串行级联系统的迭代译码研究
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摘要
本文重点研究了几类典型基于Turbo准则的串行级联系统的迭代译码算法。文章首先阐述了SCCC的编译码器结构,推导了基于格图的MAP译码算法,并由此引入一般性的SISO实现构架;其次,推导了BICM和BICM-ID的欧氏距离准则,以此为依据,对它们相关组成部分的影响作了分析;再次,本文研究了Turbo均衡的实现与性能,通过对MAPEQU算法和SCCC译码算法的联合比较给出了Turbo均衡的一般结构,推导了软ISI抵消滤波器、基于MMSE的线性滤波及判决滤波反馈这三种Turbo均衡算法;最后,针对实现级联码译码量化实现,提出了一种基于SDR的双目标规划设计算法。本文各章节均给出的相关的仿真结果,对文章的有关结论予以验证。
This dissertation mainly studies the iterative decoding algorithms in typical serial concatenated systems based on Turbo principle. Firstly, the SCCC decoding scheme is described, followed by the derivation of the MAP algorithm based on the trellis gragh. According to it, the general structure of the SISO is presented. Secondly, the Euclidean distances of the BICM and BICM-ID are formulated, which are used to analysis the performance under different channels and constellation modulations. Thirdly, the realization and performace of Turbo equalizer are studied. The general frame of Turbo equalization is obtained through comparing the MAPEQU with the SCCC decoding algorithm. Three algorithms including Soft ISI Cancellation, linear equalization and decision feedback equalization based on MMSE are presented. Finally, a scheme using the double objects programming based on SDR is purposed, and applied to the given concatenated code. Every chapter the simulation results are provided to prove the corresponding conclusions.
This dissertation mainly studies the iterative decoding algorithms in typical serial concatenated systems based on Turbo principle. Firstly, the SCCC decoding scheme is described, followed by the derivation of the MAP algorithm based on the trellis gragh. According to it, the general structure of the SISO is presented. Secondly, the Euclidean distances of the BICM and BICM-ID are formulated, which are used to analysis the performance under different channels and constellation modulations. Thirdly, the realization and performace of Turbo equalizer are studied. The general frame of Turbo equalization is obtained through comparing the MAPEQU with the SCCC decoding algorithm. Three algorithms including Soft ISI Cancellation, linear equalization and decision feedback equalization based on MMSE are presented. Finally, a scheme using the double objects programming based on SDR is purposed, and applied to the given concatenated code. Every chapter the simulation results are provided to prove the corresponding conclusions.
引文
[1] P. Elias, "Error-free coding," IEEE Trans. Inform. Theory, vol. IT-4, Sept. 1954,pp. 29-37
[2] S. Hirasawa et al., "Modified product codes," IEEE Trans. Inform.Theory, vol. IT-30, Mar. 1984, pp. 299-306
[3] G. D. Forney, Jr., Concatenated Codes. Cambridge, MA: M.I.T. Press, 1966,pp 12-17
[4] C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes (1)," in Proc.IEEE Int. Conf. Commun. (ICC), Geneva, Switzerland, May 1993,pp. 1064-1070.
[5] J. Lodge, R. Young, P. Hoeher, and J. Hagenauer, "Separable MAP 'filters' for the decoding of product and concatenated codes," in Proc. IEEE Int. Conf. Commun. (ICC), Geneva, Switzerland, May 1993, pp.1740-1745.
[6] S. Benedetto and G Montorsi, "Unveiling Turbo codes: Some results on parallel concatenated coding schemes," IEEE Trans. Inform. Theory, vol. 42, Mar. 1996, pp.409-428.
[7] Patrick Robertson ,Peter Hoeher and Emmanuelle Villebrum,"Optimal and sub-optimal maximum a posteriori algorithms suitable for Turbo decoding", European Trans, on Telecommun.,Vol. 8, No. 2, March-April 1997, p. 119-125
[8] D. Divsalar and F. Pollara, "On the design of Turbo codes," JPL TDA Progr. Rep.,vol.42,Nov.l5,1995[WWW].Available:http://tda.jpl.nasa.gov/tda/progress_report/4 2-123/123D.pdf
[9] J. Hagenauer, E. Offer, and L. Papke, "Iterative decoding of binary block and convolutional codes," IEEE Trans. Inform. Theory, vol. 42, Mar. 1996, pp. 429-445.
[10] S. Benedetto, D. Divsalar, G Montorsi, and F. Pollara, "Serial concatenation of interleaved codes: Performance analysis, design and iterative decoding," JPL TDA Progr. Rep., vol. 42 Aug. 15,1996,pp 120-126
[11] D. Divsalar and R. J. McEliece "On the Design of Concatenated Coding Systems with Interleaver", TDAProgress Report, August 15, 1998, pp42-134.
[12] Robert J. McEliece, David J. C. MacKay, Jung-Fu Cheng " Turbo Decoding as an Instance of Pearl's "Belief Propagation" Algorithm" IEEE J. Select. Areas Comm,voll6,No 2 ,Feb 1998,pp 140-152
[13] Burkert, F; Hagenauer, J.: The race to Shannon's limit: discipline high-rate codes. In: Proc. of the International Symposium on Turbo Codes, 3.-5. Sept. 1997, Brest, Frankreich, pp. 239-242
[14] F. Kschischang, B. Frey, H. Loeliger, "Factor graphs and the sum-product algorithm, " IEEE Trans, on Information Theory, vol. IT-47, no. 2, Febr. 2001, pp. 498-519.
[15] Paul H. Siegel, Dariush Divsalar, Evangelos Eleftheri, "Guest Editorial The Turbo Principle: From Theory to Practice", IEEE J. Select. Areas Comm,VOL. 19, NO. 5, MAY 2001, pp 793-799
[16] Stephan ten Brink, "Convergence Behavior of Iteratively Decoded Parallel Concatenated Codes", IEEE Transactions on communications, Vol. 49, No. 10, OCTOBER 2001, pp 1727-1737
[17] BJ Frey and FR Kschischang, "Early detection and trellis splicing: reduced-complexity iterative decoding," IEEE J. Select. Areas Comm. vol.35, August 1996, pp. 65-73
[18] S.Riedel, "New symbol-by-symbol MAP decoding algorithms for high-rate convolutional IEEE J. Select. Areas Comm., 16, Feb. 1997 pp 197-205
[19]A.Vieterbi, "An intuitive justification and a simplified implementation of the map decoder for convolutional codes",IEEE J. Select. Areas Comm, vol.16, No.2,Feb 1998,pp 1312-1317
[20] J. B. Anderson and S. M. Hladik, "Tailbiting MAP decoders" IEEE J. Select. Areas Comm., 16, Feb. 1998, pp 297--302
[21] Volker Franz, John B. Anderson, "Concatenated Decoding with a Reduced-Search BCJR Algorithm", IEEE J. Select. Areas Comm, vol. 16, no. 2, February 1998, pp.186-195
[22] Rainer Lucas, Martin Bossert, Markus Breitbach: On Iterative Soft-Decision Decoding of Linear Binary Block Codes and Product Codes. IEEE J. Select. Areas Comm.Vol 16(2) Nov 1998,pp 276-296
[23] Sergio Benedetto, Dariush Divsalar, Joachim Hagenauer "Guest Editorial Concatenated Coding Techniques and Iterative Decoding: Sailing Toward Channel Capacity" IEEE J. Select. Areas Comm, Vol.16, No. 2, Feb. 1998,pp137-139
[24] M. Isaka and H. Imai ,"On the Iterative Decoding of Multilevel Codes" IEEE J. Select. Areas Comm,May 2001, Volume 19, Number 5 ,pp.55-62
[25]G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. On Inform. Theory, vol. IT-28, January 1982, pp55-67.
[26] P. Robertson and T. Worz, "Bandwidth-efficient Turbo trellis-coded modulation using punctured component codes," IEEE J. Select. Areas Comm, vol. 16, Feb. 1998, pp. 201-218.
[27] X. Li, J. A. Ritchey, "Bit-interleaved coded modulation with iterative decoding", IEEE Communication Letter., vol. 1, Nov. 1997, pp. 169-171.
[28] Stefanov and TM Duman, "Turbo coded modulation for wireless communications withantenna diversity", in IEEE Proc. VTC-Fall, vol. 3, 1999, pp. 1565-1569
[29] Y. Liu, M. P. Fitz, and O. Y. Takeshita, "A rank criterion for QAM space-time codes," IEEE Trans. Inform. Theory, vol. 48, no. 12, Dec. 2002, pp. 3062-3079
[30] M. Valenti and B. D. Woerner, "Iterative Channel Estimation and Decoding of Pilot Symbol Assisted Turbo Codes over Flat Fading Channels", IEEE J. Select. Areas Comm, vol. 19, no. 9, Sep 2001, pp. 1697-1705
[31] C. Komninakis and R. D. Wesel, "Joint Iterative Channel Estimation and Decoding in Flat Correlated Rayleigh Fading", IEEE J. Select. Areas Comm, special issue: The Turbo Principle - From Theory to practice, Vol. 19, No. 9, September 2001, pp. 1706-1717.
[32] Petermann, T.; Kuhn, V; Kammeyer, KD "Iterative blind and non-blind channel estimation in GSM receivers" Personal, Indoor and Mobile Radio Communications, 2000. PIMRC 2000. The 11th IEEE International Symposium on, Volume: 1, pp 187-192
[33] Berthet, A.O. Unal, B.S. Visoz, R," Iterative decoding of convolutionally encoded signals over multipath Rayleigh fading channels", IEEE J. Select. Areas Comm, Volume: 19, Sep 2001, pp1729-1743
[34] Christophe Laot, Alain Glavieux, Joel Labat, "Turbo equalization: Adaptive equalization and channel decoding jointly optimized", IEEE J. Select. Areas Comm, vol. 19, no. 9, September 2001, pp. 1744-1752
[35] Z. Yang and X. Wang, "Turbo Equalization for GMSK Signaling over Multipath Channels," IEEE J. Select. Areas Comm, 19(9), Sep 2001, pp.1753-1763
[35]Michael Tuchler, Ralf Kotter.and Andrew Singer, ""Turbo equalization":principle and new results",IEEE Trans. Comm.,vol.50,May 2002,pp.754-767
[36] Michael Tuchler, Ralf Kotter,and Andrew Singer, "Minimum mean squared error(MMSE) equalization using a priors",IEEE Trans.Singal Processing,vol.50.,Mar 2002,pp.673-683
[37] L.R. Bahl, J. Cocke, F. Jeinek and Raviv, "Optimal decoding of linear codes for minimizing symbol error rate", IEEE Trans. Inform. Theory, vol. IT-20, Mar. 1974, pp. 84-287.
[38]A.O.Berthet, R. Visoz, B.Unal, P. Tortelier, "A Comparison of Several Strategies for Iteratively Decoding Serially Concatenated Convolutional Codes in Multipath Rayleigh Fading Environment", IEEE 2000,pp 121-128
[39] Aik Chindapol and James A. Ritcey, "Design, Analysis, and Performance Evaluation for BICM-ID with Square QAM Constellations in Rayleigh Fading Channels", IEEE J. Select. Areas Comm, vol.19,No.5,May 2001,pp 1421-1429
[40] E. Zehavi, "8-PSK trellis codes for a Rayleigh channel", IEEE Trans. Commun.,vol. 40, May 1992, pp. 873-884.
[41] D.Divslar, M. Simon, "The design of trellis coded MPSK for fading channel: Performance criteria", IEEE Trans. Commun., vol. 36, Sept. 1988, pp. 1004-1012.
[42] Yuheng Huang, and James A. Ritcey, "16-QAM BICM-ID in Fading Channels With Imperfect Channel State Information" , IEEE Trans, on wireless communications, No. 5, Sep. 2003 pp 944-948
[43]C.Douillard,et al, "Iterative correction of intersymbol interference:Turbo equalization",European Trans. Telecomm.,vol.6,Sept.-Oct 1995,pp.507-511
[44]Jong Park "Trellis based soft output decoding algorithms for concatenated coding system", Doctor dissertation,school of electrical and computer engineering Georgia Institute of Technology,Mar.l998,pp 125-145
[45]A.Glavieux, C.Loat, and J.Jabat. "Turbo equalization over a frequency selective channel",International Symposium on Turbo codes and related topics.Sept. 1997,pp.96-102
[46]X.Wang and H.Pool, "Iterative(Turbo) soft interference cancellation and decoding for coded CDMA",IEEE Trans. Comm.,vol.47,no.7,1999,pp. 1046-1061
[47]D.Raphaeli and Y.Zerai, "Combined Turbo equalization and Turbo decoding",IEEE Proceeding on the Global Tele.Conf.'97,vol.2,Nov.1997,pp.639-643
[48] Ralf Kotter,and Andrew Singer, Michael Tuchler, "Turbo equalization:an iterative equalization and decoding technique for coded data transminssion",IEEE Signal Processing Magazine,Jan.2004,pp.67-80
[49] J. Hagenauer, T. Stockhammer, "Channel Coding and Transmission Aspects for Wireless Multimedia", Proc of the IEEE, Vol.87, No. 10, October 1999 , pp. 1764-1777
[50] Y.Wu and B. D.Woerner, "The influence of quantization and fixed point arithmetic upon the ber performance of Turbo codes," Proc. Vehicular Technology Conf., vol. 2, 1999, pp. 1683-1687.
[51] G Montorsi and S. Benedetto, "Design of Fixed-Point Iterative Decoders for Concatenated Codes with Interleaves", IEEE J. Select. Areas Comm, Vol. 19, No. 5, May 2001,pp.871-882
[52]Jayant, N.S and Noll, P., Digital coding of Waveforms, Prentice-Hall, Inc,. Englewood Cliffs, N,J., 1984,pp 134-140
[53] Bemaed Sklar著,徐平平等译,数字通信—基础于应用(第二版),电子工业出版社,pp626-628
[54] Todd A. Summers and Stephen G. Wilson, "SNR Mismatch and Online Estimation in Turbo Decoding", IEEE Transactions on Communications, vol. 46, No. 4, April 1998, pp 421-423
[55] 王新梅,肖国镇编著,纠错码—原理与方法(修订版),西安电子科技大学出版社,1999年,pp506-516
[56] U. Dasgupta, C.N. Georghiade, "Turbo Decoding of Quantized Data", [online]wclb.tamu.edu/pub/papers/Dasgupta. pdf
[57] H.E. Gamal , "A.R.Hammons, Analyzing the Turbo decoder using the Gaussian approximation" Proc ISIT'2000 Sorrento,Itealy.June 2000,pp 322-327
[58] 钱颂迪 运筹学 清华大学出版社,1990年,pp254-258
[59] 白宝明,“Turbo码的原理及其应用”,博士论文,西安电子科技大学,1999年
[60] 刘东华,“Turbo码的原理及其应用”,博士论文,国防科技科技大学,2001年
[2] S. Hirasawa et al., "Modified product codes," IEEE Trans. Inform.Theory, vol. IT-30, Mar. 1984, pp. 299-306
[3] G. D. Forney, Jr., Concatenated Codes. Cambridge, MA: M.I.T. Press, 1966,pp 12-17
[4] C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo-codes (1)," in Proc.IEEE Int. Conf. Commun. (ICC), Geneva, Switzerland, May 1993,pp. 1064-1070.
[5] J. Lodge, R. Young, P. Hoeher, and J. Hagenauer, "Separable MAP 'filters' for the decoding of product and concatenated codes," in Proc. IEEE Int. Conf. Commun. (ICC), Geneva, Switzerland, May 1993, pp.1740-1745.
[6] S. Benedetto and G Montorsi, "Unveiling Turbo codes: Some results on parallel concatenated coding schemes," IEEE Trans. Inform. Theory, vol. 42, Mar. 1996, pp.409-428.
[7] Patrick Robertson ,Peter Hoeher and Emmanuelle Villebrum,"Optimal and sub-optimal maximum a posteriori algorithms suitable for Turbo decoding", European Trans, on Telecommun.,Vol. 8, No. 2, March-April 1997, p. 119-125
[8] D. Divsalar and F. Pollara, "On the design of Turbo codes," JPL TDA Progr. Rep.,vol.42,Nov.l5,1995[WWW].Available:http://tda.jpl.nasa.gov/tda/progress_report/4 2-123/123D.pdf
[9] J. Hagenauer, E. Offer, and L. Papke, "Iterative decoding of binary block and convolutional codes," IEEE Trans. Inform. Theory, vol. 42, Mar. 1996, pp. 429-445.
[10] S. Benedetto, D. Divsalar, G Montorsi, and F. Pollara, "Serial concatenation of interleaved codes: Performance analysis, design and iterative decoding," JPL TDA Progr. Rep., vol. 42 Aug. 15,1996,pp 120-126
[11] D. Divsalar and R. J. McEliece "On the Design of Concatenated Coding Systems with Interleaver", TDAProgress Report, August 15, 1998, pp42-134.
[12] Robert J. McEliece, David J. C. MacKay, Jung-Fu Cheng " Turbo Decoding as an Instance of Pearl's "Belief Propagation" Algorithm" IEEE J. Select. Areas Comm,voll6,No 2 ,Feb 1998,pp 140-152
[13] Burkert, F; Hagenauer, J.: The race to Shannon's limit: discipline high-rate codes. In: Proc. of the International Symposium on Turbo Codes, 3.-5. Sept. 1997, Brest, Frankreich, pp. 239-242
[14] F. Kschischang, B. Frey, H. Loeliger, "Factor graphs and the sum-product algorithm, " IEEE Trans, on Information Theory, vol. IT-47, no. 2, Febr. 2001, pp. 498-519.
[15] Paul H. Siegel, Dariush Divsalar, Evangelos Eleftheri, "Guest Editorial The Turbo Principle: From Theory to Practice", IEEE J. Select. Areas Comm,VOL. 19, NO. 5, MAY 2001, pp 793-799
[16] Stephan ten Brink, "Convergence Behavior of Iteratively Decoded Parallel Concatenated Codes", IEEE Transactions on communications, Vol. 49, No. 10, OCTOBER 2001, pp 1727-1737
[17] BJ Frey and FR Kschischang, "Early detection and trellis splicing: reduced-complexity iterative decoding," IEEE J. Select. Areas Comm. vol.35, August 1996, pp. 65-73
[18] S.Riedel, "New symbol-by-symbol MAP decoding algorithms for high-rate convolutional IEEE J. Select. Areas Comm., 16, Feb. 1997 pp 197-205
[19]A.Vieterbi, "An intuitive justification and a simplified implementation of the map decoder for convolutional codes",IEEE J. Select. Areas Comm, vol.16, No.2,Feb 1998,pp 1312-1317
[20] J. B. Anderson and S. M. Hladik, "Tailbiting MAP decoders" IEEE J. Select. Areas Comm., 16, Feb. 1998, pp 297--302
[21] Volker Franz, John B. Anderson, "Concatenated Decoding with a Reduced-Search BCJR Algorithm", IEEE J. Select. Areas Comm, vol. 16, no. 2, February 1998, pp.186-195
[22] Rainer Lucas, Martin Bossert, Markus Breitbach: On Iterative Soft-Decision Decoding of Linear Binary Block Codes and Product Codes. IEEE J. Select. Areas Comm.Vol 16(2) Nov 1998,pp 276-296
[23] Sergio Benedetto, Dariush Divsalar, Joachim Hagenauer "Guest Editorial Concatenated Coding Techniques and Iterative Decoding: Sailing Toward Channel Capacity" IEEE J. Select. Areas Comm, Vol.16, No. 2, Feb. 1998,pp137-139
[24] M. Isaka and H. Imai ,"On the Iterative Decoding of Multilevel Codes" IEEE J. Select. Areas Comm,May 2001, Volume 19, Number 5 ,pp.55-62
[25]G. Ungerboeck, "Channel coding with multilevel/phase signals," IEEE Trans. On Inform. Theory, vol. IT-28, January 1982, pp55-67.
[26] P. Robertson and T. Worz, "Bandwidth-efficient Turbo trellis-coded modulation using punctured component codes," IEEE J. Select. Areas Comm, vol. 16, Feb. 1998, pp. 201-218.
[27] X. Li, J. A. Ritchey, "Bit-interleaved coded modulation with iterative decoding", IEEE Communication Letter., vol. 1, Nov. 1997, pp. 169-171.
[28] Stefanov and TM Duman, "Turbo coded modulation for wireless communications withantenna diversity", in IEEE Proc. VTC-Fall, vol. 3, 1999, pp. 1565-1569
[29] Y. Liu, M. P. Fitz, and O. Y. Takeshita, "A rank criterion for QAM space-time codes," IEEE Trans. Inform. Theory, vol. 48, no. 12, Dec. 2002, pp. 3062-3079
[30] M. Valenti and B. D. Woerner, "Iterative Channel Estimation and Decoding of Pilot Symbol Assisted Turbo Codes over Flat Fading Channels", IEEE J. Select. Areas Comm, vol. 19, no. 9, Sep 2001, pp. 1697-1705
[31] C. Komninakis and R. D. Wesel, "Joint Iterative Channel Estimation and Decoding in Flat Correlated Rayleigh Fading", IEEE J. Select. Areas Comm, special issue: The Turbo Principle - From Theory to practice, Vol. 19, No. 9, September 2001, pp. 1706-1717.
[32] Petermann, T.; Kuhn, V; Kammeyer, KD "Iterative blind and non-blind channel estimation in GSM receivers" Personal, Indoor and Mobile Radio Communications, 2000. PIMRC 2000. The 11th IEEE International Symposium on, Volume: 1, pp 187-192
[33] Berthet, A.O. Unal, B.S. Visoz, R," Iterative decoding of convolutionally encoded signals over multipath Rayleigh fading channels", IEEE J. Select. Areas Comm, Volume: 19, Sep 2001, pp1729-1743
[34] Christophe Laot, Alain Glavieux, Joel Labat, "Turbo equalization: Adaptive equalization and channel decoding jointly optimized", IEEE J. Select. Areas Comm, vol. 19, no. 9, September 2001, pp. 1744-1752
[35] Z. Yang and X. Wang, "Turbo Equalization for GMSK Signaling over Multipath Channels," IEEE J. Select. Areas Comm, 19(9), Sep 2001, pp.1753-1763
[35]Michael Tuchler, Ralf Kotter.and Andrew Singer, ""Turbo equalization":principle and new results",IEEE Trans. Comm.,vol.50,May 2002,pp.754-767
[36] Michael Tuchler, Ralf Kotter,and Andrew Singer, "Minimum mean squared error(MMSE) equalization using a priors",IEEE Trans.Singal Processing,vol.50.,Mar 2002,pp.673-683
[37] L.R. Bahl, J. Cocke, F. Jeinek and Raviv, "Optimal decoding of linear codes for minimizing symbol error rate", IEEE Trans. Inform. Theory, vol. IT-20, Mar. 1974, pp. 84-287.
[38]A.O.Berthet, R. Visoz, B.Unal, P. Tortelier, "A Comparison of Several Strategies for Iteratively Decoding Serially Concatenated Convolutional Codes in Multipath Rayleigh Fading Environment", IEEE 2000,pp 121-128
[39] Aik Chindapol and James A. Ritcey, "Design, Analysis, and Performance Evaluation for BICM-ID with Square QAM Constellations in Rayleigh Fading Channels", IEEE J. Select. Areas Comm, vol.19,No.5,May 2001,pp 1421-1429
[40] E. Zehavi, "8-PSK trellis codes for a Rayleigh channel", IEEE Trans. Commun.,vol. 40, May 1992, pp. 873-884.
[41] D.Divslar, M. Simon, "The design of trellis coded MPSK for fading channel: Performance criteria", IEEE Trans. Commun., vol. 36, Sept. 1988, pp. 1004-1012.
[42] Yuheng Huang, and James A. Ritcey, "16-QAM BICM-ID in Fading Channels With Imperfect Channel State Information" , IEEE Trans, on wireless communications, No. 5, Sep. 2003 pp 944-948
[43]C.Douillard,et al, "Iterative correction of intersymbol interference:Turbo equalization",European Trans. Telecomm.,vol.6,Sept.-Oct 1995,pp.507-511
[44]Jong Park "Trellis based soft output decoding algorithms for concatenated coding system", Doctor dissertation,school of electrical and computer engineering Georgia Institute of Technology,Mar.l998,pp 125-145
[45]A.Glavieux, C.Loat, and J.Jabat. "Turbo equalization over a frequency selective channel",International Symposium on Turbo codes and related topics.Sept. 1997,pp.96-102
[46]X.Wang and H.Pool, "Iterative(Turbo) soft interference cancellation and decoding for coded CDMA",IEEE Trans. Comm.,vol.47,no.7,1999,pp. 1046-1061
[47]D.Raphaeli and Y.Zerai, "Combined Turbo equalization and Turbo decoding",IEEE Proceeding on the Global Tele.Conf.'97,vol.2,Nov.1997,pp.639-643
[48] Ralf Kotter,and Andrew Singer, Michael Tuchler, "Turbo equalization:an iterative equalization and decoding technique for coded data transminssion",IEEE Signal Processing Magazine,Jan.2004,pp.67-80
[49] J. Hagenauer, T. Stockhammer, "Channel Coding and Transmission Aspects for Wireless Multimedia", Proc of the IEEE, Vol.87, No. 10, October 1999 , pp. 1764-1777
[50] Y.Wu and B. D.Woerner, "The influence of quantization and fixed point arithmetic upon the ber performance of Turbo codes," Proc. Vehicular Technology Conf., vol. 2, 1999, pp. 1683-1687.
[51] G Montorsi and S. Benedetto, "Design of Fixed-Point Iterative Decoders for Concatenated Codes with Interleaves", IEEE J. Select. Areas Comm, Vol. 19, No. 5, May 2001,pp.871-882
[52]Jayant, N.S and Noll, P., Digital coding of Waveforms, Prentice-Hall, Inc,. Englewood Cliffs, N,J., 1984,pp 134-140
[53] Bemaed Sklar著,徐平平等译,数字通信—基础于应用(第二版),电子工业出版社,pp626-628
[54] Todd A. Summers and Stephen G. Wilson, "SNR Mismatch and Online Estimation in Turbo Decoding", IEEE Transactions on Communications, vol. 46, No. 4, April 1998, pp 421-423
[55] 王新梅,肖国镇编著,纠错码—原理与方法(修订版),西安电子科技大学出版社,1999年,pp506-516
[56] U. Dasgupta, C.N. Georghiade, "Turbo Decoding of Quantized Data", [online]wclb.tamu.edu/pub/papers/Dasgupta. pdf
[57] H.E. Gamal , "A.R.Hammons, Analyzing the Turbo decoder using the Gaussian approximation" Proc ISIT'2000 Sorrento,Itealy.June 2000,pp 322-327
[58] 钱颂迪 运筹学 清华大学出版社,1990年,pp254-258
[59] 白宝明,“Turbo码的原理及其应用”,博士论文,西安电子科技大学,1999年
[60] 刘东华,“Turbo码的原理及其应用”,博士论文,国防科技科技大学,2001年