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

Abstract

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

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.

Figures/Tables 16

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

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

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

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

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

References 18

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