低密度码CPM联合调制技术研究
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摘要
CPM调制是有记忆的恒包络调制方式,对功放的非线性特性不敏感;连续相位使带外辐射减小,具有较高的带宽效率;且CPM本身具有一定的编码增益,拥有较高的功率效率;采用高阶CPM调制可以提高传信率。码字很长的二进制LDPC码已被证明拥有逼近香农限的良好性能;而对于中等码长,可以通过设计定义在高阶GF(q)上的LDPC码来提高误码性能。本文研究了多进制LDPC码与高阶CPM调制相结合的串行级联系统。
但是在具体实现时,高阶CPM调制的解调以及多进制LDPC码的构造和译码都面临复杂度上的挑战。针对这一问题,本文给出了相应的解决方案。在构造多进制LDPC码的校验矩阵时,使用一种新的方法来计算泰纳图的最小环长,有效的降低了计算复杂度,改进了二次置换多项式构造准循环LDPC码的算法。且多进制LDPC码的译码采用傅立叶快速算法。同时,为降低高阶CPM解调的复杂度,采用了最小均方误差下CPM的PAM分解模型;基于该模型简化了CPM的匹配滤波器,并给出似然概率的计算方法,及CPM的软输入软输出解调器,实现了CPM解调与LDPC之间的迭代译码。
The serial concatenated system of non-binary LDPC codes over GF (q) and M-ary CPM modulation is studied in this paper. CPM is a memory modulation scheme with the advantages of constant signal envelope and excellent power and bandwidth efficiency.
LDPC codes have been shown to approach Shannon limit performance for binary LDPC with long code length, on the other hand, for moderate code lengths, the error performance can be improved by increasing q, which Non-binary LDPC is designed over GF(q). Derived from such advantages, the serial concatenation, with joint iterative decoding between the CPM detector and LDPC decoder, is designed to achieve good performance over AWGN or fading channel.
The construction, decoding of Nonbinary LDPC Codes and the detection of high-order CPM modulation face the challenge of complexity. In order to simplify, a fast algorithm, which is applied to quadratic permutation polynomials (QPP) construction, is proposed to compute the girth of Tanner graph of LDPC. Quasic-regular nonbinary LDPC construction, which can be implemented simply on hardware, is also investigated. The FFT BP algorithm is used to decoding the nonbinary LDPC. Huang and Li’s PAM approximate decomposition of CPM under MMSE is used to simplify the Match filter and detectior. A soft-in soft-out detection of CPM is designed in order to implement the iterative decoding, as well as an algorithm to approximate the likely probability.
但是在具体实现时,高阶CPM调制的解调以及多进制LDPC码的构造和译码都面临复杂度上的挑战。针对这一问题,本文给出了相应的解决方案。在构造多进制LDPC码的校验矩阵时,使用一种新的方法来计算泰纳图的最小环长,有效的降低了计算复杂度,改进了二次置换多项式构造准循环LDPC码的算法。且多进制LDPC码的译码采用傅立叶快速算法。同时,为降低高阶CPM解调的复杂度,采用了最小均方误差下CPM的PAM分解模型;基于该模型简化了CPM的匹配滤波器,并给出似然概率的计算方法,及CPM的软输入软输出解调器,实现了CPM解调与LDPC之间的迭代译码。
The serial concatenated system of non-binary LDPC codes over GF (q) and M-ary CPM modulation is studied in this paper. CPM is a memory modulation scheme with the advantages of constant signal envelope and excellent power and bandwidth efficiency.
LDPC codes have been shown to approach Shannon limit performance for binary LDPC with long code length, on the other hand, for moderate code lengths, the error performance can be improved by increasing q, which Non-binary LDPC is designed over GF(q). Derived from such advantages, the serial concatenation, with joint iterative decoding between the CPM detector and LDPC decoder, is designed to achieve good performance over AWGN or fading channel.
The construction, decoding of Nonbinary LDPC Codes and the detection of high-order CPM modulation face the challenge of complexity. In order to simplify, a fast algorithm, which is applied to quadratic permutation polynomials (QPP) construction, is proposed to compute the girth of Tanner graph of LDPC. Quasic-regular nonbinary LDPC construction, which can be implemented simply on hardware, is also investigated. The FFT BP algorithm is used to decoding the nonbinary LDPC. Huang and Li’s PAM approximate decomposition of CPM under MMSE is used to simplify the Match filter and detectior. A soft-in soft-out detection of CPM is designed in order to implement the iterative decoding, as well as an algorithm to approximate the likely probability.
引文
[1]白宝明,”Turbo码理论及其应用的研究”,博士学位论文,1991
[2]L.R. Babl, J. Cocke, F. Jeinek and J. Raviv,”Optimal decoding of linear codes for minimizing symbol error rate”,IEEE Trans.Info.Theory,vol.IT-20,pp.284-287,March 1974.
[3]J.Hagenaueran&P .Hoeher,"A viterbi algorithm with soft-decision outputs and its ap- plications,"inProc.Globecom'89, pp.1680-1696, Nov.1989
[4]Claude Berrou, Alain Glavieux,”Near optimal error correcting coding and Decoding: Turbo-codes”, IEEE Transactions on Communications, vol.44.No.10.pp.1261-1271, Octorber 1996.
[5] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara,“Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding”IEEE Trans. Inform. Theory, vol.IT-44. p3097-3104, May1998.
[6] P. Moqvist, "Serially concatenated systems: An iterative decoding approach with application to continuous phase modulation", Lic.Eng. Thesis, Chalmers Univ. of Technology, G?teborg, Sweden, 1999
[7] Shu Lin, Daniel J.Costello, Jr.”Error Control Coding”, 2nd ed.China Machine Press, 2007
[8] J. G. Proakis, Digital Communications, 4th ed. New York: McGraw-Hill, 2003. CPM Basic
[9]T. Aulin and C.-E. W. Sundberg,“Continuous phase modulation—PartI: Full response signaling,”IEEE Trans. Commun., vol. COM-29, No.3, pp. 196–209, Mar. 1981.
[10] T. Aulin, N. Rydbeck, and C.-E.W. Sundberg,“Continuous phase modulation—Part II: Partial response signaling,”IEEE Trans. Commun., vol.COM-29, no. 3, pp. 210–225, Mar. 1981. CPE+MM-Rimoldi Decomposition
[11] B. E. Rimoldi,“A decomposition approach to CPM,”IEEE Trans. Inf.Theory, vol. 34, no. 2, pp. 260–270, Mar. 1988.
[12] G. K. Kaleh,“Simple coherent receivers for partial response continuous Phase modulation,”IEEE J. Sel. Areas Commun., vol. 7, no. 9, pp.1427–1436, Dec. 1989.
[13] G. Colavolpe and R. Raheli,“Reduced-complexity detection and phase synchronization of CPM signals,”IEEE Trans. Commun., vol. 45, no. 9,pp. 1070–1079, Sep. 1997.
[14]J. Huber and W. Liu,“An alternative approach to reduced-complexity CPM-receivers,”IEEE J. Sel. Areas Commun., vol. 7, no. 9, pp.1437–1449, Dec. 1989.
[15] P. Moqvist and T. Aulin,“Orthogonalization by principal components applied to CPM,”IEEE Trans. Commun., vol. 51, no. 11, pp. 1838–1845, Nov. 2003. Laurent-PAM Decomposition
[16] P. A. Laurent,“Exact and approximate construction of digital phase modulation by superposition of amplitude modulated pulses (AMP),”IEEE Trans. Commun., vol. COM-34, no. 2, pp. 150–160, Feb. 1986.
[17] U. Mengali and M. Morelli,“Decomposition of M-ary CPM signals into PAM waveforms,”IEEE Trans. Inf. Theory, vol. 41, no. 5, pp.1265–1275, Sep. 1995. X. Huang and Y. Li- PAM Decomposition
[18]X. Huang and Y. Li,“The PAM decomposition of CPM signal with integer modulation index”, IEEE Trans. Commun., vol. 51, no. 4, pp.543–546, Apr. 2003.
[19]X. Huang and Y. Li,“MMSE optimal approximation of continuous-phase modulated signal as superposition of linearly modulated pulses,”IEEE Trans.Commun., vol. 53, No. 7, pp. 1166–1177, Jul. 2005.
[20]X. Huang and Y. Li,“Simple CPM receivers based on a switched linear modulation model”, IEEE Trans. Commun., vol. 53, no. 7, pp.1100–1103, Jul. 2005.
[21]Yunxin Li, Branka Vucetic, Yoichi Sato:“Optimum soft-output detection for channels with intersymbol interference”. IEEE Transactions on Information Theory 41(3): 704-713 ,1995
[22]X. Huang and Y. Li,“Simple Noncoherent CPM Receivers by PAM Decomposition and MMSE Equalization”, The 14th IEEE 2003 International Symposium on Persona1, lndoor and Mobile Radio Communication Proceedings, 2003 IEEE.pp.707-711,2003
[23]G. Colavolpe and R. Raheli,“Noncoherent sequence detection of continuous Phase modulations”, IEEE Trans. Commun., vol. 47, No. 9, pp.1303–1307, Sep.1999.
[24]Alan Barbieri and Giulio Colavolpe,”Simplified Soft-Output Detection of CPM Signals Over Coherent and Phase Noise Channels”,IEEE,Trans. Wireless commu.vol 6,NO.7 July 2007 LDPC Basic
[25] R. G. Gallager, Low density parity check codes. Cambridge, MA: MIT Press, 1963.
[26] D.J.C. MacKay. "Good error-correcting codes based on very sparse matrices". IEEE Trans. Inform. Theory, 45(2):pp. 399–431, March1999.
[27] T.J. Richardson, M.A. Shokrollahi and R.L. Urbanke,“Design of Capacity-Approaching irregular Low-Density Parity Check Codes,”IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, Feb. 2001.
[28] M. Fossorier, M. Mihaljevi′c and H. Imai,“Reduced Complexity Iterative Decoding of LDPC codes based on Belief Propagation,”IEEE Trans. Commun., vol. 47, pp. 673-680, May 1999.
[29] S.-Y. Chung, G. D. Forney, Jr.T. J. Richardson, and R. Urbanke,“On the design of Low-density parity-check codes within 0.0045 dB of the Shannon limit,”IEEE Commun.Letter, vol. 5, No. 2, pp. 58–60, Feb. 2001
[30] X. Y. Hu, E. Eleftheriou, and D. M. Arnold,“Regular and irregular progressive Edge-growth tanner graphs,”IEEE Trans. Inform.Theory, vol.51, pp. 386–398, Jan. 2005
[31] M. C. Davey and D. Mackay,“Low-density parity check codes over GF (q) ,”IEEE Comm. Letters, vol. 2, pp. 165–167, June 1998.
[32]Xiangming Li, M.R. Soleymani, J.Lodge and P.S. Guinand,”Good Ldpc Codes over GF (q) for Bandwidth efficient Transmission”, 2003 4th IEEE Workshop on Signal Processing, Advances in Wireless Communications, pp.95-99,2003 LDPC (q) Basic
[33]Ronghui Peng and Rong-Rong Chen,”Application of Nonbinary LDPC Codes for Communication over Fading Channels Using Higher Order Modulations”, IEEE Globecom 2006 proceedings. 1-4244-0357-X/06, 2006
[34] O. Y. Takeshita,“A new construction for LDPC codes using permutation Polynomials over integer rings,”submitted to IEEE Trans. Inform.Theory, June 2005.
[35] Shumei Song, Lingqi Zeng, Shu Lin and Khaled Abdel-Ghaffar,“Algebraic Constructions of Nonbinary Quasi-Cyclic LDPC Codes”, ISIT 2006,Seattle,USA, IEEE2006,1-4244-0504-1/06,pp.1303-1308, July 9-14,2006
[36] Z. -W. Li, L. Chen, L. -Q. Zeng, S. Lin and W. Fong,“Efficient encoding of quasi-cyclic low-density parity-check codes,”IEEE Trans. Commun.,vol.54, no. 1, pp. 71-81, Jan. 2006. Girth Compute
[37] Raphael Yuster ,Uri Zwick,”Finding Even Cycles Even Faster”, The Proceeding of the 21st International Colloquium on Automata, Languages and Programming, Jerusalem, Israel, pp. 532-543,1994
[38] R. M. Tanner,“A recursive approach to low complexity codes,”IEEE Trans. Inf. Theory, vol. IT-27, no. 6, pp. 533–547, Sep. 1981.
[39]文红,符初生,”ldpc码原理与应用”,电子科技大学出版社, 2006-5-14LDPC Encoding
[40] Thomas J. Richardson and Rüdiger L. Urbanke,“Efficient Encoding of Low-Density Parity-Check Codes”, IEEE Trans. Commun.vol.47.No.2.pp.638-656, Fabruary 2001 LDPC (q) Decoding
[41] H. Song and J. Cruz,“Reduced-complexity decoding of Q-ary LDPC codes for magnetic recoding,”IEEE Trans. Magnetics, vol. 39, pp. 1081–1087, March 2003.
[42] David Declercq, Marc Fossorier,”Decoding Algorithms for Nonbinary LDPC Codes Over GF(q)”,IEEE Trans. Commun.vol.55.No.4.pp.633-643,Aprial 2007
[43] L. Barnault and D. Declercq,”Fast Decoding Algorithm for LDPC over GF(q)”,ITW2003,Paris,France,March 31-April 4,2003
[2]L.R. Babl, J. Cocke, F. Jeinek and J. Raviv,”Optimal decoding of linear codes for minimizing symbol error rate”,IEEE Trans.Info.Theory,vol.IT-20,pp.284-287,March 1974.
[3]J.Hagenaueran&P .Hoeher,"A viterbi algorithm with soft-decision outputs and its ap- plications,"inProc.Globecom'89, pp.1680-1696, Nov.1989
[4]Claude Berrou, Alain Glavieux,”Near optimal error correcting coding and Decoding: Turbo-codes”, IEEE Transactions on Communications, vol.44.No.10.pp.1261-1271, Octorber 1996.
[5] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara,“Serial Concatenation of Interleaved Codes: Performance Analysis, Design, and Iterative Decoding”IEEE Trans. Inform. Theory, vol.IT-44. p3097-3104, May1998.
[6] P. Moqvist, "Serially concatenated systems: An iterative decoding approach with application to continuous phase modulation", Lic.Eng. Thesis, Chalmers Univ. of Technology, G?teborg, Sweden, 1999
[7] Shu Lin, Daniel J.Costello, Jr.”Error Control Coding”, 2nd ed.China Machine Press, 2007
[8] J. G. Proakis, Digital Communications, 4th ed. New York: McGraw-Hill, 2003. CPM Basic
[9]T. Aulin and C.-E. W. Sundberg,“Continuous phase modulation—PartI: Full response signaling,”IEEE Trans. Commun., vol. COM-29, No.3, pp. 196–209, Mar. 1981.
[10] T. Aulin, N. Rydbeck, and C.-E.W. Sundberg,“Continuous phase modulation—Part II: Partial response signaling,”IEEE Trans. Commun., vol.COM-29, no. 3, pp. 210–225, Mar. 1981. CPE+MM-Rimoldi Decomposition
[11] B. E. Rimoldi,“A decomposition approach to CPM,”IEEE Trans. Inf.Theory, vol. 34, no. 2, pp. 260–270, Mar. 1988.
[12] G. K. Kaleh,“Simple coherent receivers for partial response continuous Phase modulation,”IEEE J. Sel. Areas Commun., vol. 7, no. 9, pp.1427–1436, Dec. 1989.
[13] G. Colavolpe and R. Raheli,“Reduced-complexity detection and phase synchronization of CPM signals,”IEEE Trans. Commun., vol. 45, no. 9,pp. 1070–1079, Sep. 1997.
[14]J. Huber and W. Liu,“An alternative approach to reduced-complexity CPM-receivers,”IEEE J. Sel. Areas Commun., vol. 7, no. 9, pp.1437–1449, Dec. 1989.
[15] P. Moqvist and T. Aulin,“Orthogonalization by principal components applied to CPM,”IEEE Trans. Commun., vol. 51, no. 11, pp. 1838–1845, Nov. 2003. Laurent-PAM Decomposition
[16] P. A. Laurent,“Exact and approximate construction of digital phase modulation by superposition of amplitude modulated pulses (AMP),”IEEE Trans. Commun., vol. COM-34, no. 2, pp. 150–160, Feb. 1986.
[17] U. Mengali and M. Morelli,“Decomposition of M-ary CPM signals into PAM waveforms,”IEEE Trans. Inf. Theory, vol. 41, no. 5, pp.1265–1275, Sep. 1995. X. Huang and Y. Li- PAM Decomposition
[18]X. Huang and Y. Li,“The PAM decomposition of CPM signal with integer modulation index”, IEEE Trans. Commun., vol. 51, no. 4, pp.543–546, Apr. 2003.
[19]X. Huang and Y. Li,“MMSE optimal approximation of continuous-phase modulated signal as superposition of linearly modulated pulses,”IEEE Trans.Commun., vol. 53, No. 7, pp. 1166–1177, Jul. 2005.
[20]X. Huang and Y. Li,“Simple CPM receivers based on a switched linear modulation model”, IEEE Trans. Commun., vol. 53, no. 7, pp.1100–1103, Jul. 2005.
[21]Yunxin Li, Branka Vucetic, Yoichi Sato:“Optimum soft-output detection for channels with intersymbol interference”. IEEE Transactions on Information Theory 41(3): 704-713 ,1995
[22]X. Huang and Y. Li,“Simple Noncoherent CPM Receivers by PAM Decomposition and MMSE Equalization”, The 14th IEEE 2003 International Symposium on Persona1, lndoor and Mobile Radio Communication Proceedings, 2003 IEEE.pp.707-711,2003
[23]G. Colavolpe and R. Raheli,“Noncoherent sequence detection of continuous Phase modulations”, IEEE Trans. Commun., vol. 47, No. 9, pp.1303–1307, Sep.1999.
[24]Alan Barbieri and Giulio Colavolpe,”Simplified Soft-Output Detection of CPM Signals Over Coherent and Phase Noise Channels”,IEEE,Trans. Wireless commu.vol 6,NO.7 July 2007 LDPC Basic
[25] R. G. Gallager, Low density parity check codes. Cambridge, MA: MIT Press, 1963.
[26] D.J.C. MacKay. "Good error-correcting codes based on very sparse matrices". IEEE Trans. Inform. Theory, 45(2):pp. 399–431, March1999.
[27] T.J. Richardson, M.A. Shokrollahi and R.L. Urbanke,“Design of Capacity-Approaching irregular Low-Density Parity Check Codes,”IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, Feb. 2001.
[28] M. Fossorier, M. Mihaljevi′c and H. Imai,“Reduced Complexity Iterative Decoding of LDPC codes based on Belief Propagation,”IEEE Trans. Commun., vol. 47, pp. 673-680, May 1999.
[29] S.-Y. Chung, G. D. Forney, Jr.T. J. Richardson, and R. Urbanke,“On the design of Low-density parity-check codes within 0.0045 dB of the Shannon limit,”IEEE Commun.Letter, vol. 5, No. 2, pp. 58–60, Feb. 2001
[30] X. Y. Hu, E. Eleftheriou, and D. M. Arnold,“Regular and irregular progressive Edge-growth tanner graphs,”IEEE Trans. Inform.Theory, vol.51, pp. 386–398, Jan. 2005
[31] M. C. Davey and D. Mackay,“Low-density parity check codes over GF (q) ,”IEEE Comm. Letters, vol. 2, pp. 165–167, June 1998.
[32]Xiangming Li, M.R. Soleymani, J.Lodge and P.S. Guinand,”Good Ldpc Codes over GF (q) for Bandwidth efficient Transmission”, 2003 4th IEEE Workshop on Signal Processing, Advances in Wireless Communications, pp.95-99,2003 LDPC (q) Basic
[33]Ronghui Peng and Rong-Rong Chen,”Application of Nonbinary LDPC Codes for Communication over Fading Channels Using Higher Order Modulations”, IEEE Globecom 2006 proceedings. 1-4244-0357-X/06, 2006
[34] O. Y. Takeshita,“A new construction for LDPC codes using permutation Polynomials over integer rings,”submitted to IEEE Trans. Inform.Theory, June 2005.
[35] Shumei Song, Lingqi Zeng, Shu Lin and Khaled Abdel-Ghaffar,“Algebraic Constructions of Nonbinary Quasi-Cyclic LDPC Codes”, ISIT 2006,Seattle,USA, IEEE2006,1-4244-0504-1/06,pp.1303-1308, July 9-14,2006
[36] Z. -W. Li, L. Chen, L. -Q. Zeng, S. Lin and W. Fong,“Efficient encoding of quasi-cyclic low-density parity-check codes,”IEEE Trans. Commun.,vol.54, no. 1, pp. 71-81, Jan. 2006. Girth Compute
[37] Raphael Yuster ,Uri Zwick,”Finding Even Cycles Even Faster”, The Proceeding of the 21st International Colloquium on Automata, Languages and Programming, Jerusalem, Israel, pp. 532-543,1994
[38] R. M. Tanner,“A recursive approach to low complexity codes,”IEEE Trans. Inf. Theory, vol. IT-27, no. 6, pp. 533–547, Sep. 1981.
[39]文红,符初生,”ldpc码原理与应用”,电子科技大学出版社, 2006-5-14LDPC Encoding
[40] Thomas J. Richardson and Rüdiger L. Urbanke,“Efficient Encoding of Low-Density Parity-Check Codes”, IEEE Trans. Commun.vol.47.No.2.pp.638-656, Fabruary 2001 LDPC (q) Decoding
[41] H. Song and J. Cruz,“Reduced-complexity decoding of Q-ary LDPC codes for magnetic recoding,”IEEE Trans. Magnetics, vol. 39, pp. 1081–1087, March 2003.
[42] David Declercq, Marc Fossorier,”Decoding Algorithms for Nonbinary LDPC Codes Over GF(q)”,IEEE Trans. Commun.vol.55.No.4.pp.633-643,Aprial 2007
[43] L. Barnault and D. Declercq,”Fast Decoding Algorithm for LDPC over GF(q)”,ITW2003,Paris,France,March 31-April 4,2003