CCSDS标准中Turbo译码器硬件实现和性能仿真
摘要
深空通信中面临的问题之一就是如何在低信噪比信道环境下可靠地传递信息。为了能在噪声环境中可靠通信，从60年代开始，人们引入了信道编码方式。Turbo码是基于并行级联卷积码结构的纠错码，通过采用长码块结构和多次迭代的译码方法，Turbo码能够达到接近信道容量的极限的译码性能。由于这种优异特性，CCSDS遥测信道编码建议书在保留原编码方案的前提下加入了Turbo码，并维持了与CCSDS封装遥测建议书的兼容性。
根据CCSDS所建议的编码结构，文章给出了通过FPGA技术实现Turbo译码器的一种简洁有效的方法。在实现过程中，本文采用了滑动窗方式译码，并给出了一种完成Log-MAP算法中的max~*函数功能的简单方法。
首先，文章介绍了深空通信的一些背景知识，接着描述了Turbo码的通用编码结构，推导了MAP和Log-MAP两种译码算法的原理。在简要综述了CCSDS标准的编码结构之后，文章分析了影响译码性能的几个因素，然后对硬件实现过程中的相关参数的选取给出了建议。接下来的部分则描述了译码结构和FPGA实现中的相关知识。最后给出了文章设计后的一些心得和结论。
In deep space communications,one of the problems is how to transmit message credibly in low signal-to-noise ratio(SNR)channel environment.To achieve reliable communication over a noisy channel,channel coding has been used since 1960s. Turbo codes are error-correcting codes based on parallel concatenation of convolutional codes and can achieve near channel capacity performance with a long block size and many decoding iterations.Due to the near-optimum performance ,Turbo codes have been an add-on option to the CCSDS telemetry channel coding recommendation without modifying the existing coding schemes and retained compatibility with the CCSDS packet telemetry recommendation.
Given turbo encoder structure specified by CCSDS, this paper addresses the implementation of a simplified and efficient Turbo decoder in FPGA technology. To implement turbo decoder ,it adopted the sliding window method and devised a way to simplify max* function of Log-MAP algorithm.
First,this paper presents some background knowledge of deep space communications.In the next section,it describes Turbo coding/decoding principles and two decoding algorithms:MAP and Log-MAP.After a brief overview of turbo encoder of the CCSDS standard,it analyses those factors that will influence its performance with the experimental results,and introduces how to choose some variables wisely in the implementation of Log-MAP decoder.The dedicated turbo decoder architecture and the FPGA prototype are described in the next section. Finally it gives the overall conclusions of the paper.
根据CCSDS所建议的编码结构，文章给出了通过FPGA技术实现Turbo译码器的一种简洁有效的方法。在实现过程中，本文采用了滑动窗方式译码，并给出了一种完成Log-MAP算法中的max~*函数功能的简单方法。
首先，文章介绍了深空通信的一些背景知识，接着描述了Turbo码的通用编码结构，推导了MAP和Log-MAP两种译码算法的原理。在简要综述了CCSDS标准的编码结构之后，文章分析了影响译码性能的几个因素，然后对硬件实现过程中的相关参数的选取给出了建议。接下来的部分则描述了译码结构和FPGA实现中的相关知识。最后给出了文章设计后的一些心得和结论。
In deep space communications,one of the problems is how to transmit message credibly in low signal-to-noise ratio(SNR)channel environment.To achieve reliable communication over a noisy channel,channel coding has been used since 1960s. Turbo codes are error-correcting codes based on parallel concatenation of convolutional codes and can achieve near channel capacity performance with a long block size and many decoding iterations.Due to the near-optimum performance ,Turbo codes have been an add-on option to the CCSDS telemetry channel coding recommendation without modifying the existing coding schemes and retained compatibility with the CCSDS packet telemetry recommendation.
Given turbo encoder structure specified by CCSDS, this paper addresses the implementation of a simplified and efficient Turbo decoder in FPGA technology. To implement turbo decoder ,it adopted the sliding window method and devised a way to simplify max* function of Log-MAP algorithm.
First,this paper presents some background knowledge of deep space communications.In the next section,it describes Turbo coding/decoding principles and two decoding algorithms:MAP and Log-MAP.After a brief overview of turbo encoder of the CCSDS standard,it analyses those factors that will influence its performance with the experimental results,and introduces how to choose some variables wisely in the implementation of Log-MAP decoder.The dedicated turbo decoder architecture and the FPGA prototype are described in the next section. Finally it gives the overall conclusions of the paper.
引文
[1] 《TELEMETRY CHANNEL CODING》 CCSDS 101.0-B-6 BLUE BOOK October 2002
[2] 《TELEMETRY CHANNEL CODING》 CCSDS101.0-B-5 BLUE BOOK June 2001
[3] 《TELEMETRY CHANNEL CODING》 CCSDS 101.0-B-4 BLUE BOOK May 1999
[4] 《PACKET TELEMETRY SERVICES》 CCSDS 103.0-B-1 BULE BOOK May 1996
[5] 《PACKET TELEMETRY》 CCSDS 102.0-B-5 BLUE BOOK May 1996
[6] 《ADVANCED ORBITING SYSTEMS, NETWORKS AND DATA LINKS, NETWORKS AND DATA LINKS:ARCHITECTURASPECIFICATION》 CCSDS 701.0-B-2 BLUE BOOK November 1992
[7] KjetilFagervik, "Reconfiguable Turbo Codes for Wireless Data Communications" IEE Colloquium on;20/1_20/6; 22 Nov. 1999.
[8] F. Chiaraluce, E. Gambi, R. Garello等 "On the New CCSDS Standard for Space Telemetry:Turbo Codes and Symbol Synchronization". Communications, 2000. ICC 2000; 451 454 vol. 1; June 2000.
[9] Carl Fredrik Leanderson, Johan Hokfelt, Ove Edfors 等 "On the Design of Low Rate Turbo codes", Vehicular Technology Conference Proceedings, 2000. VTC 2000-Spring Tokyo. 2000 IEEE 51st; 1200_1204 vol. 2;May 2000.
[10] ERIK PAASKE, "Improved Decoding for a Concatenated Coding System Recommended by CCSDS", Communications, IEEE Transactions on; 1138_1144; Aug. 1990.
[11] Dale C. Linne von Berg, Stephen,"Improved Concatenated Coding/Decoding for Deep Space Probes", Information Theory, 1993. Proceedings;380_380;January, 1993.
[12] Michael E. Epperly, Buddy J. Walls, Martin Wasiewicz, "FPGA CCSDS Command Decoder with BCH EDAC and Level-0 Command Execution". Aerospace Conference Proceedings, 2002. IEEE; March 2002.
[13] Jeff B. Berner, "Deep Space Network Turbo Decoder Implementation". Aerospace Conference, 2001, IEEE Proceedings; 3/1149_3/1157 vol. 3; March 2001.
[14] Roberto Barello, Paola Pierleoni, and Sergio Benedetto, "Computing the Free Distance of Turbo Codes and Serially Concatenated Codes with Interleavers:Algorithms and Applications". Selected Areas in Communications, IEEE Journal on; 800_812; May 2001.
[15] Gian Paolo Calzolari#, Enrico Vassallo#, Sandi Habinc#, "CCSDS Telemry Channel Coding: the Turbo Coding Option". New Technologies, New Standards (Ref. No. 1998/519), IEE 5th CCSDS Workshop; 5/1_5/6; Nov. 1998.
[16] E.Paaske, "Alternative to NASA's Concatenated Coding System for the Galileo Galileo Mission". Communications, IEE Proceedings; Aug. 1994; 229_232.
[17] Moision, B.; Hamkins, J. "Low-complexity serially-concatenated coding for the deep space optical channel", Information Theory, 2003. Proceedings. IEEE International Symposium on, 29 June-4 July 2003
[18] Guido Masera, Gianluca Piccinini,Massimo Ruo Roch,and Maurizio Zamboni, "VLSI Architectures for Turbo Codes". IEEE Transactions on, 369_379, Sept. 1999.
[19] L.R.Bahl,J.Cocke,F.Jelinek,and J.Raviv, "Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate", Information Theory, IEEE Trans on; 284_287 vol.20; 1974.
[20] Sangho Yoon, "Turbo Decoder Implementation". Vehicular Technology Conference, 2001; 1824_1828 vol.3; Oct. 2001.
[21] Todd A. Summers and Stephen G. Wilson, "SNR Mismatch and Online Estimation in Turbo Decoding". Communications, IEEE Transactions on; 421_423; April 1998.
[22] Chunlong Bai,Jun jiang and Ping Zhang, "Simplified Recursive Structure for Turbo Decoder with Log-MAP Algorithm". Vehicular Technology Conference, 2002; 1012_1015 vol.2; May 2002.
[23] Sen Jiang,Xiang-fang Su,Dong-liang Xiao and Hong Sun, "Simplification on Log-MAP Algorithm and Its Application in Rayleigh Channel ". Communications, Computers and signal Processing, 2001. 231_233 vol.1; Aug. 2001.
[24] Fathi Raouafi,Adodo Dingninou,Claude Bererow, "Saving Memory in Turbo-decoders using the Max-Log-MAP Algorithm". (Ref. No. 1999/165), IEE Colloquium on, 14/l_14/4; Nov. 1999.
[25] Curt Schurgers,Francky Catthoor,and Marc Engels, "Memory Optimization of MAP Turbo Decoder Algorithms". Very Large Scale Integration (VLSI) Systems, IEEE Transactions on; 305_312; April 2001.
[26] Duanyi Wang and Hisashi Kobayashi, "Low-Complexity MAP Decoding for Turbo Codes". Vehicular Technology Conference Proceedings, 2000; 1035_1039 vol.2; May 2000.
[27] Jung-Fu Cheng,Tony Ottosson, "Linearly Approximated Log-MAP Algorithms for Turbo Decoding". Vehicular Technology Conference Proceedings, 2000; 2252_2256 vol.3; May 2000.
[28] Heiko Michel, Alexander Worn,Michael Munch and Norbert Wehn, "Hardware/Software Trade-offs for Advanced 3G Channel Coding". Design, Automation and Test in Europe Conference and Exhibition, 2002. Proceedings; 396_401; March 2002.
[29] Johannel Steensma,Chris Dick, "FPGA Implementation of a 3GPP Turbo Codec". Signals, Systems and Computers, 2001. 61_65 vol.1; Nov. 2001.
[30] Xiao-Jun Zeng and Zhi-Liang Hong, "Design and Implementation of a Turbo Decoder for 3G W-CDMA System". Consumer Electronics, IEEE Transactions on, 284_291; May 2002.
[31] Yufei Wu,Brian D.Woerner,and T.Keith Blankenship, "Data Width Requirements in SISO Decoding With Modulo Normalization". Communications, IEEE Transactions on; 1861_1868; Nov. 2001.
[32] Andres J.Viterbi, "An Intuitive Justification and a Simplified Implementation of the MAP Decoder for Convolutional Codes". Selected Areas in Communications, IEEE Journal on; 260_264; Feb. 1998.
[33] Arun Raghupathy,K.J Ray Liu, "A Transformation for Computational Latency Reduction in Turbo-MAP Decoding". Circuits and Systems, 1999. 402_405 vol.4, June 1999.
[34] Sanjay Sharma,Sanjay Attri,R.C.Chauhan, "A Simplified and Efficient Implementation of FPGA-Based Turbo Decoder". Performance, Computing, and Communications Conference, 2003. 207_213; April 2003.
[35] Seokhyun Yoon,Yeheskel Bar-Ness, "A Parallel MAP Algorithm for Low Latency Turbo Decoding". Communications Letters, IEEE; 288_290; July 2002.
[36] Patrick Robertson,Emmanulle Villebrun and Peter Hoeher, "A Comparison of Optimal and Sub-Optimal MAP Decoding Algorithms Operating in the Log Domain". Communications, 1995.1009_1013 vol.2;
[37] Claude Berrou and Alain Blavieux, "Near Optimum Error Correcting Coding and Decoding : Turbo-Codes". Communications, IEEE Transactions on; 1261_1271; Oct. 1996.
[38] Joachim Hagenauer,Elke Offer and Lutz Papke, "Iterative Decoding of Binary Block and Convolutional Codes". Information Theory, IEEE Transactions on; 429_445; March 1996.
[39] Zhongfeng Wang,Zhipei Chi and Keshab K.Parhi, "Area-efficient High Speed Decoding Schemes For Turbo/MAP Decoders". Acoustics, Speech, and Signal Processing, 2001. 2633_2636 vol.4; May 2001.
[40] Hiroshi Suzuki,Zhongfeng Wang ,Keshab K.Parhi, "A K=3,2Mbps Low Power Turbo Decoder for 3~(rd) Generation W-CDMA Systems". Custom Integrated Circuits Conference, 2000. 39_42; May 2000.
[41] G.Montorsi and Benedetto, "Design of Fix-Point Iterative Decoders for Concatenated Codes with Interleavers". Global Telecommunications Conference, 2000; 801_806 vol.2; Dec. 2000.
[42] Claude Berrou,Alain Glavieux and Punya Thitimajshima, "Near Shannon Limit Error-correcting Coding and Decoding:Turbo-codes". Communications, 1993. ICC '93 Geneva. 1064_1070 vol.2; May 1993.
[43] William J.Ebel, "Convergence of Iterative Decoding for Fixed-Point Implementation". Circuits and Systems, 2002; Ⅲ_625-8 vol. 3; Aug. 2002.
[44] Gibong Jeong and Dan Hsia, "Optimal Quantization for Soft-Decision Turbo Decoder". Vehicular Technology Conference, 1999. 1620_1624 vol. 3.
[45] Udayan Dasgupta and Costas N. Georghiades, "Turbo Decoding of Quantized Data". Communications, IEEE Transactions on; 56_64; Jan. 2002.
[46] David R. Pauluzzi and Norman C.Bearlieu, "A Comparison of SNR Estimation Techniques for the AWGN Channel". Communications, IEEE Transactions on; 1681_1691; Oct. 2000.
[47] Yunxiang Wu and J. R. Cruz, "Noise Predictive Turbo System". Magnetics, IEEE Transactions on; 742_747; March 2001.
[48] D. Divsalar and F. Pollara, "Multiple Turbo Codes". Military Communications Conference, 1995. 279_285 vol. 1; Nov. 1995.
[49] GC．小克拉克等著，聂涛等译：《数字通信中的纠错编码》 国防工业出版社 1988
[50] 刘玉君编著：《信道编码》 河南科学技术出版社 1992
[51] 王育民、梁传甲编著：《信息与编码理论》，西安电讯工程学院出版社，1985。
[52] 樊昌信、张甫翊等：《通信原理》，国防工业出版社，2002。
[53] 刘东华：《Turbo码原理与应用技术》，电子工业出版社，2004。
[54] 赵树杰：《信号检测与估值理论》，西安电子科技大学出版社，1998。
[55] 实现CCSDS建议的测控网链路设计作者：翟政安等来源：测控与通信
[56] 空间数据系统咨询委员会(CCSDS)的建议和报告来源：电信资料2000年3期
[57] 姜昌 中国深空通信测控(c&T)网发展途径研讨 遥控遥测 1997年1月
[58] 吴玉成、杨士中、刘嘉兴 差错控制编码在卫星通信中的应用 电讯技术2000年1期
[59] 张炜 王莹 张尔扬 基于CCSDS高级在轨系统的遥科学空间通信链路结构研究 宇航学报 第20卷 第3期 1999年7月
[60] 孙白波 加强对CCSDS标准的认识与研究 遥测遥控 1999年7月
[61] 于志坚 房鸿瑞 在我国实施CCSDS标准的基本构想遥测遥控 1999年11月
[62] Morakis, J. C.; Miller, W. H, "Coding techniques under study at NASA", Aerospace Conference, 1997. Proceedings., IEEE 1-8 Feb. 1997 559_565 vol. 3
[63] Costello, D. J., Jr.; Hagenauer, J.; Imai, H等 "Applications of error-control coding Information Theory", IEEE Transactions on Oct. 1998 2531_2560
[2] 《TELEMETRY CHANNEL CODING》 CCSDS101.0-B-5 BLUE BOOK June 2001
[3] 《TELEMETRY CHANNEL CODING》 CCSDS 101.0-B-4 BLUE BOOK May 1999
[4] 《PACKET TELEMETRY SERVICES》 CCSDS 103.0-B-1 BULE BOOK May 1996
[5] 《PACKET TELEMETRY》 CCSDS 102.0-B-5 BLUE BOOK May 1996
[6] 《ADVANCED ORBITING SYSTEMS, NETWORKS AND DATA LINKS, NETWORKS AND DATA LINKS:ARCHITECTURASPECIFICATION》 CCSDS 701.0-B-2 BLUE BOOK November 1992
[7] KjetilFagervik, "Reconfiguable Turbo Codes for Wireless Data Communications" IEE Colloquium on;20/1_20/6; 22 Nov. 1999.
[8] F. Chiaraluce, E. Gambi, R. Garello等 "On the New CCSDS Standard for Space Telemetry:Turbo Codes and Symbol Synchronization". Communications, 2000. ICC 2000; 451 454 vol. 1; June 2000.
[9] Carl Fredrik Leanderson, Johan Hokfelt, Ove Edfors 等 "On the Design of Low Rate Turbo codes", Vehicular Technology Conference Proceedings, 2000. VTC 2000-Spring Tokyo. 2000 IEEE 51st; 1200_1204 vol. 2;May 2000.
[10] ERIK PAASKE, "Improved Decoding for a Concatenated Coding System Recommended by CCSDS", Communications, IEEE Transactions on; 1138_1144; Aug. 1990.
[11] Dale C. Linne von Berg, Stephen,"Improved Concatenated Coding/Decoding for Deep Space Probes", Information Theory, 1993. Proceedings;380_380;January, 1993.
[12] Michael E. Epperly, Buddy J. Walls, Martin Wasiewicz, "FPGA CCSDS Command Decoder with BCH EDAC and Level-0 Command Execution". Aerospace Conference Proceedings, 2002. IEEE; March 2002.
[13] Jeff B. Berner, "Deep Space Network Turbo Decoder Implementation". Aerospace Conference, 2001, IEEE Proceedings; 3/1149_3/1157 vol. 3; March 2001.
[14] Roberto Barello, Paola Pierleoni, and Sergio Benedetto, "Computing the Free Distance of Turbo Codes and Serially Concatenated Codes with Interleavers:Algorithms and Applications". Selected Areas in Communications, IEEE Journal on; 800_812; May 2001.
[15] Gian Paolo Calzolari#, Enrico Vassallo#, Sandi Habinc#, "CCSDS Telemry Channel Coding: the Turbo Coding Option". New Technologies, New Standards (Ref. No. 1998/519), IEE 5th CCSDS Workshop; 5/1_5/6; Nov. 1998.
[16] E.Paaske, "Alternative to NASA's Concatenated Coding System for the Galileo Galileo Mission". Communications, IEE Proceedings; Aug. 1994; 229_232.
[17] Moision, B.; Hamkins, J. "Low-complexity serially-concatenated coding for the deep space optical channel", Information Theory, 2003. Proceedings. IEEE International Symposium on, 29 June-4 July 2003
[18] Guido Masera, Gianluca Piccinini,Massimo Ruo Roch,and Maurizio Zamboni, "VLSI Architectures for Turbo Codes". IEEE Transactions on, 369_379, Sept. 1999.
[19] L.R.Bahl,J.Cocke,F.Jelinek,and J.Raviv, "Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate", Information Theory, IEEE Trans on; 284_287 vol.20; 1974.
[20] Sangho Yoon, "Turbo Decoder Implementation". Vehicular Technology Conference, 2001; 1824_1828 vol.3; Oct. 2001.
[21] Todd A. Summers and Stephen G. Wilson, "SNR Mismatch and Online Estimation in Turbo Decoding". Communications, IEEE Transactions on; 421_423; April 1998.
[22] Chunlong Bai,Jun jiang and Ping Zhang, "Simplified Recursive Structure for Turbo Decoder with Log-MAP Algorithm". Vehicular Technology Conference, 2002; 1012_1015 vol.2; May 2002.
[23] Sen Jiang,Xiang-fang Su,Dong-liang Xiao and Hong Sun, "Simplification on Log-MAP Algorithm and Its Application in Rayleigh Channel ". Communications, Computers and signal Processing, 2001. 231_233 vol.1; Aug. 2001.
[24] Fathi Raouafi,Adodo Dingninou,Claude Bererow, "Saving Memory in Turbo-decoders using the Max-Log-MAP Algorithm". (Ref. No. 1999/165), IEE Colloquium on, 14/l_14/4; Nov. 1999.
[25] Curt Schurgers,Francky Catthoor,and Marc Engels, "Memory Optimization of MAP Turbo Decoder Algorithms". Very Large Scale Integration (VLSI) Systems, IEEE Transactions on; 305_312; April 2001.
[26] Duanyi Wang and Hisashi Kobayashi, "Low-Complexity MAP Decoding for Turbo Codes". Vehicular Technology Conference Proceedings, 2000; 1035_1039 vol.2; May 2000.
[27] Jung-Fu Cheng,Tony Ottosson, "Linearly Approximated Log-MAP Algorithms for Turbo Decoding". Vehicular Technology Conference Proceedings, 2000; 2252_2256 vol.3; May 2000.
[28] Heiko Michel, Alexander Worn,Michael Munch and Norbert Wehn, "Hardware/Software Trade-offs for Advanced 3G Channel Coding". Design, Automation and Test in Europe Conference and Exhibition, 2002. Proceedings; 396_401; March 2002.
[29] Johannel Steensma,Chris Dick, "FPGA Implementation of a 3GPP Turbo Codec". Signals, Systems and Computers, 2001. 61_65 vol.1; Nov. 2001.
[30] Xiao-Jun Zeng and Zhi-Liang Hong, "Design and Implementation of a Turbo Decoder for 3G W-CDMA System". Consumer Electronics, IEEE Transactions on, 284_291; May 2002.
[31] Yufei Wu,Brian D.Woerner,and T.Keith Blankenship, "Data Width Requirements in SISO Decoding With Modulo Normalization". Communications, IEEE Transactions on; 1861_1868; Nov. 2001.
[32] Andres J.Viterbi, "An Intuitive Justification and a Simplified Implementation of the MAP Decoder for Convolutional Codes". Selected Areas in Communications, IEEE Journal on; 260_264; Feb. 1998.
[33] Arun Raghupathy,K.J Ray Liu, "A Transformation for Computational Latency Reduction in Turbo-MAP Decoding". Circuits and Systems, 1999. 402_405 vol.4, June 1999.
[34] Sanjay Sharma,Sanjay Attri,R.C.Chauhan, "A Simplified and Efficient Implementation of FPGA-Based Turbo Decoder". Performance, Computing, and Communications Conference, 2003. 207_213; April 2003.
[35] Seokhyun Yoon,Yeheskel Bar-Ness, "A Parallel MAP Algorithm for Low Latency Turbo Decoding". Communications Letters, IEEE; 288_290; July 2002.
[36] Patrick Robertson,Emmanulle Villebrun and Peter Hoeher, "A Comparison of Optimal and Sub-Optimal MAP Decoding Algorithms Operating in the Log Domain". Communications, 1995.1009_1013 vol.2;
[37] Claude Berrou and Alain Blavieux, "Near Optimum Error Correcting Coding and Decoding : Turbo-Codes". Communications, IEEE Transactions on; 1261_1271; Oct. 1996.
[38] Joachim Hagenauer,Elke Offer and Lutz Papke, "Iterative Decoding of Binary Block and Convolutional Codes". Information Theory, IEEE Transactions on; 429_445; March 1996.
[39] Zhongfeng Wang,Zhipei Chi and Keshab K.Parhi, "Area-efficient High Speed Decoding Schemes For Turbo/MAP Decoders". Acoustics, Speech, and Signal Processing, 2001. 2633_2636 vol.4; May 2001.
[40] Hiroshi Suzuki,Zhongfeng Wang ,Keshab K.Parhi, "A K=3,2Mbps Low Power Turbo Decoder for 3~(rd) Generation W-CDMA Systems". Custom Integrated Circuits Conference, 2000. 39_42; May 2000.
[41] G.Montorsi and Benedetto, "Design of Fix-Point Iterative Decoders for Concatenated Codes with Interleavers". Global Telecommunications Conference, 2000; 801_806 vol.2; Dec. 2000.
[42] Claude Berrou,Alain Glavieux and Punya Thitimajshima, "Near Shannon Limit Error-correcting Coding and Decoding:Turbo-codes". Communications, 1993. ICC '93 Geneva. 1064_1070 vol.2; May 1993.
[43] William J.Ebel, "Convergence of Iterative Decoding for Fixed-Point Implementation". Circuits and Systems, 2002; Ⅲ_625-8 vol. 3; Aug. 2002.
[44] Gibong Jeong and Dan Hsia, "Optimal Quantization for Soft-Decision Turbo Decoder". Vehicular Technology Conference, 1999. 1620_1624 vol. 3.
[45] Udayan Dasgupta and Costas N. Georghiades, "Turbo Decoding of Quantized Data". Communications, IEEE Transactions on; 56_64; Jan. 2002.
[46] David R. Pauluzzi and Norman C.Bearlieu, "A Comparison of SNR Estimation Techniques for the AWGN Channel". Communications, IEEE Transactions on; 1681_1691; Oct. 2000.
[47] Yunxiang Wu and J. R. Cruz, "Noise Predictive Turbo System". Magnetics, IEEE Transactions on; 742_747; March 2001.
[48] D. Divsalar and F. Pollara, "Multiple Turbo Codes". Military Communications Conference, 1995. 279_285 vol. 1; Nov. 1995.
[49] GC．小克拉克等著，聂涛等译：《数字通信中的纠错编码》 国防工业出版社 1988
[50] 刘玉君编著：《信道编码》 河南科学技术出版社 1992
[51] 王育民、梁传甲编著：《信息与编码理论》，西安电讯工程学院出版社，1985。
[52] 樊昌信、张甫翊等：《通信原理》，国防工业出版社，2002。
[53] 刘东华：《Turbo码原理与应用技术》，电子工业出版社，2004。
[54] 赵树杰：《信号检测与估值理论》，西安电子科技大学出版社，1998。
[55] 实现CCSDS建议的测控网链路设计作者：翟政安等来源：测控与通信
[56] 空间数据系统咨询委员会(CCSDS)的建议和报告来源：电信资料2000年3期
[57] 姜昌 中国深空通信测控(c&T)网发展途径研讨 遥控遥测 1997年1月
[58] 吴玉成、杨士中、刘嘉兴 差错控制编码在卫星通信中的应用 电讯技术2000年1期
[59] 张炜 王莹 张尔扬 基于CCSDS高级在轨系统的遥科学空间通信链路结构研究 宇航学报 第20卷 第3期 1999年7月
[60] 孙白波 加强对CCSDS标准的认识与研究 遥测遥控 1999年7月
[61] 于志坚 房鸿瑞 在我国实施CCSDS标准的基本构想遥测遥控 1999年11月
[62] Morakis, J. C.; Miller, W. H, "Coding techniques under study at NASA", Aerospace Conference, 1997. Proceedings., IEEE 1-8 Feb. 1997 559_565 vol. 3
[63] Costello, D. J., Jr.; Hagenauer, J.; Imai, H等 "Applications of error-control coding Information Theory", IEEE Transactions on Oct. 1998 2531_2560