Turbo码的译码算法比较研究以及在CPM技术中的应用
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摘要
纠错编码技术作为改善数字通信可靠性的一种有效的手段，在数字通信的各个领域都得到了广泛的应用。1993年，法国的C.Berrou等人提出了一种将递归系统卷积码通过交织器并行级联的编码方案，称之为Turbo码。传统的Turbo码山两个经交织器连接的分量码编码器级联而成，且Turbo码的译码采用了软输入软输出的算法思想和迭代译码的方法，使子译码器之间可以相互传递软信息，保证编码信息的充分利用。
本文首先研究了Turbo码的(log-)MAP、Max-log-MAP以及SOVA算法在不同参数下的性能比较，设想了一种融合串行、并行级联卷积码译码思想的串行级联Turbo码的编码方案；并在此基础上对BCJR算法以及Log-MAP算法进行了统计意义上的分析与比较，从仿真的角度说明了Log-MAP算法虽然在本质上是等同于BCJR算法的，但是Log-MAP算法中用于最后判决的对数似然比序列LLR相对于呈高斯分布的BCJR算法来说，其概率密度的分布比较杂乱，但是其均值和方差随着信噪比的改变近似呈线性关系。此外本文还通过大量的仿真还证明了log-MAP译码算法对信道中叠加的噪声方差估计值的精度要求并不高。
另外，本文还结合了网格编码调制(TCM)的概念，对Turbo码与连续相位调制(CPM)串行级联的结合方案中调制信号之间的最小欧氏距离以及Turbo码的最优化编码结构进行了搜索与研究，在分析数据结果的同时将搜索结果与卷积码进行了比较，从最小欧氏距离与误码率性能成反比关系的理论基础上证明了Turbo码与卷积码相比的优越性所在。
The technology of Error-Correcting Coding has been widely used in the digital communications as an effective means of decreasing bit error rates. In 1993, a Frenchman named C.Berrou advanced an exciting coding structure called Turbo-codes. The Turbo-codes' encoder is comprised of Recursive Systematic Convolutional Codes, which is connected by an interweaver. And the decoding algorithm of Turbo-codes, such as (log) MAP, Max-log-MAP and SOVA, are all based on the soft input and soft output (SISO) module.
First of all, the research emphasis of this paper is placed on the performance comparison of some kinds of decoding algorithm of Turbo-codes such as (log-)MAP, Max-log-MAP and SOVA in a wide range. And through simulation, this paper proves that: (1) The distribution of LLR sequence of Log-MAP is unorderly, compared with that of BCJR decoding algorithm. (2) The performance of Log-MAP is hardly influenced by the accuracy of the estimation of noise's power in AWGN channel. (3) The mean and the variance of LLR sequence of Log-MAP decoding algorithm change with the SNR in approximately linear order respectively.
On the other hand, this paper also does some research on the technology of the combination of Turbo-codes and CPM. The research emphasis is placed on the Minimum Euclidean Distance of the modulated signals and the best Turbo codes, and the result from computer research is compared with the one of convolutional coded CPM, which has strongly proved the better performance of Turbo-codes.
本文首先研究了Turbo码的(log-)MAP、Max-log-MAP以及SOVA算法在不同参数下的性能比较，设想了一种融合串行、并行级联卷积码译码思想的串行级联Turbo码的编码方案；并在此基础上对BCJR算法以及Log-MAP算法进行了统计意义上的分析与比较，从仿真的角度说明了Log-MAP算法虽然在本质上是等同于BCJR算法的，但是Log-MAP算法中用于最后判决的对数似然比序列LLR相对于呈高斯分布的BCJR算法来说，其概率密度的分布比较杂乱，但是其均值和方差随着信噪比的改变近似呈线性关系。此外本文还通过大量的仿真还证明了log-MAP译码算法对信道中叠加的噪声方差估计值的精度要求并不高。
另外，本文还结合了网格编码调制(TCM)的概念，对Turbo码与连续相位调制(CPM)串行级联的结合方案中调制信号之间的最小欧氏距离以及Turbo码的最优化编码结构进行了搜索与研究，在分析数据结果的同时将搜索结果与卷积码进行了比较，从最小欧氏距离与误码率性能成反比关系的理论基础上证明了Turbo码与卷积码相比的优越性所在。
The technology of Error-Correcting Coding has been widely used in the digital communications as an effective means of decreasing bit error rates. In 1993, a Frenchman named C.Berrou advanced an exciting coding structure called Turbo-codes. The Turbo-codes' encoder is comprised of Recursive Systematic Convolutional Codes, which is connected by an interweaver. And the decoding algorithm of Turbo-codes, such as (log) MAP, Max-log-MAP and SOVA, are all based on the soft input and soft output (SISO) module.
First of all, the research emphasis of this paper is placed on the performance comparison of some kinds of decoding algorithm of Turbo-codes such as (log-)MAP, Max-log-MAP and SOVA in a wide range. And through simulation, this paper proves that: (1) The distribution of LLR sequence of Log-MAP is unorderly, compared with that of BCJR decoding algorithm. (2) The performance of Log-MAP is hardly influenced by the accuracy of the estimation of noise's power in AWGN channel. (3) The mean and the variance of LLR sequence of Log-MAP decoding algorithm change with the SNR in approximately linear order respectively.
On the other hand, this paper also does some research on the technology of the combination of Turbo-codes and CPM. The research emphasis is placed on the Minimum Euclidean Distance of the modulated signals and the best Turbo codes, and the result from computer research is compared with the one of convolutional coded CPM, which has strongly proved the better performance of Turbo-codes.
引文
[1] C.Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon Limit Error-Correcting Coding: Turbo Codes," Proc. 1993 IEEE International Conference on Communications, Geneva, Switzerland, pp. 1064-1070, May 1993
[2] 王新梅、肖国镇，“纠错码—原理与方法(修订版)”，西安电子科技大学出版社
[3] C.E.Shannon, "A Mathematical Theory of Communication", The Bell System Technical Journal, Vol. 27, pp. 379-423,623-656, July, October, 1948
[4] G. Ungerboeck, "Channel Coding with multi-level/phase signals", IEEE Trans. Info. Theory, pp.55-67, Jan. 1982
[5] William E. Ryan, "A Turbo Code Tutorial", New Mexico State University, Box 30001 Dept. 3-O, Las Cruces, NM 88003, wryan@nmsu.edu
[6] Sergio. Benedetto, Guido.Montorsi,"Unveiling Turbo Codes: Some Results on Parallel Concatenated Coding Schemes", IEEE. Trans. Inform. Theory, vol. 42, No. 2, Mar. 1996
[7] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, "A soft-Input Soft-Output Maximum A Posteriori(MAP) Module to Decode Parallel and Serial Concatenated Codes", TDA Progress Report 42-127, November 1996 from JPL web site
[8] Lance C. Perez, Member, IEEE, Jan Seghers, and Daniel J. Costello, Jr., Fellow, IEEE, "A Distance Spectrum Interpretation of Turbo Codes", IEEE. Trans. Inform. Theory, Vol. 42, NO. 6, November 1996
[9] Patrick Robertson, Peter Hoeher, and Emmanuelle Villebrum, "Optimal and Sub-Optimal Maximum A Posteriori Algorithms Suitable for Turbo Decoding",
[10] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, "A soft-Input Soft-Output Maximum A Posteriori(MAP) Module to Decode Parallel and Serial Concatenated Codes", TDA Progress Report 42-127, November 1996 from JPL web site
[11] Ling Li, "BCJR algorithm", http://www. cs.caltech.edu/～ling/course/ee127c/ee127cpjls.pdf
[12] J. Hagenauer and P. Hoeher, "A Viterbi algorithm with soft-decision outputs and its application", in Proc. Globecom, Dallas, TX, Nov.1989, pp. 1680-1686
[13] T. Aulin and C.-E. Sundberg, "Continuous phase modulation—Part Ⅰ and Part Ⅱ", IEEE Trans. Commun., vol. COM-29, pp. 196-225, May 1981
[14] Mark R. Shane and Richard D. Wesel, "Parallel Concatenated Turbo Codes for Continuous Phase Modulation",
http://www. ee.ucla.edu/～wesel/documents/wcnc addendum.pdf
[15] Steven V. Pizzi, Stephen G. Wilson, "Convolutional Coding Combined with Continuous Phase Modulation", IEEE. Trans. Communications, vol. Com-33. No.1, Jan. 1985
[16] S.Benedetto, D. Dibsalar, G. Montorsi, and F. Pollara, "Parallel concatenated trellis coded modulation", IEEE International Conference on Communication, June 1996
[17] Paul K. M. HO and Peter J. Mclane, "Spectrum, Distance and Receiver Complexity of Encoded Continuous Phase Modulation", IEEE Trans. Information Theory, vol. 34 No. 5, September 1988
[18] J. Seghers, "On the free distance of Turbo codes and related product codes", Final Rep., Diploma Project SS 1995, NO. 6613, Swiss Federal Institute of Technology, Zurith, Switzerland, Aug. 1995
[19] J. A. Erfanian, S.Pasupathy, and G. gu;ak, "Reduced complexity symbol detectors with parallel structures for ISI channels," IEEE Trans. Commun., Vol. 42, pp. 1661-1671, February/March/April 1994.
[20] 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, December 1990
[21] Bixio E. Rimoldi, "A Decomposition Approach to CPM", IEEE Transactions on Information Theory, Vol., 34, NO. 2, March 1988
[22] S.Benedetto and G.Montorsi, "Iterative Decoding of Serially Concatenated Convolutional Codes
[2] 王新梅、肖国镇，“纠错码—原理与方法(修订版)”，西安电子科技大学出版社
[3] C.E.Shannon, "A Mathematical Theory of Communication", The Bell System Technical Journal, Vol. 27, pp. 379-423,623-656, July, October, 1948
[4] G. Ungerboeck, "Channel Coding with multi-level/phase signals", IEEE Trans. Info. Theory, pp.55-67, Jan. 1982
[5] William E. Ryan, "A Turbo Code Tutorial", New Mexico State University, Box 30001 Dept. 3-O, Las Cruces, NM 88003, wryan@nmsu.edu
[6] Sergio. Benedetto, Guido.Montorsi,"Unveiling Turbo Codes: Some Results on Parallel Concatenated Coding Schemes", IEEE. Trans. Inform. Theory, vol. 42, No. 2, Mar. 1996
[7] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, "A soft-Input Soft-Output Maximum A Posteriori(MAP) Module to Decode Parallel and Serial Concatenated Codes", TDA Progress Report 42-127, November 1996 from JPL web site
[8] Lance C. Perez, Member, IEEE, Jan Seghers, and Daniel J. Costello, Jr., Fellow, IEEE, "A Distance Spectrum Interpretation of Turbo Codes", IEEE. Trans. Inform. Theory, Vol. 42, NO. 6, November 1996
[9] Patrick Robertson, Peter Hoeher, and Emmanuelle Villebrum, "Optimal and Sub-Optimal Maximum A Posteriori Algorithms Suitable for Turbo Decoding",
[10] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, "A soft-Input Soft-Output Maximum A Posteriori(MAP) Module to Decode Parallel and Serial Concatenated Codes", TDA Progress Report 42-127, November 1996 from JPL web site
[11] Ling Li, "BCJR algorithm", http://www. cs.caltech.edu/～ling/course/ee127c/ee127cpjls.pdf
[12] J. Hagenauer and P. Hoeher, "A Viterbi algorithm with soft-decision outputs and its application", in Proc. Globecom, Dallas, TX, Nov.1989, pp. 1680-1686
[13] T. Aulin and C.-E. Sundberg, "Continuous phase modulation—Part Ⅰ and Part Ⅱ", IEEE Trans. Commun., vol. COM-29, pp. 196-225, May 1981
[14] Mark R. Shane and Richard D. Wesel, "Parallel Concatenated Turbo Codes for Continuous Phase Modulation",
http://www. ee.ucla.edu/～wesel/documents/wcnc addendum.pdf
[15] Steven V. Pizzi, Stephen G. Wilson, "Convolutional Coding Combined with Continuous Phase Modulation", IEEE. Trans. Communications, vol. Com-33. No.1, Jan. 1985
[16] S.Benedetto, D. Dibsalar, G. Montorsi, and F. Pollara, "Parallel concatenated trellis coded modulation", IEEE International Conference on Communication, June 1996
[17] Paul K. M. HO and Peter J. Mclane, "Spectrum, Distance and Receiver Complexity of Encoded Continuous Phase Modulation", IEEE Trans. Information Theory, vol. 34 No. 5, September 1988
[18] J. Seghers, "On the free distance of Turbo codes and related product codes", Final Rep., Diploma Project SS 1995, NO. 6613, Swiss Federal Institute of Technology, Zurith, Switzerland, Aug. 1995
[19] J. A. Erfanian, S.Pasupathy, and G. gu;ak, "Reduced complexity symbol detectors with parallel structures for ISI channels," IEEE Trans. Commun., Vol. 42, pp. 1661-1671, February/March/April 1994.
[20] 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, December 1990
[21] Bixio E. Rimoldi, "A Decomposition Approach to CPM", IEEE Transactions on Information Theory, Vol., 34, NO. 2, March 1988
[22] S.Benedetto and G.Montorsi, "Iterative Decoding of Serially Concatenated Convolutional Codes