LDPC的分段多因子最小和译码算法

doi:10.12305/j.issn.1001-506X.2025.05.32

Abstract

Abstract:

In order to solve the issue of inaccurate check node updates and the resulting decoding performance limitations in the minimum sum (MS) decoding algorithm for low-density parity-check (LDPC) codes, a method is proposed to compensate for the verification node updates. This method incorporates segmented correction and linear minimum mean square error estimation parameters. The resulting algorithm is referred to as the linear minimum mean square error segmented multi-factor MS (LMMSE-SMFMS) decoding algorithm. Firstly, a comparative analysis is conducted to assess the performance of the MS decoding algorithm and the belief propagation (BP) decoding algorithm. Subsequently, a compensation method for check node updates is employed using three sets of correction factors based on linear minimum mean square error estimation. Finally, a layered scheduling approach is implemented to expedite the convergence speed during the information propagation process. Theoretical analysis and simulation results demonstrate that for quasi-cyclic-LDPC (QC-LDPC), under the conditions of utilizing linear minimum mean square error estimation and segmented correction factors, the proposed algorithm demonstrates technical gains compared to the MS algorithm in terms of bit error rate, information convergence speed, and other performance aspects.

Key words: low-density parity-check (LDPC), minimum sum (MS) decoding algorithm, segmented multi-factor (SMF), hierarchical scheduling

CLC Number:

TN911.22

Zhiguo SUN, Yike WANG, Xiaoyan NING. Segmented multi-factor minimum sum decoding algorithm for LDPC[J]. Systems Engineering and Electronics, 2025, 47(5): 1698-1705.

Figures/Tables 13

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References 30

1	GALLAGER R G . Low density parity check codes[J]. IRE Transactions on Information Theory, 1962, 8 (1): 21- 28. doi: 10.1109/TIT.1962.1057683
2	MACKAY D J C , NEAL R M . Near Shannon limit performance of low density parity check codes[J]. Electronics Letters, 1996, 33, 457- 458.
3	CHANVAT R, GARCIA-PENA A, PAONNI M. On efficient and low-complexity decoding of binary LDPC-coded CSK signals for GNSS links with increased data rates[C]//Proc. of the IEEE/ION Position, Location and Navigation Symposium, 2020: 1202-1213.
4	MAHDI A , KANISTRA N , PALIOURAS V . A multirate fully parallel LDPC encoder for the IEEE 802.11n/ac/ax QC-LDPC codes based on reduced complexity XOR trees[J]. IEEE Trans.on Very Large Scale Integration (VLSI) Systems, 2021, 29 (1): 51- 64. doi: 10.1109/TVLSI.2020.3034046
5	LEE S J , PARK S S , JANG B S , et al. Multi-mode QC-LDPC decoding architecture with novel memory access scheduling for 5G new-radio standard[J]. IEEE Trans.on Circuits and Systems Ⅰ: Regular Papers, 2022, 69 (5): 2035- 2048. doi: 10.1109/TCSI.2022.3150022
6	RICHARDSON T J , URBANKE R L . The capacity of low-density parity-check codes under message-passing decoding[J]. IEEE Trans.on Information Theory, 2002, 47 (2): 599- 618.
7	FOSSORIER M P C , MIHALIEVIC M , LMAI H , et al. Reduced complexity iterative decoding of low-density parity check codes based on belief propagation[J]. IEEE Trans.on Communications, 1999, 47 (5): 673- 680. doi: 10.1109/26.768759
8	LIU X C , ZHANG Y B , CUI R . Variable-node-based dynamic scheduling strategy for belief-propagation decoding of LDPC codes[J]. IEEE Communications Letters, 2015, 19 (2): 147- 150. doi: 10.1109/LCOMM.2014.2385096
9	CHEN J , FOSSORIER M P C . Near optimum universal belief propagation based decoding of low-density parity check codes[J]. IEEE Trans.on Communications, 2002, 50 (3): 406- 414. doi: 10.1109/26.990903
10	CHEN J , FOSSORIER M P C . Density evolution for two improved BP-based decoding algorithms of LDPC codes[J]. IEEE Communications Letters, 2002, 6 (5): 208- 210. doi: 10.1109/4234.1001666
11	范亚楠, 王丽冲, 姚秀娟, 等. 一种交叠的Shuffled-BP LDPC译码算法[J]. 电子与信息学报, 2016, 38 (11): 2908- 2915.
	FAN Y N , WANG L C , YAO X J , et al. An overlapped Shuffled-BP LDPC decoding algorithm[J]. Journal of Electronics & Information Technology, 2016, 38 (11): 2908- 2915.
12	YEDIDIA J S , WANG Y , DRAPER S C . Divide and concur and difference-map BP decoders for LDPC codes[J]. IEEE Trans.on Information Theory, 2011, 57 (2): 786- 802. doi: 10.1109/TIT.2010.2094815
13	DARABIHA A, CARUSON A C, KSCHISCHANG F R. A bit-serial approximate min-sum LDPC decoder and FPGA implementation[C]//Proc. of the IEEE International Symposium on Circuits & Systems, 2006: 4-7.
14	WU Z J , SU K X , GUO L T . A modified min sum decoding algorithm based on LMMSE for LDPC codes[J]. AEUE-International Journal of Electronics and Communications, 2014, 68 (10): 994- 999.
15	WANG X M , CAO W L , LI J , et al. Improved min-sum algorithm based on density evolution for low-density parity check codes[J]. IET Communications, 2017, 11 (10): 1582- 1586. doi: 10.1049/iet-com.2017.0014
16	陈发堂, 张友寿, 杜铮. 5G低密度奇偶校验码的低复杂度偏移最小和算法[J]. 计算机应用, 2020, 40 (7): 2028- 2032.
	CHEN F T , ZHANG Y S , DU Z . Low complexity offset min-sum algorithm for 5G low density parity check codes[J]. Journal of Computer Applications, 2020, 40 (7): 2028- 2032.
17	陈发堂, 李贺宾, 李平安. 基于偏移最小和的LDPC译码改进算法[J]. 系统工程与电子技术, 2022, 44 (7): 2350- 2356. doi: 10.12305/j.issn.1001-506X.2022.07.32
	CHEN F T , LI H B , LI P A . Improved algorithm based on offset min-sum decoding for LDPC codes[J]. Systems Engineering and Electronics, 2022, 44 (7): 2350- 2356. doi: 10.12305/j.issn.1001-506X.2022.07.32
18	CAI H H, YANG Y K, YI Q. A low complexity decoding algorithm design based on quasi-cyclic LDPC codes[C]//Proc. of the International Conference on Computing, Electronics & Communications Engineering, 2020: 45-50.
19	宁晓燕, 孙晶晶, 孙志国, 等. LDPC码的分层类拟合修正最小和译码算法[J]. 哈尔滨工业大学学报, 2022, 54 (11): 88- 94.
	NING X Y , SUN J J , SUN Z G , et al. Layered class fitting modified minimum sum decoding algorithm for LDPC codes[J]. Journal of Harbin Institute of Technology, 2022, 54 (11): 88- 94.
20	JIAO X P , MU J J , WEI H Y . Reduced complexity node-wise scheduling of ADMM decoding for LDPC codes[J]. IEEE Communications Letters, 2017, 21 (3): 472- 475. doi: 10.1109/LCOMM.2016.2643629
21	CUI H X , GHAFFARI F , LE K , et al. Design of high-performance and area-efficient decoder for 5G LDPC codes[J]. IEEE Trans.on Circuits and Systems Ⅰ: Regular Papers, 2021, 68 (2): 879- 891. doi: 10.1109/TCSI.2020.3038887
22	JIAO X P , MU J J , HE Y C , et al. Efficient ADMM decoding of LDPC codes using lookup tables[J]. IEEE Trans.on Communications, 2017, 65 (4): 1425- 1437. doi: 10.1109/TCOMM.2017.2659733
23	BAI J , CHI Y H , YUEN C . Efficient MP decoding via fast G-BADMM approach for binary LDPC codes[J]. IEEE Communications Letters, 2023, 27 (3): 782- 786. doi: 10.1109/LCOMM.2022.3232703
24	LIU H Y , HE P Q , JIANG Y , et al. A simple check polytope projection penalized algorithm for ADMM decoding of LDPC codes[J]. IEEE Access, 2023, 11, 2524- 2530. doi: 10.1109/ACCESS.2023.3234182
25	XIA Q Q , LIN Y , TANG S D , et al. A fast approximate check polytope projection algorithm for ADMM decoding of LDPC codes[J]. IEEE Communications Letters, 2019, 23 (9): 1520- 1523. doi: 10.1109/LCOMM.2019.2926085
26	胡东伟. 5G LDPC码译码器实现[J]. 电子与信息学报, 2021, 43 (4): 1112- 1119.
	HU D W . On the implementation of 5G LDPC decoder[J]. Journal of Electronics & Information Technology, 2021, 43 (4): 1112- 1119.
27	TIAN K D , WANG H . A novel base graph based static sche-duling scheme for layered decoding of 5G LDPC codes[J]. IEEE Communications Letters, 2022, 26 (7): 1450- 1453. doi: 10.1109/LCOMM.2022.3171658
28	LIANG Y H , LAM C T , NG B K. . A low complexity neural normalized min-sum LDPC decoding algorithm using tensor-train decomposition[J]. IEEE Communications Letters, 2022, 26 (12): 2914- 2918. doi: 10.1109/LCOMM.2022.3207506
29	CHEN J H , DHOLAKIA A , ELEFTHERIOU E , et al. Reduced-complexity decoding of LDPC codes[J]. IEEE Trans.on Communications, 2005, 53 (8): 1288- 1299. doi: 10.1109/TCOMM.2005.852852
30	LEI Y M , JIN Y , ZHANG J J . Check-node lazy scheduling approach for layered belief propagation decoding algorithm[J]. Electronics Letters, 2014, 50 (4): 278- 279. doi: 10.1049/el.2013.3199

算法	取幂	对数	乘法	除法	加法	比较	异或
BP	2ω	2ω	0	2ω	6ω－L	0	6ω－L
MS	0	0	0	0	0	2ω	2ω－L
NMS	0	0	ω	0	0	2ω	2ω－L
OMS	0	0	0	0	ω	3ω	2ω－L
OR-OMS	0	0	0	0	ω	3ω	2ω－L
LMMSE-MS	0	0	ω	0	ω	3ω	2ω－L
LMMSE-SMFMS	0	0	ω	0	ω	4ω	2ω－L

码长	信噪比/dB
码长	1.4	1.6	1.8	2.0
2016	0.003 9/0.006 8	0.000 7/0.001 4	9.6×10^-5/1.9×10^-4	3.9×10^-6/1.6×10^-5
768	0.012/0.014	0.005 1/0.006 5	0.002 2/0.002 9	6.0×10^-4/8.0×10^-4

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Segmented multi-factor minimum sum decoding algorithm for LDPC

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