基于平均概率和停止准则的多元LDPC码加权符号翻转译码算法

doi:10.11959/j.issn.1000-436x.2016029

通信学报 ›› 2016, Vol. 37 ›› Issue (2): 44-53.doi: 10.11959/j.issn.1000-436x.2016029

基于平均概率和停止准则的多元LDPC码加权符号翻转译码算法

郭锐¹,刘春于¹,王美洁¹,潘鹏¹,包建荣^1,²,郭春生¹

¹ 杭州电子科技大学通信工程学院，浙江杭州 310018
² 东南大学移动通信国家重点实验室，江苏南京 210096

出版日期:2016-02-26 发布日期:2016-02-26
基金资助:
浙江省自然科学基金资助项目;浙江省重点科技创新团队基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;浙江省公益性技术应用研究计划基金资助项目;东南大学移动通信国家重点实验室开放研究基金资助项目

Weighted symbol-flipping decoding for non-binary LDPC codes based on average probability and stopping criterion

Rui GUO¹,Chun-yu LIU¹,Mei-jie WANG¹,Peng PAN¹,Jian-rong BAO^1,²,Chun-sheng GUO¹

¹ Communication Engineering Institute, Hangzhou Dianzi University, Hangzhou 310018, China
² National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096,China

Online:2016-02-26 Published:2016-02-26
Supported by:
Zhejiang Provincial Natural Science Foundation of China;Zhejiang Province Science and Technology Innovation Program Foundation;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;Zhejiang Province Public Welfare Technology Application Research Project Foundation;Foundation of State Key Laboratory of Mobile Communications. Southeast University

摘要/Abstract

摘要：

为了提高多元低密度奇偶校验(LDPC, low density parity-check)码符号翻转译码算法的性能并降低译码的复杂度，提出了基于平均概率和停止准则的多元 LDPC 码加权符号翻转译码(APSCWSF, average probability and stopping criterion weighted symbol flipping)算法。该算法将校验节点邻接符号节点的平均概率信息作为权重，使翻转函数更加有效，提高符号的翻转效率，进而改善译码性能。并且通过设置迭代停止准则进一步加快算法的收敛速度。仿真结果显示，在加性高斯白噪声信道下，误符号率为10^-5;时，相比WSF 算法、NSCWSF 算法(Osc=10)和NSCWSF算法(Osc=6)，APSCWSF算法(Osc=10)分别获得约0.68dB、0.83dB和0.96dB的增益。同时，APSCWSF算法(Osc=6)的平均迭代次数也分别降低78.60% ～79.32%、74.89% ～ 75.95% 和 67.20% ～70.80%。

关键词: 多元低密度奇偶校验码, 加权符号翻转译码, 平均概率, 停止准则, 翻转函数

Abstract:

In order to improve the decoding performance and reduce the decoding complexity of weighted symbols flipping decoding algorithm for nonbinary low density parity-check(LDPC)code, a weighted symbols flipping decoding for nonbinary LDPC codes based on average probability and stopping criterion was proposed. The algorithm puts the average probability of all the information nodes adjacent to the check node as weights to make the flipping-function more effectively and improve the efficiency of the flipping-symbols, and then improves the decoding performance. At the same time, the algorithm adds a stopping criterion controlling decoding iterations to further improve the decoding speed. Simulation results show that compared to WSF algorithm, NSCWSF algorithm(Osc=10)and NSCWSF algorithm(Osc=6), the new algorithm proposed(O =10)is gotten about 0.68dB, 0.83dBand 0.96dBgain at the symbol error rate of 10^-5in thesc presence of additive white Gaussian noise(AWGN), meanwhile, the average number of decoding iterations is also reduced by 78.60%～79.32%, 74.89%～75.95% and 67.2%～70.8%, respectively.

Key words: non-binary low density parity-check codes, weighted symbols flipping decoding, average probability, stopping criterion, flipping-function

郭锐,刘春于,王美洁,潘鹏,包建荣,郭春生. 基于平均概率和停止准则的多元LDPC码加权符号翻转译码算法[J]. 通信学报, 2016, 37(2): 44-53.

Rui GUO,Chun-yu LIU,Mei-jie WANG,Peng PAN,Jian-rong BAO,Chun-sheng GUO. Weighted symbol-flipping decoding for non-binary LDPC codes based on average probability and stopping criterion[J]. Journal on Communications, 2016, 37(2): 44-53.

图/表 16

表1

5种不同译码算法实数运算的复杂度"

译码算法	加法运算次数	乘法运算次数
WSF	A₁[(q?1)d_cd_v+N?1+q?2+blbb]	0
NSCWSF	A₂[(q?1)d_cd_v+N?1+q?2+blbb+2lw]	0
MV-SF	$A_{3} [2 ((d_{c} - 1) M + L) + 2 d_{c} M L + N q + M \sum_{i = d - h}^{d_{c}} i]$	2(d_cM+h)
APWSF	A₄[(q?1)d_c d_v+N?1+q?2+blbb]	0
APSCWSF	A₅[(q?1)d_cd_v+N?1+q?2+blbb+2lw]	0

表1

图1

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

表2

SER=10-5时，相比已有的算法，本文提出的新算法获得的增益统计"

译码算法		码A			码B			码C
译码算法	$\frac{E_{b}}{N_{0}} / dB$		增益/dB	$\frac{E_{b}}{N_{0}} / dB$		增益/dB	$\frac{E_{b}}{N_{0}} / dB$		增益/dB
APWSF	3.52		—	1.70		—	5.25		—
APSCWSF(O =10)sc	3.70		0.18	1.87		0.17	5.28		0.03
APSCWSF(Osc=6)	3.78		0.26	1.96		0.26	5.23		0.07
WSF	4.42		0.90	2.55		0.85	5.70		0.45
NSCWSF(O =10)sc	4.45		0.93	2.70		1.00	5.72		0.47
NSCWSF(O =6)sc	4.53		1.01	2.83		1.13	5.78		0.53

表2

表3

FER=10-3时，相比已有的算法，本文提出的新算法获得的增益统计"

译码算法		码D			码E
译码算法	$\frac{E_{b}}{N_{0}} / dB$		增益/dB	$\frac{E_{b}}{N_{0}} / dB$		增益/dB
APWSF	3.75		—	3.50		—
APSCWSF(Osc=3)	3.80		0.05	3.63		0.13
MV-SF( =2)L	4.75		1.00	4.55		1.05
MV-SF( =6)L	4.70		0.95	4.50		1.00
WSF	4.50		0.75	4.20		0.70
NSCWSF(O =3)sc	4.63		0.83	4.30		0.80

表3

表4

码A在2dB和3dB时，APSCWSF算法(Osc=6,Osc=10)和其他算法的迭代次数比较"

译码算法		$\frac{E_{b}}{N_{0}} = 2dB$			$\frac{E_{b}}{N_{0}} = 3dB$
译码算法	平均迭代次数	相对降低次数	下降比例/%	平均迭代次数	相对降低次数	下降比例/%
APSCWSF(Osc=6)	16.52	—	—	4.41	—	—
APSCWSF(O =10)sc	16.86	0.34	2.02	4.94	0.53	10.72
APWSF	17.35	0.83	4.78	5.22	0.81	15.51
NSCWSF(O =6)sc	50.33	33.81	67.20	15.11	10.70	70.80
NSCWSF(O =10)sc	65.78	49.26	74.89	18.34	13.93	75.95
WSF	77.18	60.66	78.60	21.33	16.92	79.32

表4

表5

码A在2dB和3dB时，各种译码算法所需的译码复杂度"

译码算法	$\frac{E_{b}}{N_{0}} = 2dB$			$\frac{E_{b}}{N_{0}} = 3dB$
译码算法	加法运算的平均总次数	下降比例/%	加法运算的平均总次数		下降比例/%
APSCWSF(Osc=6)	37 253	—	9 945		—
APSCWSF(O =10)sc	38 019	2.01	11 140		10.73
APWSF	38 777	3.93	11 667		14.76
NSCWSF(O =6)sc	113 495	67.17	34 073		70.81
NSCWSF(O =10)sc	148 334	74.69	41 357		75.95
WSF	159 087	76.58	47 673		79.14

表5

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基于平均概率和停止准则的多元LDPC码加权符号翻转译码算法

Weighted symbol-flipping decoding for non-binary LDPC codes based on average probability and stopping criterion

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