分布式视频编码的关键技术研究
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摘要
传统视频压缩技术(如H.26x等)主要在编码端进行复杂的变换、预测、熵编码等以挖掘视频的冗余信息,达到信息压缩的目的,这导致编码过程复杂,对编码器要求较高。然而,随着低成本的视频传感器网络、移动多媒体等的出现,使得传统视频编码技术已经不能满足新情况的要求。所以,分布式视频编码(Distributed Video Coding:DVC)方案开始受到了人们的关注。该编码方案将复杂的运算放在了译码端进行,从而减轻编码端的计算复杂度。
本文在基于Turbo码的分布式视频编码框架的基础上,主要做了以下工作：
1.阐述了Turbo码的编译码原理。重点研究了其最大后验概率译码算法,使其能更好的应用于分布式视频编译码系统的译码器中。分布式视频编码器采用Turbo码编码器,并采用基于删余矩阵的校验子请求机制,在译码失败时向译码端传送更多的校验信息。仿真结果表明,该方案的编码压缩效率高于传统帧内预测压缩编码方案(与H.263+相比较),但与传统帧间预测编码方案(双向预测)相比仍存在一定差距。
2.文章研究了边信息常用的生成算法：外推插值法和内插插值法。基于本文分布式编码框架结构,我们采用内插插值法来生成边信息。文章重点分析了边信息的平均内插生成算法和基于块匹配的运动补偿内插生成算法各自的优缺点,并采用了组合算法。仿真结果表明,该方案比单纯的采用平均内插算法或单纯的采用基于块匹配的运动补偿算法取得到更好的率失真效果。
3.本文还研究了分布式视频编码的虚拟信道模型,提出新的参数估计方案,仿真结果表明,在高量化比特的条件下,该方案能取得比整视频序列使用单一虚拟信道参数的更好的率失真效果。
The traditional video compression technologies (such as H.26x, etc.)mainly implement complicated transformation, prediction and entropy coding at the encoder to achieve the purpose of information compression, which leads a complex encoding process and needs an encoder with a high complexity. However, with the development of the low-cost video sensor network and mobile multimedia, the traditional video coding can not meet the need of the new situation. So, the Distributed Video Coding (DVC) scheme is becoming more and more attractive.This coding scheme makes the complexity calculation on the decoder side to reduce the complexity of the encoder.
Based on the Turbo codes DVC,the main works done in the paper are as follows:
1.The Turbo encoding and decoding theory are expatiated. And we mainly study the Maximum A Posteriori decoding algorithm to make it more suitable to implement the decoder of DVC.Turbo encoder is used as the encoder of DVC with the difference of using request scheme based on the puncturing matrix when the decoding fails.The simulation results show that the proposed scheme has better performance than the traditional intra prediction coding scheme (H263+),but with some gap with the inter prediction coding scheme (bidirectional).
2.Side information generation algorithm,such as extrapolation and interpolation, is studied.Under the framework of DVC,interpolation algorithm is used to generate the side information. Average interpolation and motion compensation interpolation based on block matching are studied. We analyze both the advantages and disadvantages of the two methods, and then, a combined algorithm is proposed. The simulation results show that the proposed scheme makes a better performance than anyone of the two methods.
3.Virtual channel model in DVC is also studied in the paper, we proposed a new parameter estimation scheme, experimental result shows that the proposed scheme makes a better performance than that of using one parameter in the whole video sequence in the condition of high bit quantization.
本文在基于Turbo码的分布式视频编码框架的基础上,主要做了以下工作：
1.阐述了Turbo码的编译码原理。重点研究了其最大后验概率译码算法,使其能更好的应用于分布式视频编译码系统的译码器中。分布式视频编码器采用Turbo码编码器,并采用基于删余矩阵的校验子请求机制,在译码失败时向译码端传送更多的校验信息。仿真结果表明,该方案的编码压缩效率高于传统帧内预测压缩编码方案(与H.263+相比较),但与传统帧间预测编码方案(双向预测)相比仍存在一定差距。
2.文章研究了边信息常用的生成算法：外推插值法和内插插值法。基于本文分布式编码框架结构,我们采用内插插值法来生成边信息。文章重点分析了边信息的平均内插生成算法和基于块匹配的运动补偿内插生成算法各自的优缺点,并采用了组合算法。仿真结果表明,该方案比单纯的采用平均内插算法或单纯的采用基于块匹配的运动补偿算法取得到更好的率失真效果。
3.本文还研究了分布式视频编码的虚拟信道模型,提出新的参数估计方案,仿真结果表明,在高量化比特的条件下,该方案能取得比整视频序列使用单一虚拟信道参数的更好的率失真效果。
The traditional video compression technologies (such as H.26x, etc.)mainly implement complicated transformation, prediction and entropy coding at the encoder to achieve the purpose of information compression, which leads a complex encoding process and needs an encoder with a high complexity. However, with the development of the low-cost video sensor network and mobile multimedia, the traditional video coding can not meet the need of the new situation. So, the Distributed Video Coding (DVC) scheme is becoming more and more attractive.This coding scheme makes the complexity calculation on the decoder side to reduce the complexity of the encoder.
Based on the Turbo codes DVC,the main works done in the paper are as follows:
1.The Turbo encoding and decoding theory are expatiated. And we mainly study the Maximum A Posteriori decoding algorithm to make it more suitable to implement the decoder of DVC.Turbo encoder is used as the encoder of DVC with the difference of using request scheme based on the puncturing matrix when the decoding fails.The simulation results show that the proposed scheme has better performance than the traditional intra prediction coding scheme (H263+),but with some gap with the inter prediction coding scheme (bidirectional).
2.Side information generation algorithm,such as extrapolation and interpolation, is studied.Under the framework of DVC,interpolation algorithm is used to generate the side information. Average interpolation and motion compensation interpolation based on block matching are studied. We analyze both the advantages and disadvantages of the two methods, and then, a combined algorithm is proposed. The simulation results show that the proposed scheme makes a better performance than anyone of the two methods.
3.Virtual channel model in DVC is also studied in the paper, we proposed a new parameter estimation scheme, experimental result shows that the proposed scheme makes a better performance than that of using one parameter in the whole video sequence in the condition of high bit quantization.
引文
[1]毕厚杰.新一代视频压缩编码标准——H.264/AVC.人民邮电出版社,2004.
[2]David Slepian, Jack K. Wolf. Noiseless Coding of Correlated Information Sources.IEEE Trans.Inf. Theory,1973,(19) 4:471-480
[3]Aaron D.Wyner, Jacob Ziv. The Rate-Distortion Function for Source Coding with Side Information at the Decoder. IEEE Trans.Inf. Theory,1976, (22) 1:1-10
[4]Anne Aaron, Bernd Girod. Compression with Side Information Using Turbo Codes.Proc. DCC'02,Snowbird, UT,2003.4:252-261
[5]Javier Garcia-Frias, Ying Zhao.Compression of Correlated Binary Sources Using Turbo Codes.IEEE Communication Letters,2001.10,(5)10:417-419
[6]Ying Zhao, Javier Garcia-Frias.Joint Estimation and Compression of Correlated Nonbinary Sources Using Punctured Turbo Codes.IEEE Trans.Com.,2005,(53) 3:385-390
[7]Angelos D.Livers, Zixiang Xiong, Costas N.Georghiades.Compression of Binary Sources with Side Information at the Decoder Using LDPC Codes.IEEE Commun. Lett., 2002,(6)10:440-442
[8]Yang Yang. Samuel Cheng.Zixiang Xiong. Wei Zhao.Wyner-Ziv Coding Based on TCQ and LDPC Codes.Proc Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA,2003
[9]Angelos D.Livers, Zixiang Xiong, Costas N.Georghiades.A Distributed Source Coding Technique for Correlated Images Using Turbo Codes.IEEE Commun. Lett.,2002,6 (9): 379-381
[10]Zixiang Xiong, Angelos D.Livers, Samuel Cheng, Zhixin Liu. Nested Quantization and Slepian-Wolf Coding:A Wyner-Ziv Coding Paradigm for I.i.d Sources.Proc IEEE Workshop on Statistical Signal Processing, St. Louis, MO,2003
[11]Angelos D.Livers, Zixiang Xiong, Costas N.Georghiades.Joint source-channel coding of binary sources with side information at the decoder using IRA codes.Proc of Multi-media Signal Processing Workshop.Cirgin Islands,2002.
[12]Bernd Girod,Anne Aaron,Shantanu Rane,David Rebollo-Monedero.Distributed Video Coding.IEEE Special Issues on Advances in Video Coding and Delivery:1-12
[13]Anne Aaron, Eric Setton, Bernd Girod, Towards Practical Wyner-Ziv Coding of Video. Proc IEEE International Conference on Image Processing, Barcelona, Spain,2003
[14]Anne Aaron, Shantanu Rane,Eric Setton, Bernd Girod. Transform-domain Wyner-Ziv Codec for Video.Proc SPIE Visual Communications and Image Processing, San Jose CA, 2004
[15]Anne Aaron, Shantanu Rane,Bernd Girod.Wyner-Ziv Coding with Hash based Motion Compensation at the Receiver. Proc IEEE International Conference on Image Processing, Singapore,2004-10
[16]Anne Aaron, Rui Zhang, Bernd Girod.Wyner-Ziv Coding of Motion Video.Asilomar Conference on Signals, Systems and Computers, Pacific Grove, USA,2002.11
[17]Anne Aaron, Shantanu Rane, Bernd Girod. Wyner-Ziv Coding for Video:Applications to Compression and Error Resilience.Proc IEEE Data Compression Conference, Snowbird, UT,2003:93-102
[18]David Varodayan, Yao-Chung Lin, Aditya Mavlankar, Markus Flierlm,Bernd Gird. Wyner-Ziv Coding of Stereo Images with Unsupervised Learning of Disparity. Proceedings of the Picture Coding Symposium,Lisbon, Portugal,2007
[19]David Varodayan, David Chen, Markus Flierlm,Bernd Gird. Wyner-Ziv Coding of Video with Unsupervised Motion Vector Learning.Signal Processing:Images Communication, 2008(23)5:369-378
[20]X.Artigas, J.Ascenso,M.Dalai,S.Klomp, D.Kubasov, M.Ouaret. The DISCOVER Codec:Architecture.Techniques and Evaluation.Picture Coding Symposium.Lisbon. Portugal,2007,11
[21]S.Sandeep Pradhan, Kannan Ramchandran. Distributed Source Coding:Symmetric Rates and Applications to Sensor network. Proc IEEE Data Compression Conference, Snowbird, UT,2000:361-370
[22]S.Sandeep Pradhan, Jim Chou, Kannan Ramchandran. Duality between Source Coding and Channel Coding and its Extension to the Side Information Case.IEEE Trans Inf. Theory,2003,(49) 5:1181-1203
[23]S.Sandeep Pradhan, Kannan Ramchandran. Distributed Source Coding Using Syndromes (DISCUS):Design and Construction. IEEE Trans.Theory,2003,(49) 2:626-643
[24]Rohit Puri,Abhik Majumdar, Kannan Ramchandran. PRISM:A Video Coding Paradigm with Motion Estimation at the Decoder. IEEE Trans.Image Proc.2007, (16)10:2436-2448
[25]Zhe Li, Sheng Fang, Guofu Huang,Lan Bai.A New Framework of Scalable Video Compression with High Error Resilience Based on Wavelet Using Wyner-Ziv Technique. IEEE Conference on Multimedia Information Networking and Security,2009:218-221
[26]Zhe Li, Sheng Fang, Xujian Li, Ke Xu. A New Paradigm of Coding for Scalable Video Coding with Wavelet-based. IEEE Conference on Communication Technology, 2008,:649-652
[27]Jin-Jun Xiao, Alejandro Ribeiro, Zhi-Quan Luo,Georogios B.Giannakis.Distributed Compression Estimation Using Wireless Sensor Networks.IEEE Signal Proc 2006, (23) 4:27-41
[28]Arun Avudainayagam, John M.Shwa, Dapeng Wu. A Hyper-Trellis based Turbo Decoder for Wyner-Ziv Video Coding.IEEE Globecom,2005:1412:1417
[29]蒋刚毅,金智鹏,郁梅.分布式视频编码方法研究.中国图象图形学报,2008,13(3)：386-393
[30]Bruno Macchiavello, Fernanda Brandi, Eduardo Peixoto, Ricardo L.de Queiroz, Debargha Mukherjee.Side-Information Generation for Temporally and Spatially Scalable Wyner-Ziv Codecs.EURASIP Journal on Image and Video Processing,2009: 1-11
[31]Pierre Ferre, Dimitris Agrafiotis,David Bull.Fusion Methods for Side Information Generation in Multi-View Distributed Video Coding Systems.IEEE Conferences on Image Proc.,2007, IV-409-IV-412
[32]Luis Natariol,Catarina Brites, Joao Ascenso, Fernando Pereira. Extrapolating Side Information for Low-Delay Pixel-Domain Distributed Video. Coding.Lecture Notes in. Computer Science,2005
[33]干宗良,齐丽娜,朱秀昌.Wyner-Ziv视频系统中的解码算法研究.信号处理,2008,24(4)：609-613
[34]Ming-Hui Cheng, Jin-Jang Leou. A New Side Information Generation Scheme for Distributed Video Coding. PCM 2008,LNCS 5353,2008:782-785
[35]Xiaodong Liu, Qionghai Dai, Rui Wang.An Improved Side Information Refinement Method in Distributed Video Coding.2009 World Congress on Computer Science and Information Engineering,2009:312-315
[36]Charles Mathis, Thomas M.Cover. A Statistic for Measuring the Influence of Side Information in Investment. IEEE Conference on Information Theory,2005:1156-1157
[37]Catarina Brites, Joao Ascenso, Fernando Pereira. Modeling Correlation Noise Statistics at Decoder for Pixel Based Wyner-Ziv Video Coding. IEEE International Conference on Image Proc.,2006
[38]王崇彦,陆锦辉.信息论基础.兵器工业出版社,1992.4
[39]John G. Proakis.Digital Communications,Fourth edition. McGraw-Hill Companies.2001
[40]吴湛击.现代纠错编码与调制理论及应用：Theory and application.人民邮电出版社,2008
[41]C E Shannon, A Mathematical Theory of Communication. Bell Syst. Tech. J.,1948,27: 379-423
[42]P Elias.Coding for Noisy Channles.IRE Conv. Rec.,1955
[43]A J Viterbi.Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm.IEEE Trans.Inform.Theory,1967,13:260-269
[44]冀复生,Turbo码给我们的启示,中国科学院计算技术研究所内部刊物-信息技术快报,2004,8
[45]Claude Berrou, Alain Glavieux, Punya Thitimajshima. Near Shannon Limit Error Correcting Coding and Decoding.Proc.IEEE International Conference on Communication,Genva,Switzerland,1993.5:1064-1070
[46]L.R.Bahl, J. Cocke, F. Jelinek, J.Raviv. Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate.IEEE Trans.Inform.Theory.1974:284-287
[47]D.Divsalar, F. Pollara. On the Design of Turbo Codes.TDA Progress Report 42-123, 1995:99-121
[48]刘东华.Turbo码原理与应用技术.电子工业出版社,2004
[49]Douglas N.Rowitch, Laurence B.Milstein. On the Performance of Hybrid FEC/ARQ Systems Using Rate Compatible Punctured Turbo (RCPT) Codes.IEEE Trans.on-Communication,2000,(48)6:948-959
[50]Shu Lin, Daniel J.Costello,Jr..Error Contrl Coding, Second Edition. Pearson Education. 2004
[51]卿粼波,何小海,吕瑞,曾强宇.基于比特概率优化算法的分布式视频编码.光电子激光,2008,19(5)：620-624
[52]Yongpeng Li,Siwei Ma, Debin Zhao, Wen Gao.Modeling Correlation Noise Statistics at Decoder for Multi-view Distributed Video Coding.IEEE International Symposium on Circuits and Systems,2009:2597-2600
[53]房胜,李哲,梁永全,钟玉琢.分布式视频编码虚拟依赖信道模型研究.计算机学报,2009,32(7)：1404-1412
[54]卿粼波,何小海,张志亮.分布式视频编码中虚拟信道模型的动态估计.光学精密工程,2009,17(4)：923-929
[55]Catarina Brites, Joao Ascenso, Fernando Pereira. Studying Temporal Correlation Noise Modeling for Pixel Based Wyner-Ziv Coding. IEEE International Conference on Image Processing,2006:273-276
[56]Jurgen Slowack, Stefaan Mys,Jozef Skorupa, Peter Lambert, Rik Van de Walle, Christos Grecos.Accounting for Quantization Noise in Online Correlation Noise Estimation for Distributed Video Coding.IEEE Picture Coding Symposium,2009:1-4
[2]David Slepian, Jack K. Wolf. Noiseless Coding of Correlated Information Sources.IEEE Trans.Inf. Theory,1973,(19) 4:471-480
[3]Aaron D.Wyner, Jacob Ziv. The Rate-Distortion Function for Source Coding with Side Information at the Decoder. IEEE Trans.Inf. Theory,1976, (22) 1:1-10
[4]Anne Aaron, Bernd Girod. Compression with Side Information Using Turbo Codes.Proc. DCC'02,Snowbird, UT,2003.4:252-261
[5]Javier Garcia-Frias, Ying Zhao.Compression of Correlated Binary Sources Using Turbo Codes.IEEE Communication Letters,2001.10,(5)10:417-419
[6]Ying Zhao, Javier Garcia-Frias.Joint Estimation and Compression of Correlated Nonbinary Sources Using Punctured Turbo Codes.IEEE Trans.Com.,2005,(53) 3:385-390
[7]Angelos D.Livers, Zixiang Xiong, Costas N.Georghiades.Compression of Binary Sources with Side Information at the Decoder Using LDPC Codes.IEEE Commun. Lett., 2002,(6)10:440-442
[8]Yang Yang. Samuel Cheng.Zixiang Xiong. Wei Zhao.Wyner-Ziv Coding Based on TCQ and LDPC Codes.Proc Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA,2003
[9]Angelos D.Livers, Zixiang Xiong, Costas N.Georghiades.A Distributed Source Coding Technique for Correlated Images Using Turbo Codes.IEEE Commun. Lett.,2002,6 (9): 379-381
[10]Zixiang Xiong, Angelos D.Livers, Samuel Cheng, Zhixin Liu. Nested Quantization and Slepian-Wolf Coding:A Wyner-Ziv Coding Paradigm for I.i.d Sources.Proc IEEE Workshop on Statistical Signal Processing, St. Louis, MO,2003
[11]Angelos D.Livers, Zixiang Xiong, Costas N.Georghiades.Joint source-channel coding of binary sources with side information at the decoder using IRA codes.Proc of Multi-media Signal Processing Workshop.Cirgin Islands,2002.
[12]Bernd Girod,Anne Aaron,Shantanu Rane,David Rebollo-Monedero.Distributed Video Coding.IEEE Special Issues on Advances in Video Coding and Delivery:1-12
[13]Anne Aaron, Eric Setton, Bernd Girod, Towards Practical Wyner-Ziv Coding of Video. Proc IEEE International Conference on Image Processing, Barcelona, Spain,2003
[14]Anne Aaron, Shantanu Rane,Eric Setton, Bernd Girod. Transform-domain Wyner-Ziv Codec for Video.Proc SPIE Visual Communications and Image Processing, San Jose CA, 2004
[15]Anne Aaron, Shantanu Rane,Bernd Girod.Wyner-Ziv Coding with Hash based Motion Compensation at the Receiver. Proc IEEE International Conference on Image Processing, Singapore,2004-10
[16]Anne Aaron, Rui Zhang, Bernd Girod.Wyner-Ziv Coding of Motion Video.Asilomar Conference on Signals, Systems and Computers, Pacific Grove, USA,2002.11
[17]Anne Aaron, Shantanu Rane, Bernd Girod. Wyner-Ziv Coding for Video:Applications to Compression and Error Resilience.Proc IEEE Data Compression Conference, Snowbird, UT,2003:93-102
[18]David Varodayan, Yao-Chung Lin, Aditya Mavlankar, Markus Flierlm,Bernd Gird. Wyner-Ziv Coding of Stereo Images with Unsupervised Learning of Disparity. Proceedings of the Picture Coding Symposium,Lisbon, Portugal,2007
[19]David Varodayan, David Chen, Markus Flierlm,Bernd Gird. Wyner-Ziv Coding of Video with Unsupervised Motion Vector Learning.Signal Processing:Images Communication, 2008(23)5:369-378
[20]X.Artigas, J.Ascenso,M.Dalai,S.Klomp, D.Kubasov, M.Ouaret. The DISCOVER Codec:Architecture.Techniques and Evaluation.Picture Coding Symposium.Lisbon. Portugal,2007,11
[21]S.Sandeep Pradhan, Kannan Ramchandran. Distributed Source Coding:Symmetric Rates and Applications to Sensor network. Proc IEEE Data Compression Conference, Snowbird, UT,2000:361-370
[22]S.Sandeep Pradhan, Jim Chou, Kannan Ramchandran. Duality between Source Coding and Channel Coding and its Extension to the Side Information Case.IEEE Trans Inf. Theory,2003,(49) 5:1181-1203
[23]S.Sandeep Pradhan, Kannan Ramchandran. Distributed Source Coding Using Syndromes (DISCUS):Design and Construction. IEEE Trans.Theory,2003,(49) 2:626-643
[24]Rohit Puri,Abhik Majumdar, Kannan Ramchandran. PRISM:A Video Coding Paradigm with Motion Estimation at the Decoder. IEEE Trans.Image Proc.2007, (16)10:2436-2448
[25]Zhe Li, Sheng Fang, Guofu Huang,Lan Bai.A New Framework of Scalable Video Compression with High Error Resilience Based on Wavelet Using Wyner-Ziv Technique. IEEE Conference on Multimedia Information Networking and Security,2009:218-221
[26]Zhe Li, Sheng Fang, Xujian Li, Ke Xu. A New Paradigm of Coding for Scalable Video Coding with Wavelet-based. IEEE Conference on Communication Technology, 2008,:649-652
[27]Jin-Jun Xiao, Alejandro Ribeiro, Zhi-Quan Luo,Georogios B.Giannakis.Distributed Compression Estimation Using Wireless Sensor Networks.IEEE Signal Proc 2006, (23) 4:27-41
[28]Arun Avudainayagam, John M.Shwa, Dapeng Wu. A Hyper-Trellis based Turbo Decoder for Wyner-Ziv Video Coding.IEEE Globecom,2005:1412:1417
[29]蒋刚毅,金智鹏,郁梅.分布式视频编码方法研究.中国图象图形学报,2008,13(3)：386-393
[30]Bruno Macchiavello, Fernanda Brandi, Eduardo Peixoto, Ricardo L.de Queiroz, Debargha Mukherjee.Side-Information Generation for Temporally and Spatially Scalable Wyner-Ziv Codecs.EURASIP Journal on Image and Video Processing,2009: 1-11
[31]Pierre Ferre, Dimitris Agrafiotis,David Bull.Fusion Methods for Side Information Generation in Multi-View Distributed Video Coding Systems.IEEE Conferences on Image Proc.,2007, IV-409-IV-412
[32]Luis Natariol,Catarina Brites, Joao Ascenso, Fernando Pereira. Extrapolating Side Information for Low-Delay Pixel-Domain Distributed Video. Coding.Lecture Notes in. Computer Science,2005
[33]干宗良,齐丽娜,朱秀昌.Wyner-Ziv视频系统中的解码算法研究.信号处理,2008,24(4)：609-613
[34]Ming-Hui Cheng, Jin-Jang Leou. A New Side Information Generation Scheme for Distributed Video Coding. PCM 2008,LNCS 5353,2008:782-785
[35]Xiaodong Liu, Qionghai Dai, Rui Wang.An Improved Side Information Refinement Method in Distributed Video Coding.2009 World Congress on Computer Science and Information Engineering,2009:312-315
[36]Charles Mathis, Thomas M.Cover. A Statistic for Measuring the Influence of Side Information in Investment. IEEE Conference on Information Theory,2005:1156-1157
[37]Catarina Brites, Joao Ascenso, Fernando Pereira. Modeling Correlation Noise Statistics at Decoder for Pixel Based Wyner-Ziv Video Coding. IEEE International Conference on Image Proc.,2006
[38]王崇彦,陆锦辉.信息论基础.兵器工业出版社,1992.4
[39]John G. Proakis.Digital Communications,Fourth edition. McGraw-Hill Companies.2001
[40]吴湛击.现代纠错编码与调制理论及应用：Theory and application.人民邮电出版社,2008
[41]C E Shannon, A Mathematical Theory of Communication. Bell Syst. Tech. J.,1948,27: 379-423
[42]P Elias.Coding for Noisy Channles.IRE Conv. Rec.,1955
[43]A J Viterbi.Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm.IEEE Trans.Inform.Theory,1967,13:260-269
[44]冀复生,Turbo码给我们的启示,中国科学院计算技术研究所内部刊物-信息技术快报,2004,8
[45]Claude Berrou, Alain Glavieux, Punya Thitimajshima. Near Shannon Limit Error Correcting Coding and Decoding.Proc.IEEE International Conference on Communication,Genva,Switzerland,1993.5:1064-1070
[46]L.R.Bahl, J. Cocke, F. Jelinek, J.Raviv. Optimal Decoding of Linear Codes for Minimizing Symbol Error Rate.IEEE Trans.Inform.Theory.1974:284-287
[47]D.Divsalar, F. Pollara. On the Design of Turbo Codes.TDA Progress Report 42-123, 1995:99-121
[48]刘东华.Turbo码原理与应用技术.电子工业出版社,2004
[49]Douglas N.Rowitch, Laurence B.Milstein. On the Performance of Hybrid FEC/ARQ Systems Using Rate Compatible Punctured Turbo (RCPT) Codes.IEEE Trans.on-Communication,2000,(48)6:948-959
[50]Shu Lin, Daniel J.Costello,Jr..Error Contrl Coding, Second Edition. Pearson Education. 2004
[51]卿粼波,何小海,吕瑞,曾强宇.基于比特概率优化算法的分布式视频编码.光电子激光,2008,19(5)：620-624
[52]Yongpeng Li,Siwei Ma, Debin Zhao, Wen Gao.Modeling Correlation Noise Statistics at Decoder for Multi-view Distributed Video Coding.IEEE International Symposium on Circuits and Systems,2009:2597-2600
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