Spatially coupled LDPC codes based on multi-weight circulant matrix decomposition

Hongmei KANG; Ming JIANG; Qiang WANG

doi:10.16511/j.cnki.qhdxxb.2025.27.042

PDF(3915 KB)

Journal of Tsinghua University(Science and Technology) ›› 2025, Vol. 65 ›› Issue (11) : 2024-2031. DOI: 10.16511/j.cnki.qhdxxb.2025.27.042

Frontiers in New-Quality Communication Technology

Spatially coupled LDPC codes based on multi-weight circulant matrix decomposition

Author information +

History +

Abstract

Objective: Spatially coupled low-density parity-check (SC-LDPC) codes have attracted considerable interest in recent years owing to their exceptional decoding performance, low latency, and unique coupling structure, which notably enables error correction capabilities. These codes leverage the threshold saturation effect, allowing their performance to approach the Shannon limit closely. Their capability to deliver high reliability with reduced decoding complexity positions them as a promising choice for next-generation communication systems, including 6G networks and satellite communications. This paper introduces a novel construction method for SC-LDPC codes, referred to as SC multi-weight circulant quasi-cyclic LDPC (SC-MQC-LDPC) codes, based on multi-weight circulant matrix decomposition. These codes are designed to be compatible with a wide range of code lengths and code rates, offering increased flexibility and applicability in diverse scenarios. Methods: The construction process begins with the design of MQC-LDPC codes, where a lifting value matrix is determined using a simplified error minimization progressive edge growth algorithm; this algorithm is specifically tailored to optimize the structural properties and decoding performance of the codes. By accounting for the presence of short cycles and the extrinsic message degree of check nodes, the algorithm effectively mitigates the error floor, thereby enhancing the overall reliability and efficiency of the MQC-LDPC codes. These base codes are then extended using a split-replication process to construct SC-MQC-LDPC codes. This extension preserves the beneficial characteristics of the original MQC-LDPC codes while introducing spatial coupling, which further improves error-correction capabilities and supports a broad range of communication requirements. The paper also introduces a recursive encoding method for SC-MQC-LDPC codes, which offers low implementation complexity and reduced latency, increasing its suitability for practical deployment. Additionally, an improved sliding window decoding algorithm is introduced to further optimize the decoding process. This low-complexity algorithm enhances decoding efficiency by balancing memory usage and computational requirements. With a modest increase in memory overhead, the algorithm successfully mitigates error propagation and improves overall decoding performance, ensuring robust data transmission even under challenging conditions, such as low signal-to-noise ratios. Results: The performance of the proposed SC-MQC-LDPC codes is rigorously evaluated through comprehensive simulations. The experimental results show the following: 1) The proposed SC-MQC-LDPC codes, designed for compatibility with various code lengths and rates, achieve a performance gain of over 0.50 dB compared with SC-5G-LDPC codes at a bit error rate of 10^-6, when used in combination with the modified sliding window decoding (SWD) algorithm. Furthermore, under identical code length and rate conditions, they demonstrate clear performance advantages over the newly extended 5G-NR LDPC codes, particularly in the low E_b/N₀ region. Additionally, the modified SWD algorithm significantly improves decoding performance across all tested SC-MQC-LDPC code variants compared to the conventional SWD algorithm, with the improvements becoming more pronounced as the code length increases. 2) In terms of computational complexity, SC-MQC-LDPC codes decoded with the modified SWD algorithm achieve substantial reductions of approximately 1/5 and 1/3 compared with SC-5G-LDPC and 5G new radio LDPC codes, respectively. At E_b/N₀=6.0 dB, the decoding complexity of the modified algorithm is nearly half that of the traditional SWD algorithm, highlighting its advantage for low-complexity, high-efficiency decoding. Conclusions: Overall, the SC-MQC-LDPC codes proposed in this study mark a remarkable advancement in error-correction coding, effectively addressing the growing demand for high reliability, low latency, and computational efficiency. These characteristics make them highly suitable for modern communication environments that demand adaptable, efficient, and robust performance in dynamic and challenging scenarios.

Key words

spatially-coupled low-density parity-check codes / multi-weight circulant matrix / rate compatibility / sliding window decoding

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

Hongmei KANG , Ming JIANG , Qiang WANG. Spatially coupled LDPC codes based on multi-weight circulant matrix decomposition[J]. Journal of Tsinghua University(Science and Technology). 2025, 65(11): 2024-2031 https://doi.org/10.16511/j.cnki.qhdxxb.2025.27.042

References

List( Publishing order | Descend order by publishing year | Descend order by cited within ) Chart analysis

1	3GPP. Multiplexing and channel coding (Release 17): ETSI TS 38.212 V 17.4.0 [S]. France: ETSI, 2023. Cited in this article [1]

2	COSTELLO D J , DOLECEK L , FUJA T E , et al. Spatially coupled sparse codes on graphs: theory and practice[J]. IEEE Communications Magazine, 2014, 52 (7): 168- 176. https://doi.org/10.1109/MCOM.2014.6852099 Cited in this article [1]

3	XU Y , JIANG M , ZHU M Y , et al. Reduced-complexity decoding of 3D product codes for satellite communications[J]. Space: Science & Technology, 2024, 4, 0096. Cited in this article [1]

4	LI J, LIN S, ABDEL-GHAFFAR K, et al. Globally coupled LDPC codes [C]// Proceedings of the 2016 Information Theory and Applications Workshop. La Jolla, USA: IEEE, 2016: 1-10. Cited in this article [1]

5	RAM E , CASSUTO Y . Spatially coupled LDPC codes with sub-block locality[J]. IEEE Transactions on Information Theory, 2021, 67 (5): 2739- 2757. https://doi.org/10.1109/TIT.2021.3059751 Cited in this article [1]

6	KUDEKAR S , RICHARDSON T J , URBANKE R L . Threshold saturation via spatial coupling: why convolutional LDPC ensembles perform so well over the BEC[J]. IEEE Transactions on Information Theory, 2011, 57 (2): 803- 834. https://doi.org/10.1109/TIT.2010.2095072 Cited in this article [1]

7	PUSANE A E , SMARANDACHE R , VONTOBEL P O , et al. Deriving good LDPC convolutional codes from LDPC block codes[J]. IEEE Transactions on Information Theory, 2011, 57 (2): 835- 857. https://doi.org/10.1109/TIT.2010.2095211 Cited in this article [3]

8	石双颖. 空间耦合LDPC码研究与设计[D]. 南京: 南京信息工程大学, 2023. SHI S Y. Research and design of spatially coupled LDPC codes [D]. Nanjing: Nanjing University of Information Science and Technology, 2023. (in Chinese) Cited in this article [3]

9	SCHLÜTER M, HASSAN N U, FETTWEIS G P. On the construction of protograph based SC-LDPC codes for windowed decoding [C]// Proceedings of the 2018 IEEE Wireless Communications and Networking Conference. Barcelona, Spain: IEEE, 2018: 1-6. Cited in this article [1]

10	ZHU M Y , JIANG M , ZHAO C M . On the global and local decoding of q -Ary SC-LDPC codes with moderate coupling length[J]. IEEE Communications Letters, 2021, 25 (9): 2815- 2819. https://doi.org/10.1109/LCOMM.2021.3096273 Cited in this article [2]

11	BATTAGLIONI M , CHIARALUCE F , BALDI M , et al. Optimizing quasi-cyclic spatially coupled LDPC codes by eliminating harmful objects[J]. EURASIP Journal on Wireless Communications and Networking, 2023, 2023 (1): 67. https://doi.org/10.1186/s13638-023-02273-0 Cited in this article [1]

12	LIU K K , EL-KHAMY M , LEE J . Finite-length algebraic spatially-coupled quasi-cyclic LDPC codes[J]. IEEE Journal on Selected Areas in Communications, 2016, 34 (2): 329- 344. https://doi.org/10.1109/JSAC.2015.2504273 Cited in this article [2]

13	LIU Y , HE J L , WANG B , et al. Design of two-dimensional spatially coupled LDPC codes for combating burst erasures[J]. High Technology Letters, 2023, 29 (3): 288- 294. Cited in this article [1]

14	SHI X Y , HAN T Z , TIAN H , et al. Design of raptor-like rate compatible SC-LDPC codes[J]. ZTE Communications, 2022, 20 (S1): 16- 21. Cited in this article [3]

15	吴小宁. 原型图低密度奇偶校验码编译码方法研究[D]. 南京: 东南大学, 2019. WU X N. Research on encoding and decoding methods of protograph-based LDPC codes [D]. Nanjing: Southeast University, 2019. (in Chinese) Cited in this article [2]

16	HU X Y , ELEFTHERIOU E , ARNOLD D M . Regular and irregular progressive edge-growth tanner graphs[J]. IEEE Transactions on Information Theory, 2005, 51 (1): 386- 398. https://doi.org/10.1109/TIT.2004.839541

17	SHARON E , LITSYN S . Constructing LDPC codes by error minimization progressive edge growth[J]. IEEE Transactions on Communications, 2008, 56 (3): 359- 368. https://doi.org/10.1109/TCOMM.2008.050658 Cited in this article [2]

18	IYENGAR A R , PAPALEO M , SIEGEL P H , et al. Windowed decoding of protograph-based LDPC convolutional codes over erasure channels[J]. IEEE Transactions on Information Theory, 2012, 58 (4): 2303- 2320. https://doi.org/10.1109/TIT.2011.2177439 Cited in this article [1]

19	LIAN Q F , CHEN Q W , ZHOU L , et al. Adaptive decoding algorithm with variable sliding window for double SC-LDPC coding system[J]. IEEE Communications Letters, 2023, 27 (2): 404- 408. https://doi.org/10.1109/LCOMM.2022.3222560 Cited in this article [1]

20	ALI I , KIM J H , KIM S H , et al. Improving windowed decoding of SC LDPC codes by effective decoding termination, message reuse, and amplification[J]. IEEE Access, 2018, 6, 9336- 9346. https://doi.org/10.1109/ACCESS.2017.2771375 Cited in this article [2]

21	Consultative Committee for Space Data Systems. Low density parity check codes for use in near-earth and deep space applications [S/OL]. (2007-09) [2024-10]. https://public.ccsds.org/Pubs/131x1o2e2s.pdf. Cited in this article [1]