基于高斯近似的LDPC码TDMP算法分析
|
摘要
针对目前缺少对LDPC码TDMP算法理论分析的问题,提出了TDMP算法的高斯近似.基于BP算法和对称条件,得到结果收敛的TDMP算法的高斯近似.利用高斯近似来分析TDMP算法的译码收敛性,为论证TDMP算法的优越性能提供了理论依据.基于Wimax标准,分别对BP算法和TDMP算法的高斯近似进行仿真.仿真结果表明,在相同情况下,TDMP算法译码收敛速度更快,需要的迭代次数更少.同时,给出了TDMP算法分别采用高斯近似和密度进化时的门限值,它们的差别仅为0.03~0.08dB.
To solve the problem of lacking of a theoretical analysis of TDMP algorithm of LDPC codes,the Gaussian Approximation(GA)of TDMP algorithm was proposed.Based on BP algorithm and symmetry conditions,the convergent GA of TDMP algorithm could be obtained.When using GA to analyze the decoding convergence of TDMP algorithm,the theoretical basis for proving the superiority of TDMP algorithm could be provided.GAs of BP algorithm and TDMP algorithm were simulated based on the Wimax standard respectively.Simulation results show that the decoding convergence speed of TDMP algorithm is faster and its number of iterations is fewer compared with BP algorithm under the same condition. Meanwhile,the thresholds of GA and Density Evolution(DE)of TDMP algorithm were presented respectively.The gap of thresholds between GA and DE was 0.03~0.08 dB.
To solve the problem of lacking of a theoretical analysis of TDMP algorithm of LDPC codes,the Gaussian Approximation(GA)of TDMP algorithm was proposed.Based on BP algorithm and symmetry conditions,the convergent GA of TDMP algorithm could be obtained.When using GA to analyze the decoding convergence of TDMP algorithm,the theoretical basis for proving the superiority of TDMP algorithm could be provided.GAs of BP algorithm and TDMP algorithm were simulated based on the Wimax standard respectively.Simulation results show that the decoding convergence speed of TDMP algorithm is faster and its number of iterations is fewer compared with BP algorithm under the same condition. Meanwhile,the thresholds of GA and Density Evolution(DE)of TDMP algorithm were presented respectively.The gap of thresholds between GA and DE was 0.03~0.08 dB.
引文
[1]GALLAGER R.Low-density parity-check codes[J].IRE Transactions on Information Theory,1962,8(1):21-28.
[2]王秀敏,洪芳菲,单良,等.LDPC/Turbo双模译码器技术发展与前景综述[J].中国计量学院学报,2016,27(1):63-67.WANG X M,HONG F F,SHAN L,et al.The advance overview on LDCP/Turbo dual-mode decoders[J].Journal of China University of Metrology,2016,27(1):63-67.
[3]MACKAY D J C,NEAL R M.Near Shannon limit performance of low density parity check codes[J].Electric Lett,1996,32:1645-1646.
[4]MACKAY D J C.Good error-correcting codes based on very sparse matrices[J].IEEE Trans on Information Theory,1999,45(2):399-431.
[5]RICHARDSON T J,URBANKE R L.The capacity of low-density parity-check codes under message-passing decoding[J].IEEE Transaction on Information Theory,2001,47:599-618.
[6]肖娟,王琳,邓礼钊.不规则LDPC码的密度进化方法及其门限值确定[J].电子与信息学报,2005,27(4):617-620.XIAO J,WANG L,DENG L Z.Density evolution method and threshold decision for irregular LDPC codes[J].Journal of Electronics and Information Technology,2005,27(4):617-620.
[7]袁东风,张海刚.LDPC码理论与研究[M].北京:人民邮电出版社,2008:122-123.
[8]CHUNG S Y,RICHARDSON T J,URBANKE R L.Analysis of sum-product decoding of low-density parity-check codes using agaussian approximation[J].IEEE Transaction on Information Theory,2001,47:657-670.
[9]HOCEVAR D E.A reduced complexity decoder architecture via layered decoding of LDPC codes[C]//IEEE Workshop on Signal Processing Systems.Austin:IEEE,2004:107-112.
[10]MANSOUR M M.A Turbo-decoding message-passing algorithm for sparse parity-check matrix codes[J].IEEE Transaction on Signal Processing,2006,54(11):4376-4392.
[11]SUN Y,CAVALLARO J R.A flexible LDPC/Turbo decoder architecture[J].Journal of Signal Processing Systems,2011,64(1):1-16.
[12]ZEINEDDINE H,MANSOUR M M.A reconfigurable TDMP decoder for raptor codes[J].Journal of Signal Processing Systems,2012,69(3):293-304.
[13]洪芳菲.基于DDE理论的LDPC双模译码器研究[D].杭州:中国计量大学,2016.HONG F F.The Research of dual-mode LDPC decoder based on DDE[D].Hangzhou:China Jiliang University,2016.
[2]王秀敏,洪芳菲,单良,等.LDPC/Turbo双模译码器技术发展与前景综述[J].中国计量学院学报,2016,27(1):63-67.WANG X M,HONG F F,SHAN L,et al.The advance overview on LDCP/Turbo dual-mode decoders[J].Journal of China University of Metrology,2016,27(1):63-67.
[3]MACKAY D J C,NEAL R M.Near Shannon limit performance of low density parity check codes[J].Electric Lett,1996,32:1645-1646.
[4]MACKAY D J C.Good error-correcting codes based on very sparse matrices[J].IEEE Trans on Information Theory,1999,45(2):399-431.
[5]RICHARDSON T J,URBANKE R L.The capacity of low-density parity-check codes under message-passing decoding[J].IEEE Transaction on Information Theory,2001,47:599-618.
[6]肖娟,王琳,邓礼钊.不规则LDPC码的密度进化方法及其门限值确定[J].电子与信息学报,2005,27(4):617-620.XIAO J,WANG L,DENG L Z.Density evolution method and threshold decision for irregular LDPC codes[J].Journal of Electronics and Information Technology,2005,27(4):617-620.
[7]袁东风,张海刚.LDPC码理论与研究[M].北京:人民邮电出版社,2008:122-123.
[8]CHUNG S Y,RICHARDSON T J,URBANKE R L.Analysis of sum-product decoding of low-density parity-check codes using agaussian approximation[J].IEEE Transaction on Information Theory,2001,47:657-670.
[9]HOCEVAR D E.A reduced complexity decoder architecture via layered decoding of LDPC codes[C]//IEEE Workshop on Signal Processing Systems.Austin:IEEE,2004:107-112.
[10]MANSOUR M M.A Turbo-decoding message-passing algorithm for sparse parity-check matrix codes[J].IEEE Transaction on Signal Processing,2006,54(11):4376-4392.
[11]SUN Y,CAVALLARO J R.A flexible LDPC/Turbo decoder architecture[J].Journal of Signal Processing Systems,2011,64(1):1-16.
[12]ZEINEDDINE H,MANSOUR M M.A reconfigurable TDMP decoder for raptor codes[J].Journal of Signal Processing Systems,2012,69(3):293-304.
[13]洪芳菲.基于DDE理论的LDPC双模译码器研究[D].杭州:中国计量大学,2016.HONG F F.The Research of dual-mode LDPC decoder based on DDE[D].Hangzhou:China Jiliang University,2016.