Turbo码的性能仿真及其在静止图像传输中的应用研究
|
摘要
Turbo码，由C.Berrou等在ICC’93会议上提出，它巧妙地将卷积码和随机交织器结合在一起，实现了随机编码的思想，同时，采用软输入软输出迭代译码来逼近最大似然译码，具有近Shannon限的性能。由于Turbo码的优异性能不是从理论研究的角度给出，而是计算机仿真的结果。因此，直至目前，Turbo码的理论基础还不完善，仍需不断探讨研究。本文系统地研究了Turbo码在AWGN信道和Rayleigh衰落信道下的性能，并探讨了Turbo码在静止图像传输系统中的应用，取得了一些有意义的成果。主要内容包括：
1．详细推导了MAP译码算法，以及MAP算法在对数域中的修正算法(Max-Log-MAP和Log-MAP算法)，并对Turbo码在高斯白噪声信道下的性能进行了仿真分析。
2．针对移动通信信道的特点，对Log-MAP译码算法进行修正，使之适用于瑞利衰落信道。在此基础上，进一步研究Turbo码在瑞利衰落信道中的性能，仿真结果表明，Turbo码具有很强的抗衰落和抗多径效应能力。
3．将Turbo码应用于静止图像传输系统，信源编码采用矢量量化编码，分别在AWGN信道和Rayleigh衰落信道下，对不采用信道编码和采用Turbo码作为信道编码的各种情况进行仿真。结果表
广西大学硕士学位论文：Turb。码的性能仿真及其在静止图像传输中的应用研究
明，Turbo码不仅提高了图像传输系统的可靠性，而且大大节省
了系统发射功率。
本文的工作得到了广西教育厅科研项目（桂教科研K 392号）
由资助。
Turbo codes were presented by C.Berrou in International Conference on Communications in 1993. They hang convolutional code and random interleaver together to realize the idea of random coding, and adopt soft input/soft output (SISO) iterated decoding to approach maximum likelihood decoding (MLD). Turbo codes come closer to approaching Shannon's limit. The excellent performances of Turbo codes were the results of the computer simulations, not from the theory investigation, so the foundational theory of Turbo codes are still unperfect up to the present. They still need to be studied. This thesis systematically studies the performances of Turbo codes over both AWGN channels and Rayleigh fading channels, and discusses the applications of Turbo codes in still image transmission systems. Some significative conclusions are obtained. The main contents are:
1. Deriving formulas of MAP algorithm and its modified algorithms in the log domain (including Max-Log-MAP and Log-MAP), and
simulating the performances of Turbo codes over additive white Gaussian noise (AWGN).
2. Modifying Log-MAP algorithm to be suitable for Rayleigh fading channels, and researching the performances of Turbo codes over Rayleigh fading channels based on above deriving. Simulation results show that Turbo codes exhibit superior error correction performance over fading channels.
3. Studying still image transmission systems without channel coding or with Turbo codes over both AWGN and Rayleigh fading channels by Matlab simulation. Simulation results show that Turbo codes not only advance the dependability of communication systems, but also reduce channel signal-to-noise ratio(SNR).
This project is supported by scientific research project of Guangxi Education Department (N0.[2000]392).
1．详细推导了MAP译码算法，以及MAP算法在对数域中的修正算法(Max-Log-MAP和Log-MAP算法)，并对Turbo码在高斯白噪声信道下的性能进行了仿真分析。
2．针对移动通信信道的特点，对Log-MAP译码算法进行修正，使之适用于瑞利衰落信道。在此基础上，进一步研究Turbo码在瑞利衰落信道中的性能，仿真结果表明，Turbo码具有很强的抗衰落和抗多径效应能力。
3．将Turbo码应用于静止图像传输系统，信源编码采用矢量量化编码，分别在AWGN信道和Rayleigh衰落信道下，对不采用信道编码和采用Turbo码作为信道编码的各种情况进行仿真。结果表
广西大学硕士学位论文：Turb。码的性能仿真及其在静止图像传输中的应用研究
明，Turbo码不仅提高了图像传输系统的可靠性，而且大大节省
了系统发射功率。
本文的工作得到了广西教育厅科研项目（桂教科研K 392号）
由资助。
Turbo codes were presented by C.Berrou in International Conference on Communications in 1993. They hang convolutional code and random interleaver together to realize the idea of random coding, and adopt soft input/soft output (SISO) iterated decoding to approach maximum likelihood decoding (MLD). Turbo codes come closer to approaching Shannon's limit. The excellent performances of Turbo codes were the results of the computer simulations, not from the theory investigation, so the foundational theory of Turbo codes are still unperfect up to the present. They still need to be studied. This thesis systematically studies the performances of Turbo codes over both AWGN channels and Rayleigh fading channels, and discusses the applications of Turbo codes in still image transmission systems. Some significative conclusions are obtained. The main contents are:
1. Deriving formulas of MAP algorithm and its modified algorithms in the log domain (including Max-Log-MAP and Log-MAP), and
simulating the performances of Turbo codes over additive white Gaussian noise (AWGN).
2. Modifying Log-MAP algorithm to be suitable for Rayleigh fading channels, and researching the performances of Turbo codes over Rayleigh fading channels based on above deriving. Simulation results show that Turbo codes exhibit superior error correction performance over fading channels.
3. Studying still image transmission systems without channel coding or with Turbo codes over both AWGN and Rayleigh fading channels by Matlab simulation. Simulation results show that Turbo codes not only advance the dependability of communication systems, but also reduce channel signal-to-noise ratio(SNR).
This project is supported by scientific research project of Guangxi Education Department (N0.[2000]392).
引文
[1] C. E. Shannon. A mathematical theory of communication [J]. BSTJ.vol.27, pp.379-423, July and pp.623-656, Dec. 1948.
[2] G. D. Forney. Concatenated codes. Cambridge. MA: MIT Press. 1966.
[3] J.Hagneauer, E.Offer and L.Papke. Matching Viterbi decoders and Reed-Solomon decoders in a concatenated system. In Reed-Solomon Codes and Their Applications, S.Wicker and V.K.Bhargava, Eds. New York: IEEE Press, 1994 Ch. 11, pp.242-271.
[4] J. L. Massey. Threshold Decoding. Cambridge, MA: MIT Press, 1963.
[5] L.R.Babh, J.Cocke, E.Jelinek et al. Optimum decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inform. Theory. voh20, pp.284-287, Mar. 1974.
[6] G. D. Forney, Jr. Concatenated Codes. Sc.D.Thesis. M.I.T., Cambridge, Mass, 1965
[7] D.Chase. A class of algorithms for decoding block codes with channels measurement information. IEEE Trans. Inform. Theory. 1976, 23:514-517.
[8] J. Hagenauer, P. Hoeher. A viterbi algorithm with soft-decision outputs and its applications, in Proc. Globecom'89, pp. 1680-1686, Nov. 1989.
[9] V. Buttigieg, P.G. Farrell. A maximum aposteriori (MAP) decoding algorithm for variable length error-correcting codes, in Codes and ciphers: Cryptography and coding IV, Essex, England, the Institute of Mathematics and its Applications, pp. 103-119,1995.
[10] J.Hagenauer, E.Offer, L.Papke. Iterative decoding of binary block and convolution codes. IEEE Trans. Inf. Theory. vol.42, no.2, pp.429-445, Mar., 1996.
[11] J.Hagenauer, P. Hoeher. A Viterbi algorithm with soft-decision outputs and its applications, in Proc. Globecom'89, pp. 1680-1686. Nov. 1989.
[12] C.Nill and C.W. Sundberg. List and soft symbol output viterbi algorithms: Extensions and comparisons [J]. IEEE Trans. Commun., voh43, no.2/3/4, pp.277-287, Feb./Mar./April 1995
[13] C.Berrou, A.Glavieux and P. Thitimajshima. Near Shannon limit error-correcting coding and decoding: Turbo codes (1). ICC'93, pp. 1064-1074.1993
[14] P. Robertson. Illuminating the structure of code and decoder of parallel concatenated recursive systematic (turbo) codes, in Proc. Globecom '94,pp.1298-1303, 1994.
[15] S.Benedetto, G. Montorsi. Unveiling turbo codes: Some results on parallel concatenated
codings schemes. IEEE Trans. Inf. Theory, vol.42, no.2, pp.409-428, Mar. 1996.
[16] D.J.Costello. Applications of error-control coding. IEEE Trans. Inform. Theory, vol.44, no.6, pp.2531-2560, Oct. 1998.
[17] W.E.Ryan. A turbo code tutorial, unpublished. [Online] http://www.ece.arizona.edu/～ryan
[18] M.C.Valenti. Turbo codes and iterative processing, in Proc. IEEE New Zealand Wireless Commun. Symp., (Auckland New Zealand), Nov. 1998.
[19] G. Battail. A conceptual framework for understanding turbo codes. IEEE J.Select. Areas Commun.,vol. 16, no.2,pp.245-254,Feb. 1998.
[20] 吴伟陵．通向信道编码定理的Turbo码及其性能分析．电子学报，1998，26(7)：36-40．
[21] 叶中行，Victor Wei.Turbo码的若干新进展．电子学报，1998，26(7)：41-46．
[22] E.K.HalI, S.G. Wilson. Design and Performance Analysis of Turbo Codes on Rayleigh Fading Channels. Proc. of CISS'96, Mar. 1996.
[23] E.K.Hall, S.G. Wilson. Design and Analysis of Turbo Codes on Rayleigh Fading Channels. Proc. Globecom'96, Nov. 1996.
[24] M.C.Valenti, B.D.Woerner. Performance of Turbo codes in interleaved flat fading channels with estimated channel state information, in Proc. IEEE Veh. Tech. Conf., May 1998, pp.66-70.
[25] P. Robertson, P. Hoeher and E.Villebrun. A comparison of optimal and sub-optimal MAP decoding algorithms operating in the Log domain, in Proc. ICC'95, pp. 1009-1013, 1995
[26] M.P.C.Fossorier, F. Burkert, S.Lin, et al. On the equivalence between SOVA and Max-log-MAP decodings. IEEE Commun. Letters, vol.2, no.5, pp. 137-139, May 1998.
[27] M.C.Reed, P.D. Alexander, J.A. Asenstorfer, et al. Near Single User Performance using Iterative Multi-User Detection for CDMA with Turbo-Code Decoders. http://citeseer.nj.nec.com/correct/189864,1997
[28] Y. Zhang, R.S. Blum. Iterative Multiuser Detection for Turbo Coded Synchronous CDMA in Gaussian and Non-Gaussian Impulsive Noise. Conference on Information Sciences and Systems, March 15-17, 2000
[29] J.M.Hsu, C.L.Wang. A Low-Complexity Iterative Multiuser Receiver for Turbo-Coded DS-CDMA Systems. IEEE Journal on Selected Areas in Communications, 2001,19(9): 1775-1783
[30] M.C.Reed, P. Alexander, J.Asenstorfer, et al. Iterative multi-user detection for DS-CDMA with FEC. Internationsl Symposium on Turbo codes, France, 1997.
[31] 祝谷乔，郑宝王．一种低复杂度的Turbo多用户检测技术．南京邮电学院学报(自然科学版)，2001，21(1)：19-22．
[32] A.Glavieux, C.Laot and J.Laba. Turbo equalization over a frequency selective channel. International Symposium on Turbo codes related topics, pp.96-102, September 1997.
[33] G. Norbert. On the iterative approximation of optimal joint source-channel decoding. IEEE Journal on selected areas in communications, vol. 19, no.9, Sept.2001, pp. 1662-1670.
[34] P. Robertson and T. Worz. Bandwidth-efficient turbo trellis-coded modulation using punctured component codes. IEEE J.Select Areas Commun, vol. 16,no.2,pp.206-218,Feb. 1998.
[35] D.Divsalar and F. Pollara. Turbo trellis coded modulation with iterative decoding for mobile satellite communications. JPL TDA Progress Report, 1997.
[36] D.Divsalar and F. Pollara. Turbo codes for Deep-Space communications. TDA Progress Report, 1995:29-39.
[37] D.Divsalar, F. Pollara. Turbo Codes for PCS Applications. Process of IEEE ICC 1995:54-59.
[38] P. Jung, J.Plechinger, M.Doetsch, et al. Advances on the application of turbo-codes to data services in third generation mobile networks, in Proceedings of International Symposium on Turbo Codes, France, 1997.
[39] S.Benedetto, G. Montorsi. Unveiling Turbo-codes: Some results on parallel concatenated coding schemes. IEEE Transactions on Information Theory, 1996,42(2): 409～429.
[40] Z.Peng, Y.F. Huang. Turbo codes for image transmission—a joint channel and source decoding approach. IEEE Journal on selected areas in communications, vol. 18, no.6, June 2000.
[41] W. Xiang, S.A.Barbulescu. Turbo Diversity Scheme applied to JPEG Image Transmission. 3rd AusCTW, Canberra, Australia, Feb. 4-5, 2002.
[42] J.He, D. J. Costello, Jr., Y.-F. Huang, et al. On the Application of Turbo Codes to the Robust Transmission of Compressed Images. http ://citeseer.nj.nec.com/correct/352179.
[43] R. Gallager. Low density parity-check code. IRE Trans. Inf. Theory. pp.21-28, Jan. 1962.
[44] P. Robertson, E. Villebrun, and P. Hoeher. A comparison of optimal and sub-optimal MAP decoding algorithm operation in the log domain, in Proc., IEEE Int. Conf. on Commun., pp.
1009-1013,1995.
[45] S.Benedetto, D. Divsalar, G. Montorsi, et al. Soft-output decoding algorithms in iterative decoding of turbo codes. JPL TDA Progress Report, vol. 42-124,Feb. 15,1996.
[46] J.A.Erfanian, S.Pasupathy, and G. Gulak. Reduced complexity symbol detectors with parallel structures for ISI channels. IEEE Trans. Commun., vol. 42, pp. 1661-1671, February/March/April 1994.
[47] W. Koch and A. Baier. Optimum and sub-optimum detection of coded data disturbed by time-varying intersymbol interference, in Proc. GLOBECOM'90, pp. 1679-1684, Dec. 1990.
[48] Y. Wu. Design and implementation of parallel and serial concatenated convolutional codes. Virginia, Doctor's thesis, May, 1999.
[49] M. S. C. Ho, S. S. Pietrobon and T. Giles. Interleavers for punctured turbo codes. IEEE Asia-Pacific Conf. on Commun. and Singapore Int. Conf. on Commun. Systems, vol.2, pp. 520-524, Nov. 1998.
[50] 徐韦峰，秦东，刘石等．Turbo码中的交织器设计及其改进．微电子学，2000(4)：92-96．
[51] 王嘉梅．Turbo码译码性能与循环迭代次数探讨[J]．电讯技术，1999，39(3)：24-28
[52] 刘东华，唐朝京．基于交叉熵最小化的Turbo码迭代译码停止准则．国防科技大学学报．2000，22(5)：46-50．
[53] 徐衡平，潘晟，赵勋等．Turbo码中迭代译码的迭代终止准则研究．电视技术，2001(6)：64-66．
[54] I. Land and P. A. Hoeher. Using the mean reliability as a design and stopping criterion for turbo codes, in Proc. IEEE Inform. Theory Workshop, Cairns, Australia, Sept. 2001.
[55] Y. Wu, B. D. Woerner, and William J. Ebel. A simple stopping criterion for turbo decoding. IEEE Commun. Letters, Nov. 1999.
[56] S.Wilson. Digital Modulation and Coding. Prentice Hall, 1996.
[57] B.Sklar. Rayleigh fading channels in mobile digital communication systems Part 1: Characterization. IEEE Commun. Mag.vol.35, no.7, pp.90-100, July 1997.
[58] J.G.Proakis. Digital communications. 3rd ed. New York: McGraw-Hill. 1995.
[59] T.S.Rappaport. Wireless Communications: Principles and Practice. Englewood Cliffs.NJ: Prentice-Hall. 1996.
[60] E.K.Hall and S.G. Wilson. Design and Analysis of turbo codes on Rayleign fading channels.
IEEE J.Select. Areas Commun., 1998,16(2): 160～174.
[61] M.C.Valenti and B. D. Woerner. Refined channel estimation for coherent detection of turbo codes over flat-fading channels. Electron. Lett., vol. 34, pp. 1648-1649, Aug., 1998.
[62] M.C. Valenti and B.D. Woerner. Iterative Channel Estimation and Decoding of Pilot Symbol Assisted Turbo Codes Over Flat-Fading Channels. IEEE Journal on selected areas in communications, vol. 19, no.9, pp. 1697-1705, Sep.2001.
[63] M.C.Valenti. Iterative channel estimation for turbo codes over fading channels, in Proc. IEEE Wireless Commun. Network. Conf., Chicago, IL, Sept. 2000, invited paper, pp. 1019-1024.
[64] ITU-T Recommendation T. 126 (1995). Multipoint Still Image and Annotation Protocol.
[65] H.Gharavi, S.M.Alamouti. Video transmission for Third Generation Wireless Communication Systems. Journal of Research of the National Institute of Standards and Technology, vol. 106, no.2, March-April 2001, pp.455-469.
[66] C.Berrou and A.Giavieux. Near optimum error correcting coding and decoding: turbo-codes. IEEE Trans. Commun., vol. 44, no. 10, pp. 1261-1271, Oct. 1996.
[67] H. Nickl, J. Hagenauer, F. Burkert. Approaching Shannon% capacity limit by 0.27dB using Hamming codes in a 'Turbo-decoding scheme'. Proc., IEEE Int. Symp. on Inf. Theory, pp. 12,1997.
[68] ITU-T Recommendation H.263. Video coding for Low Bitrate communication. February 998.
[69] MPEG-1 International standard coding of moving pictures and assisted audio for digital storage media up to about 1.5Mbit/s, Part 1-3, Video Recommendation ITU-T H.262, ISO/IEC 13818-2, January 20, 1995.
[70] MPEG-2 International Standard, Video Recommendation ITU-T H.262, 1995.
[71] ISO/IEC JTC1/SC29/WG11, Information Technology: Coding of audio-visual objects, ISO/IEC 14496-2, March 1998.
[72] 谭明新，徐根深．差错非均匀保护Turbo码．哈尔滨工程大学学报，vol．22，no．4，2001，pp．43-45
[73] W. Xiang, S.A.Barbulescu, S.S.Pietrobon. Unequal Error Protection applied to JPEG Image Transmission using Turbo Codes. ITW2001, Cairns, Australia, Sept. 2-7, 2001.
[74] 赵光玲，吴乐南．具有不均匀保护特性的Turbo码多级编码调制方案．电路与系统学报，vol．6，no．3，2001，pp．41-44．
[75] P. Cherriman, C. H. Wong, and L. Hanzo. Turbo- and BCH-coded wide-band burst-by-burst adaptive H.263-assisted wireless video telephony. IEEE Trans. on Circuits and Systems for Video Tech., vol. 10, pp. 1355-1363,Dec. 2000.
[76] C.W. Lee, J.W. Kim. Robust Wireless Video Transmission Employing Byte-aligned Variable-length Turbo Code. http://citeseer.nj.nec.com/correct/496201.2002.
[77] W. Kumwilaisak, et al. Reliable video transmission over fading wireless channel with joint source-channel adaptation, http://citeseer.nj.nec.com/correct/468806, 2001.
[78] M. Bystrom and J. W. Modestino.Combined source-channel coding schemes for video transmission over additive white Gaussian noise channel. IEEE Journal on Selected Areas in Commun., vol. 18, pp. 880-890, June 2000.
[79] 吴乐南．数据压缩的原理与应用，电子工业出版社，1995．
[80] 张基宏，谢维信．一种快速模糊矢量量化图像编码算法．电子学报，vol．27，no．2，1999，PP．106-108．
[81] 冯前进，陈武凡，林亚忠．一种新的模糊矢量量化算法．中国医学物理学杂志，2001，18(4)：199-201．
[82] J. Makhoul, S. Roucos, and H. Gish. Vector quantization in speech coding. Proc. IEEE, 73(11), 1551-1588 (1985).
[83] Y. Linde, A.Buzo and R.M.Gray. An algorithm for vector quantizer design. IEEE Trans., COM-28 (1), 84-95(1980).
[84] J.B.Anderson. Sequential decoding based on an error criterion. IEEE Trans. Inform. Theory. 1992, vol.38, pp.987-1001.
[85] 王嘉梅．Turbo码译码性能与循环迭代次数探讨[J]．电讯技术，1999，39(3)：24-28
[86] 杨大成．cdma2000技术．北京邮电大学出版社，2000，11．
[87] 张平，王卫东，陶小峰．WCDMA移动通信系统．人民邮电出版社，2001：123-130
[88] 吴伟陵．移动通信中的关键技术．北京邮电大学出版社．2000，11．
[89] 冉隆科．移动多媒体通信离我们有多远?网络世界在线版，第39期，2000，10．
[2] G. D. Forney. Concatenated codes. Cambridge. MA: MIT Press. 1966.
[3] J.Hagneauer, E.Offer and L.Papke. Matching Viterbi decoders and Reed-Solomon decoders in a concatenated system. In Reed-Solomon Codes and Their Applications, S.Wicker and V.K.Bhargava, Eds. New York: IEEE Press, 1994 Ch. 11, pp.242-271.
[4] J. L. Massey. Threshold Decoding. Cambridge, MA: MIT Press, 1963.
[5] L.R.Babh, J.Cocke, E.Jelinek et al. Optimum decoding of linear codes for minimizing symbol error rate. IEEE Trans. Inform. Theory. voh20, pp.284-287, Mar. 1974.
[6] G. D. Forney, Jr. Concatenated Codes. Sc.D.Thesis. M.I.T., Cambridge, Mass, 1965
[7] D.Chase. A class of algorithms for decoding block codes with channels measurement information. IEEE Trans. Inform. Theory. 1976, 23:514-517.
[8] J. Hagenauer, P. Hoeher. A viterbi algorithm with soft-decision outputs and its applications, in Proc. Globecom'89, pp. 1680-1686, Nov. 1989.
[9] V. Buttigieg, P.G. Farrell. A maximum aposteriori (MAP) decoding algorithm for variable length error-correcting codes, in Codes and ciphers: Cryptography and coding IV, Essex, England, the Institute of Mathematics and its Applications, pp. 103-119,1995.
[10] J.Hagenauer, E.Offer, L.Papke. Iterative decoding of binary block and convolution codes. IEEE Trans. Inf. Theory. vol.42, no.2, pp.429-445, Mar., 1996.
[11] J.Hagenauer, P. Hoeher. A Viterbi algorithm with soft-decision outputs and its applications, in Proc. Globecom'89, pp. 1680-1686. Nov. 1989.
[12] C.Nill and C.W. Sundberg. List and soft symbol output viterbi algorithms: Extensions and comparisons [J]. IEEE Trans. Commun., voh43, no.2/3/4, pp.277-287, Feb./Mar./April 1995
[13] C.Berrou, A.Glavieux and P. Thitimajshima. Near Shannon limit error-correcting coding and decoding: Turbo codes (1). ICC'93, pp. 1064-1074.1993
[14] P. Robertson. Illuminating the structure of code and decoder of parallel concatenated recursive systematic (turbo) codes, in Proc. Globecom '94,pp.1298-1303, 1994.
[15] S.Benedetto, G. Montorsi. Unveiling turbo codes: Some results on parallel concatenated
codings schemes. IEEE Trans. Inf. Theory, vol.42, no.2, pp.409-428, Mar. 1996.
[16] D.J.Costello. Applications of error-control coding. IEEE Trans. Inform. Theory, vol.44, no.6, pp.2531-2560, Oct. 1998.
[17] W.E.Ryan. A turbo code tutorial, unpublished. [Online] http://www.ece.arizona.edu/～ryan
[18] M.C.Valenti. Turbo codes and iterative processing, in Proc. IEEE New Zealand Wireless Commun. Symp., (Auckland New Zealand), Nov. 1998.
[19] G. Battail. A conceptual framework for understanding turbo codes. IEEE J.Select. Areas Commun.,vol. 16, no.2,pp.245-254,Feb. 1998.
[20] 吴伟陵．通向信道编码定理的Turbo码及其性能分析．电子学报，1998，26(7)：36-40．
[21] 叶中行，Victor Wei.Turbo码的若干新进展．电子学报，1998，26(7)：41-46．
[22] E.K.HalI, S.G. Wilson. Design and Performance Analysis of Turbo Codes on Rayleigh Fading Channels. Proc. of CISS'96, Mar. 1996.
[23] E.K.Hall, S.G. Wilson. Design and Analysis of Turbo Codes on Rayleigh Fading Channels. Proc. Globecom'96, Nov. 1996.
[24] M.C.Valenti, B.D.Woerner. Performance of Turbo codes in interleaved flat fading channels with estimated channel state information, in Proc. IEEE Veh. Tech. Conf., May 1998, pp.66-70.
[25] P. Robertson, P. Hoeher and E.Villebrun. A comparison of optimal and sub-optimal MAP decoding algorithms operating in the Log domain, in Proc. ICC'95, pp. 1009-1013, 1995
[26] M.P.C.Fossorier, F. Burkert, S.Lin, et al. On the equivalence between SOVA and Max-log-MAP decodings. IEEE Commun. Letters, vol.2, no.5, pp. 137-139, May 1998.
[27] M.C.Reed, P.D. Alexander, J.A. Asenstorfer, et al. Near Single User Performance using Iterative Multi-User Detection for CDMA with Turbo-Code Decoders. http://citeseer.nj.nec.com/correct/189864,1997
[28] Y. Zhang, R.S. Blum. Iterative Multiuser Detection for Turbo Coded Synchronous CDMA in Gaussian and Non-Gaussian Impulsive Noise. Conference on Information Sciences and Systems, March 15-17, 2000
[29] J.M.Hsu, C.L.Wang. A Low-Complexity Iterative Multiuser Receiver for Turbo-Coded DS-CDMA Systems. IEEE Journal on Selected Areas in Communications, 2001,19(9): 1775-1783
[30] M.C.Reed, P. Alexander, J.Asenstorfer, et al. Iterative multi-user detection for DS-CDMA with FEC. Internationsl Symposium on Turbo codes, France, 1997.
[31] 祝谷乔，郑宝王．一种低复杂度的Turbo多用户检测技术．南京邮电学院学报(自然科学版)，2001，21(1)：19-22．
[32] A.Glavieux, C.Laot and J.Laba. Turbo equalization over a frequency selective channel. International Symposium on Turbo codes related topics, pp.96-102, September 1997.
[33] G. Norbert. On the iterative approximation of optimal joint source-channel decoding. IEEE Journal on selected areas in communications, vol. 19, no.9, Sept.2001, pp. 1662-1670.
[34] P. Robertson and T. Worz. Bandwidth-efficient turbo trellis-coded modulation using punctured component codes. IEEE J.Select Areas Commun, vol. 16,no.2,pp.206-218,Feb. 1998.
[35] D.Divsalar and F. Pollara. Turbo trellis coded modulation with iterative decoding for mobile satellite communications. JPL TDA Progress Report, 1997.
[36] D.Divsalar and F. Pollara. Turbo codes for Deep-Space communications. TDA Progress Report, 1995:29-39.
[37] D.Divsalar, F. Pollara. Turbo Codes for PCS Applications. Process of IEEE ICC 1995:54-59.
[38] P. Jung, J.Plechinger, M.Doetsch, et al. Advances on the application of turbo-codes to data services in third generation mobile networks, in Proceedings of International Symposium on Turbo Codes, France, 1997.
[39] S.Benedetto, G. Montorsi. Unveiling Turbo-codes: Some results on parallel concatenated coding schemes. IEEE Transactions on Information Theory, 1996,42(2): 409～429.
[40] Z.Peng, Y.F. Huang. Turbo codes for image transmission—a joint channel and source decoding approach. IEEE Journal on selected areas in communications, vol. 18, no.6, June 2000.
[41] W. Xiang, S.A.Barbulescu. Turbo Diversity Scheme applied to JPEG Image Transmission. 3rd AusCTW, Canberra, Australia, Feb. 4-5, 2002.
[42] J.He, D. J. Costello, Jr., Y.-F. Huang, et al. On the Application of Turbo Codes to the Robust Transmission of Compressed Images. http ://citeseer.nj.nec.com/correct/352179.
[43] R. Gallager. Low density parity-check code. IRE Trans. Inf. Theory. pp.21-28, Jan. 1962.
[44] P. Robertson, E. Villebrun, and P. Hoeher. A comparison of optimal and sub-optimal MAP decoding algorithm operation in the log domain, in Proc., IEEE Int. Conf. on Commun., pp.
1009-1013,1995.
[45] S.Benedetto, D. Divsalar, G. Montorsi, et al. Soft-output decoding algorithms in iterative decoding of turbo codes. JPL TDA Progress Report, vol. 42-124,Feb. 15,1996.
[46] J.A.Erfanian, S.Pasupathy, and G. Gulak. Reduced complexity symbol detectors with parallel structures for ISI channels. IEEE Trans. Commun., vol. 42, pp. 1661-1671, February/March/April 1994.
[47] W. Koch and A. Baier. Optimum and sub-optimum detection of coded data disturbed by time-varying intersymbol interference, in Proc. GLOBECOM'90, pp. 1679-1684, Dec. 1990.
[48] Y. Wu. Design and implementation of parallel and serial concatenated convolutional codes. Virginia, Doctor's thesis, May, 1999.
[49] M. S. C. Ho, S. S. Pietrobon and T. Giles. Interleavers for punctured turbo codes. IEEE Asia-Pacific Conf. on Commun. and Singapore Int. Conf. on Commun. Systems, vol.2, pp. 520-524, Nov. 1998.
[50] 徐韦峰，秦东，刘石等．Turbo码中的交织器设计及其改进．微电子学，2000(4)：92-96．
[51] 王嘉梅．Turbo码译码性能与循环迭代次数探讨[J]．电讯技术，1999，39(3)：24-28
[52] 刘东华，唐朝京．基于交叉熵最小化的Turbo码迭代译码停止准则．国防科技大学学报．2000，22(5)：46-50．
[53] 徐衡平，潘晟，赵勋等．Turbo码中迭代译码的迭代终止准则研究．电视技术，2001(6)：64-66．
[54] I. Land and P. A. Hoeher. Using the mean reliability as a design and stopping criterion for turbo codes, in Proc. IEEE Inform. Theory Workshop, Cairns, Australia, Sept. 2001.
[55] Y. Wu, B. D. Woerner, and William J. Ebel. A simple stopping criterion for turbo decoding. IEEE Commun. Letters, Nov. 1999.
[56] S.Wilson. Digital Modulation and Coding. Prentice Hall, 1996.
[57] B.Sklar. Rayleigh fading channels in mobile digital communication systems Part 1: Characterization. IEEE Commun. Mag.vol.35, no.7, pp.90-100, July 1997.
[58] J.G.Proakis. Digital communications. 3rd ed. New York: McGraw-Hill. 1995.
[59] T.S.Rappaport. Wireless Communications: Principles and Practice. Englewood Cliffs.NJ: Prentice-Hall. 1996.
[60] E.K.Hall and S.G. Wilson. Design and Analysis of turbo codes on Rayleign fading channels.
IEEE J.Select. Areas Commun., 1998,16(2): 160～174.
[61] M.C.Valenti and B. D. Woerner. Refined channel estimation for coherent detection of turbo codes over flat-fading channels. Electron. Lett., vol. 34, pp. 1648-1649, Aug., 1998.
[62] M.C. Valenti and B.D. Woerner. Iterative Channel Estimation and Decoding of Pilot Symbol Assisted Turbo Codes Over Flat-Fading Channels. IEEE Journal on selected areas in communications, vol. 19, no.9, pp. 1697-1705, Sep.2001.
[63] M.C.Valenti. Iterative channel estimation for turbo codes over fading channels, in Proc. IEEE Wireless Commun. Network. Conf., Chicago, IL, Sept. 2000, invited paper, pp. 1019-1024.
[64] ITU-T Recommendation T. 126 (1995). Multipoint Still Image and Annotation Protocol.
[65] H.Gharavi, S.M.Alamouti. Video transmission for Third Generation Wireless Communication Systems. Journal of Research of the National Institute of Standards and Technology, vol. 106, no.2, March-April 2001, pp.455-469.
[66] C.Berrou and A.Giavieux. Near optimum error correcting coding and decoding: turbo-codes. IEEE Trans. Commun., vol. 44, no. 10, pp. 1261-1271, Oct. 1996.
[67] H. Nickl, J. Hagenauer, F. Burkert. Approaching Shannon% capacity limit by 0.27dB using Hamming codes in a 'Turbo-decoding scheme'. Proc., IEEE Int. Symp. on Inf. Theory, pp. 12,1997.
[68] ITU-T Recommendation H.263. Video coding for Low Bitrate communication. February 998.
[69] MPEG-1 International standard coding of moving pictures and assisted audio for digital storage media up to about 1.5Mbit/s, Part 1-3, Video Recommendation ITU-T H.262, ISO/IEC 13818-2, January 20, 1995.
[70] MPEG-2 International Standard, Video Recommendation ITU-T H.262, 1995.
[71] ISO/IEC JTC1/SC29/WG11, Information Technology: Coding of audio-visual objects, ISO/IEC 14496-2, March 1998.
[72] 谭明新，徐根深．差错非均匀保护Turbo码．哈尔滨工程大学学报，vol．22，no．4，2001，pp．43-45
[73] W. Xiang, S.A.Barbulescu, S.S.Pietrobon. Unequal Error Protection applied to JPEG Image Transmission using Turbo Codes. ITW2001, Cairns, Australia, Sept. 2-7, 2001.
[74] 赵光玲，吴乐南．具有不均匀保护特性的Turbo码多级编码调制方案．电路与系统学报，vol．6，no．3，2001，pp．41-44．
[75] P. Cherriman, C. H. Wong, and L. Hanzo. Turbo- and BCH-coded wide-band burst-by-burst adaptive H.263-assisted wireless video telephony. IEEE Trans. on Circuits and Systems for Video Tech., vol. 10, pp. 1355-1363,Dec. 2000.
[76] C.W. Lee, J.W. Kim. Robust Wireless Video Transmission Employing Byte-aligned Variable-length Turbo Code. http://citeseer.nj.nec.com/correct/496201.2002.
[77] W. Kumwilaisak, et al. Reliable video transmission over fading wireless channel with joint source-channel adaptation, http://citeseer.nj.nec.com/correct/468806, 2001.
[78] M. Bystrom and J. W. Modestino.Combined source-channel coding schemes for video transmission over additive white Gaussian noise channel. IEEE Journal on Selected Areas in Commun., vol. 18, pp. 880-890, June 2000.
[79] 吴乐南．数据压缩的原理与应用，电子工业出版社，1995．
[80] 张基宏，谢维信．一种快速模糊矢量量化图像编码算法．电子学报，vol．27，no．2，1999，PP．106-108．
[81] 冯前进，陈武凡，林亚忠．一种新的模糊矢量量化算法．中国医学物理学杂志，2001，18(4)：199-201．
[82] J. Makhoul, S. Roucos, and H. Gish. Vector quantization in speech coding. Proc. IEEE, 73(11), 1551-1588 (1985).
[83] Y. Linde, A.Buzo and R.M.Gray. An algorithm for vector quantizer design. IEEE Trans., COM-28 (1), 84-95(1980).
[84] J.B.Anderson. Sequential decoding based on an error criterion. IEEE Trans. Inform. Theory. 1992, vol.38, pp.987-1001.
[85] 王嘉梅．Turbo码译码性能与循环迭代次数探讨[J]．电讯技术，1999，39(3)：24-28
[86] 杨大成．cdma2000技术．北京邮电大学出版社，2000，11．
[87] 张平，王卫东，陶小峰．WCDMA移动通信系统．人民邮电出版社，2001：123-130
[88] 吴伟陵．移动通信中的关键技术．北京邮电大学出版社．2000，11．
[89] 冉隆科．移动多媒体通信离我们有多远?网络世界在线版，第39期，2000，10．