501 Vol.1.
[14]R W Hamming.Error Detecting and Error Correcting Codes.Bell System Tech.J., Vol,29.pp.147-16,1950
[15]Paul C Hershey,Nthony Ethony Ephremids,and Pamk.Khatria.Performance of RS-BCH Concatenated Codes and BCH Single-Stage Codes on an Interferance Satellite Channel.IEEE Transactions on Communications.Vol.Com-35,No.5,May 1987,PP.550-556
[16]R G Gallager.Low-Density Parity-Check Codes.IRE Transcations on Information Theory,pp.21-28,Jan.1962
[17]GallagerR. G "Low-densityparity-checkcodes, "IRETrans.Inform.Theory,v01T-8. PP.21-28. Ian.1962
[18]Gallager.R.G Low-Density Parity-Check Codes. MIT Press, Cambridge, Mass, 1963.
[19]Shu Lin, Daniel J, Jr著晏坚等译”差错控制编码”(原书第2版).北京：机械工业出版社.
[20]Chung.S.Y,Forney.G.D,Jr,etal."On the Design of low-density-parity-check codes within 0.0045 dB ofthe Shannon Limit". IEEE Communications Letters,2001,5(2): 58-60.
[21]周亮.纠错编码原理与方法.成都：电子科技大学,2008.
[22]王新梅.纠错码---原理与方法.西安：西安电子科技大学出版社,2002.
[23]Tanner.R.M, "A recursive approach to low complexity codes", IEEE Trans Information Theory 1981,It-27:533-547.
[24]M G Luby,MMitzenmcher,M A Shaokrollah,D A Sepilman.Improved low-density Parity-check Codes Using Irregular Graphs.IEEE Transaction on Information Theory.Vol.47,Issue 2,pp.585-598,Feb.2001
[25]M G Luby,M Mitzenmacher,M A Shokrollahi,and D A Spielman.Analysis of Low-density Parity-check and Improved Designs Using Irregular Graphs.Proceedings of the 30th Annual Symposium on Theory of Computing,pp.249-258,1998
[26]T Richardson and R Urbanke.Efficient Encoding of Low-density Parity-check Codes.IEEE Transactions on Information Theory,Vol.47,pp.638-656,Feb.2001
[27]F R Kschischang,B J Frey,and H-A Loegliger,"Factor graphs and the sum-product algorithm,"IEEE Trans.Inform.Theory,vol.47,pp.498-519,Feb.2001;
[28]M Fossorier,M Mihaljevic,H.Imai,"Reduced complexity iterative decoding of low-density parity check codes based on belief propagation,"IEEE Trans.on Commun, Vol.47,no.5,pp.673-680,May 1999.
[29]L R Bahl, J Cocke,F Jelinek,and J Raviv,"Optimal decoding of linear codes for minimizing symbol error rate",IEEE,Trans.Inform.Theory,vol.20,284-287,Mar.1974
[30]P Roberston,E Villebrun,and P Hoeher,"A comparsion of optimal and sub-optimal MAP decoding algorithms operating in the log domain,"in Proc.IEEE Int.Conf.Communication, vol.2,pp.1009-1013 June 1995.
[31]J Hagenauer,E Offer,and L Papke,"Iterative decoding of binary block and convolutional codes,"IEEE Trans.Inform.Theory,vol.42,pp.429-445,Mar.1996.
[32]X Y Hu,E Eleftheriou,D M Arnold,and A Dholakia.,"Efficient implementations of the sum-product algorithm for decoding LDPC codes,"in Proc.IEEE GLOBECOM,San Antonio,TX,vol.2,pp.1036-1036E,2001.
[33]E Eleftheriou,T Mittelholzer,and A Dholakia,"Reduced-complexity decoding for low-density parity-check codes,"IEEE Electron.Lett.,vol.37,pp.102-104,Jan.2001
[34]A Anastasopoulos,"A comparison between the sum-product and the min-sum iterative detection algorithms based on density evolution,"in Proc.IEEE Globecom,San Antonio,TX,pp.1021-1025,Nov.2001.
[35]叶芳,刘钧雷,朱琦,LDPC码的译码算法,南京邮电学院学报,第23卷,第3期；
[36]尹晓琦,LDPC码编码及译码算法的研究,南京师范大学硕士学位论文；
[37]刘洋,SCFDE系统中的编码研究,山东大学硕十学位论文；
[38]王竞,单载波频域均衡SCFDE与多载波OFDM的性能研究,同济大学硕士学位论文；
[39]孙韶辉,慕建君,王新梅,低密度校验码研究及其最新进展,西安电子科技大学学报(自然科学版),2001年6月,第28卷,第3期；
[40]张晓林,赵玲,张展,苏琳琳,一种基于奇偶校验矩阵的LDPC码的译码方法及译码器,北京航空航天大学,发明专利公开号：CN 101232288 A;
[41]马丕明,宋珍珍,一种准循环LDPC译码器及译码方法,山东大学,发明 专利公开号：CN 102195655 A；
[42]Li Ping Member;IEEE and W.K.Leung Student Member;IEEE Decoding Low Density Parity Check Codes with Finite Quantization Bits;
[43]Dale E.Hocevar DSP Solutions R&D Center Texas Instruments-Dallas TX A Reduced Complexity Decoder Architecture Via Layered Decoding Of LDPC Codes;
[44]G.Masera F.Quaglio and F.Vacca Finite precision inplementation of LDPC decoders;
[45]Kiran K.Gunnam, Gwan S.Choi, Mark B.Yeary and Mohammed Atiquzzaman Department of ECE,Texas A&M University,College Station,TX-77843 School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK-73109 School of Computer Science, University of Oklahoma, Norman, OK-73109. VLSI Architectures for Layered Decoding for Irregular LDPC codes of WiMax.
[46]Tsung-Han Tsai and Cheng-Hung Lin,"A low complexity channel estimation algorithm and architecture design in turbo codes with early termination techniques," Emerging Technologies:Frontiers of Mobile and WirelessCommunication,2004. Proceedings of the IEEE 6th Circuits and Systems Symposium on,vol.1,pp.213-216, 2004.
[47]Richard Bresnan,William Marname,and Massiliano Sala,"Efficient low-density parity-check decoding,"ISSC,Belfast,Ireland,June 2004.
[48]Richard Bresnan, William Marnane, andMassimiliano Sala, "Efficient low-density parity-check decoding, "ISSC, Belfast, Ireland, June 2004;
[49]Brack T, Alles M, Kienle F, and Wehn N, "A Synthesizable IP core for WIMAX 802.16e LDPC Code Decoding, "Personal, Indoor and Mobile Radio Communications,2006 IEEE 17th International Symposium on, pp,1-5, Sept.2006;
[50]吴江,吴伟陵.未来无线通信中的单载波频域均衡技术.数据通信.2004年第5期.PP：4-7.
[51]杨娇瑜.高速移动无线信道自适应均衡研究.北京交通大学硕士学位论文.2006.12.
[52]刘婷婷.新一代无线通信系统中的自适应均衡技术研究.电子科技大学硕士学位论文.2006.4.
[53]孙永梅,李晖.数字通信系统中自适应均衡技术的研究.信息技术.2006第4期.PP：53-56.
[54]高科.多径衰减信道中自适应均衡技术的研究.电子科技大学硕士学位论文. 2006.1.
[55]征学银、王志新、李建东.OFDM的时域与频域均衡技术.空间电子技术.2006增刊.PP：19.26.
[56]Ali Saidi. Decimation-in-Time-Frequency FFT Algorithm. IEEE.1994. PP:453-456.
[2]The International Forum on Future Mobile Telecommunication & China-EU Post. Conference on Beyond 3G,The High Technology Research and Development Center. of MOST(HTRDC) Future Coordination Committee of 863 Program, (FuTURE),Conference proceedings,Nov.20-22,Beijing,China
[3]http://ieee802.org/16
[4]Falconer D,Ariyavisitakul S L, and Benyamin-Seeyar A, et al.Frequency domain equalization for single-carrier broadBand wireless systems. IEEE Commun. Mag., 2002,33(4):58-66.
[5]Falconer D and Ariyavisitakul S L. BroadBand wireless using single carrier and frequency domain equalization. The 5th International Symposium on Wireless Personal Multimedia Communications, Honolulu, Hawaii,2002,1:27-36.
[6]T. Walzman and M.Schwartz, "Automatic Equalization Using the Discrete FrequencyDomain",IEEETrans.Info.Theory,V01.IT-19,No.1,Jan,1973,Page(s):59-68.
[7]E.R.Ferrara,Jr.,"Frequency-Domain Adaptive Filtering",in Adaptive Filters,C.F.N.Cowan and P.M.Grant,editors,Prentice-Hall,1985.
[8]Falconer,D.; Ariyavisitakul,S.L.; Benyamin-Seeyar,A.;Eidson,B.;"Frequency domain equalization for single-carrier broadBand wireless systems",Communications Magazine, IEEE Volume 40,Issue 4, April 2002, Page(s):58-66.
[9]Tingting Shi, Shidong Zhou, Yan Yao, "Capacity of single carrier systems with frequency-domain equalization", Emerging Technologies:Frontiers of Mobile and Wireless Communication,2004. Proceedings of the IEEE 6th Circuits and Systems Symposium on Volume 2,31 May-2 June 2004 Page(s):429-432 V01.2.
[10]Falconer,D.D.; Ariyavisitakul, S.L.; "BroadBand wireless using single carrier and frequency domain equalization",Wireless Personal Multimedia Communications, 2002. The 5th International Symposium on Volume 1,27-30 Oct.2002 Page(s):27-36 vol.1
[11]Mendicute, M.; Altuna,J.;Atxa,V. and Zabalegui,J.M.; "Performance comparison of OFDM and FDE single-carrier modulation for spatial multiplexing MIMO systems", Signal Processing Advances in Wireless Communications,2004 IEEE 5th Workshop on 11-14 July 2004;Page(s):532-535.
[12]Reirdlardt,s.; Weigel,R.; "Pilot aided timing synchronization for SC-FDE and OFDM:a comparison". Communications and Information Technology,2004.ISCIT 2004. IEEE International Symposium on Volume 1,26-29 oct.2004 Page(s):628-633 v01.1.
[13]Yeesoo Han; Heon Huh; Krogmeier,J.V.; "Comparison of error probability for OFDM and SC-FDE", Signals, Systems and Computers,2003.Conference Record ofthe Thirty-Seventh Asilomar Conference on Volume 1,9-12 Nov.2003 Page(s):497-501 Vol.1.
[14]R W Hamming.Error Detecting and Error Correcting Codes.Bell System Tech.J., Vol,29.pp.147-16,1950
[15]Paul C Hershey,Nthony Ethony Ephremids,and Pamk.Khatria.Performance of RS-BCH Concatenated Codes and BCH Single-Stage Codes on an Interferance Satellite Channel.IEEE Transactions on Communications.Vol.Com-35,No.5,May 1987,PP.550-556
[16]R G Gallager.Low-Density Parity-Check Codes.IRE Transcations on Information Theory,pp.21-28,Jan.1962
[17]GallagerR. G "Low-densityparity-checkcodes, "IRETrans.Inform.Theory,v01T-8. PP.21-28. Ian.1962
[18]Gallager.R.G Low-Density Parity-Check Codes. MIT Press, Cambridge, Mass, 1963.
[19]Shu Lin, Daniel J, Jr著晏坚等译”差错控制编码”(原书第2版).北京：机械工业出版社.
[20]Chung.S.Y,Forney.G.D,Jr,etal."On the Design of low-density-parity-check codes within 0.0045 dB ofthe Shannon Limit". IEEE Communications Letters,2001,5(2): 58-60.
[21]周亮.纠错编码原理与方法.成都：电子科技大学,2008.
[22]王新梅.纠错码---原理与方法.西安：西安电子科技大学出版社,2002.
[23]Tanner.R.M, "A recursive approach to low complexity codes", IEEE Trans Information Theory 1981,It-27:533-547.
[24]M G Luby,MMitzenmcher,M A Shaokrollah,D A Sepilman.Improved low-density Parity-check Codes Using Irregular Graphs.IEEE Transaction on Information Theory.Vol.47,Issue 2,pp.585-598,Feb.2001
[25]M G Luby,M Mitzenmacher,M A Shokrollahi,and D A Spielman.Analysis of Low-density Parity-check and Improved Designs Using Irregular Graphs.Proceedings of the 30th Annual Symposium on Theory of Computing,pp.249-258,1998
[26]T Richardson and R Urbanke.Efficient Encoding of Low-density Parity-check Codes.IEEE Transactions on Information Theory,Vol.47,pp.638-656,Feb.2001
[27]F R Kschischang,B J Frey,and H-A Loegliger,"Factor graphs and the sum-product algorithm,"IEEE Trans.Inform.Theory,vol.47,pp.498-519,Feb.2001;
[28]M Fossorier,M Mihaljevic,H.Imai,"Reduced complexity iterative decoding of low-density parity check codes based on belief propagation,"IEEE Trans.on Commun, Vol.47,no.5,pp.673-680,May 1999.
[29]L R Bahl, J Cocke,F Jelinek,and J Raviv,"Optimal decoding of linear codes for minimizing symbol error rate",IEEE,Trans.Inform.Theory,vol.20,284-287,Mar.1974
[30]P Roberston,E Villebrun,and P Hoeher,"A comparsion of optimal and sub-optimal MAP decoding algorithms operating in the log domain,"in Proc.IEEE Int.Conf.Communication, vol.2,pp.1009-1013 June 1995.
[31]J Hagenauer,E Offer,and L Papke,"Iterative decoding of binary block and convolutional codes,"IEEE Trans.Inform.Theory,vol.42,pp.429-445,Mar.1996.
[32]X Y Hu,E Eleftheriou,D M Arnold,and A Dholakia.,"Efficient implementations of the sum-product algorithm for decoding LDPC codes,"in Proc.IEEE GLOBECOM,San Antonio,TX,vol.2,pp.1036-1036E,2001.
[33]E Eleftheriou,T Mittelholzer,and A Dholakia,"Reduced-complexity decoding for low-density parity-check codes,"IEEE Electron.Lett.,vol.37,pp.102-104,Jan.2001
[34]A Anastasopoulos,"A comparison between the sum-product and the min-sum iterative detection algorithms based on density evolution,"in Proc.IEEE Globecom,San Antonio,TX,pp.1021-1025,Nov.2001.
[35]叶芳,刘钧雷,朱琦,LDPC码的译码算法,南京邮电学院学报,第23卷,第3期；
[36]尹晓琦,LDPC码编码及译码算法的研究,南京师范大学硕士学位论文；
[37]刘洋,SCFDE系统中的编码研究,山东大学硕十学位论文；
[38]王竞,单载波频域均衡SCFDE与多载波OFDM的性能研究,同济大学硕士学位论文；
[39]孙韶辉,慕建君,王新梅,低密度校验码研究及其最新进展,西安电子科技大学学报(自然科学版),2001年6月,第28卷,第3期；
[40]张晓林,赵玲,张展,苏琳琳,一种基于奇偶校验矩阵的LDPC码的译码方法及译码器,北京航空航天大学,发明专利公开号：CN 101232288 A;
[41]马丕明,宋珍珍,一种准循环LDPC译码器及译码方法,山东大学,发明 专利公开号：CN 102195655 A；
[42]Li Ping Member;IEEE and W.K.Leung Student Member;IEEE Decoding Low Density Parity Check Codes with Finite Quantization Bits;
[43]Dale E.Hocevar DSP Solutions R&D Center Texas Instruments-Dallas TX A Reduced Complexity Decoder Architecture Via Layered Decoding Of LDPC Codes;
[44]G.Masera F.Quaglio and F.Vacca Finite precision inplementation of LDPC decoders;
[45]Kiran K.Gunnam, Gwan S.Choi, Mark B.Yeary and Mohammed Atiquzzaman Department of ECE,Texas A&M University,College Station,TX-77843 School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK-73109 School of Computer Science, University of Oklahoma, Norman, OK-73109. VLSI Architectures for Layered Decoding for Irregular LDPC codes of WiMax.
[46]Tsung-Han Tsai and Cheng-Hung Lin,"A low complexity channel estimation algorithm and architecture design in turbo codes with early termination techniques," Emerging Technologies:Frontiers of Mobile and WirelessCommunication,2004. Proceedings of the IEEE 6th Circuits and Systems Symposium on,vol.1,pp.213-216, 2004.
[47]Richard Bresnan,William Marname,and Massiliano Sala,"Efficient low-density parity-check decoding,"ISSC,Belfast,Ireland,June 2004.
[48]Richard Bresnan, William Marnane, andMassimiliano Sala, "Efficient low-density parity-check decoding, "ISSC, Belfast, Ireland, June 2004;
[49]Brack T, Alles M, Kienle F, and Wehn N, "A Synthesizable IP core for WIMAX 802.16e LDPC Code Decoding, "Personal, Indoor and Mobile Radio Communications,2006 IEEE 17th International Symposium on, pp,1-5, Sept.2006;
[50]吴江,吴伟陵.未来无线通信中的单载波频域均衡技术.数据通信.2004年第5期.PP：4-7.
[51]杨娇瑜.高速移动无线信道自适应均衡研究.北京交通大学硕士学位论文.2006.12.
[52]刘婷婷.新一代无线通信系统中的自适应均衡技术研究.电子科技大学硕士学位论文.2006.4.
[53]孙永梅,李晖.数字通信系统中自适应均衡技术的研究.信息技术.2006第4期.PP：53-56.
[54]高科.多径衰减信道中自适应均衡技术的研究.电子科技大学硕士学位论文. 2006.1.
[55]征学银、王志新、李建东.OFDM的时域与频域均衡技术.空间电子技术.2006增刊.PP：19.26.
[56]Ali Saidi. Decimation-in-Time-Frequency FFT Algorithm. IEEE.1994. PP:453-456.