空间耦合量子LDPC码的双窗口滑动译码

doi:10.19665/j.issn1001-2400.20230301

西安电子科技大学学报 ›› 2024, Vol. 51 ›› Issue (1): 11-20.doi: 10.19665/j.issn1001-2400.20230301

空间耦合量子LDPC码的双窗口滑动译码

王云江¹^,²(), 朱高辉¹(), 杨宇霆¹(), 马钟³(), 魏璐³()

1.西安电子科技大学通信工程学院,陕西西安 710071
2.西安电子科技大学广州研究院,广东广州 510555
3.西安微电子技术研究所,陕西西安 710065

收稿日期:2022-09-19 出版日期:2024-01-20 发布日期:2023-08-31
通讯作者: 马钟(1984—),男,高级工程师,E-mail:mazhong@mail.com
作者简介:王云江(1980—),男,副教授,E-mail:yunjiangw@xidian.edu.cn；
朱高辉(1998—),男,西安电子科技大学硕士研究生,E-mail:ghzhu_1@stu.xidian.edu.cn；
杨宇霆(1997—),男,西安电子科技大学硕士研究生,E-mail:20011210442@stu.xidian.edu.cn；
魏璐(1990—),女,工程师,E-mail:13991210602@163.com；
石莎(1980—),女,副教授,E-mail:sshi@xidian.edu.cn
基金资助:
国家自然科学基金(61771377);陕西省重点研发计划项目(2023-YBGY-206);陕西省重点研发计划项目(2020ZDLGY08-06);广东省自然科学基金(2023A1515010671)

Double windows sliding decoding of spatially-coupled quantum LDPC codes

WANG Yunjiang¹^,²(), ZHU Gaohui¹(), YANG Yuting¹(), MA Zhong³(), WEI Lu³()

1. School of Telecommunications Engineering,Xidian University,Xi’an 710071,China
2. Guangzhou Institute of Technology,Xidian University,Guangzhou 510555,China
3. Xi’an Microelectronics Technology Institute,Xi’an 710065,China

Received:2022-09-19 Online:2024-01-20 Published:2023-08-31

摘要/Abstract

摘要：

量子纠错码是应对量子计算过程中不可避免的噪声干扰的关键途径。和其经典情形一样,空间耦合量子LDPC码理论上也可在纠错性能和译码时延间取得良好的均衡。考虑到目前采用常规置信传播算法(BPA)的空间耦合量子LDPC(SC-QLDPC)码在译码过程中仍存在复杂度高和译码时延长的问题,受经典滑窗译码算法的启发,并结合和利用SC-QLDPC码所对应的两个奇偶校验矩阵在主对角线和副对角线上具有非零对角带的结构特点,提出了针对量子SC-QLDPC码的滑窗译码算法(称为量子双窗口滑动译码算法)。在该策略中,通过窗口在两个经典校验矩阵主副对角线上的同时滑动,保证了相应量子比特部分译码所需的相位与比特翻转错误图样信息的提取,从而使其在译码性能和时延之间取得良好均衡。对所提量子双窗口滑动译码算法进行仿真验证,结果表明其不仅能提供灵活的低时延译码输出,并且当窗口扩大时,其译码性能逼近标准的量子置信传播算法,显著提升了SC-QLDPC码的应用范围。

关键词: LDPC码, 空间耦合, 量子码, 双窗口滑动, BP译码

Abstract:

Quantum error-correcting codes are the key way to address the issue caused by the inevitable noise along with the quantum computing process.Spatially coupled quantum LDPC codes,as their classical counterparts,can achieve a good balance between the error-correcting capacity and the decoding delay in principle.By considering the problems of high complexity and long decoding delay caused by the standard belief propagation algorithm(BPA) for decoding the spatially coupled quantum LDPC codes(SC-QLDPCs),a quantum version of the sliding decoding scheme,named the double window sliding decoding algorithm is proposed in this paper.The proposed algorithm is inspired by the idea of classical sliding window decoding strategies and by exploiting the non-zero diagonal bands on the principal and sub-diagonals structure of the corresponding two parity-check matrices(PCMs) of the concerned SC-QLDPC.The phase and bit flipping error syndromes of the received codeword are obtained by sliding the two windows along the principal and sub-diagonals of the two classical PCMs simultaneously,which enables a good trade-off between complexity and decoding delay to be obtained by using the proposed strategy,with numerical results given to verify the performance of the proposed double window sliding decoding scheme.Simulation results show that the proposed algorithm can not only offer a low latency decoding output but also provide a decoding performance approaching that of the standard BPA when enlarging the window size,thus improving the application scenarios of the SC-QLDPC significantly.

Key words: LDPC codes, spatially-coupled, quantum codes, double windows sliding, BP decoding

中图分类号:

TN911.22

王云江, 朱高辉, 杨宇霆, 马钟, 魏璐. 空间耦合量子LDPC码的双窗口滑动译码[J]. 西安电子科技大学学报, 2024, 51(1): 11-20.

WANG Yunjiang, ZHU Gaohui, YANG Yuting, MA Zhong, WEI Lu. Double windows sliding decoding of spatially-coupled quantum LDPC codes[J]. Journal of Xidian University, 2024, 51(1): 11-20.

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参考文献 19

[1]	ALEXEEV Y, BACON D, BROWN K R, et al. Quantum Computer Systems for Scientific Discovery[J]. PRX Quantum, 2021, 2(1):1-19.
[2]	HENSINGER W K. Quantum Computer Based on Shuttling Trapped Ions[J]. Nature, 2021, 592(7853):190-191. doi: 10.1038/d41586-021-00844-z
[3]	魏璐, 马钟, 刘倩玉. 量子计算模拟平台发展综述[J]. 微电子学与计算机, 2022, 39(11):1-10.
	WEI Lu, MA Zhong, LIU Qianyu. Overview of Quantum Computing Simulation Platforms[J]. Microelectronics & Computer, 2022, 39(11):1-10.
[4]	赵超, 牛伟纳, 杨俊闯. 基于量子计算的分类和聚类算法综述[J]. 微电子学与计算机, 2020, 37(8):1-5.
	ZHAO Chao, NIU Weina, YANG Junchuang. A Survey on Quantum Classification and Clustering Algorithms[J]. Microelectronics & Computer, 2020, 37(8):1-5.
[5]	GOTTESMAN D. Fault-Tolerant Quantum Computation with Constant Overhead[J]. Quantum Information & Computation, 2014, 14(15-16):1338-1372.
[6]	STEANE A M. Error Correcting Codes in Quantum Theory[J]. Physical Review Letters, 1996, 77(5):793-797. pmid: 10062908
[7]	CALDERBANK A R, SHOR P W. Good Quantum Error-Correcting Codes Exist[J]. Physical Review A, 1998, 54(2):1098-1105. doi: 10.1103/PhysRevA.54.1098
[8]	CAMARA T, OLLIVIER H, TILLICH J P. A Class of Quantum LDPC Codes:Construction and Performances under Iterative Decoding[C]//2007 IEEE International Symposium on Information Theory. Piscataway:IEEE, 2007:811-815.
[9]	NIKOLAS P B, JENS N E. Quantum Low-Density Parity-Check Codes[J]. PRX Quantum, 2021, 2(4):1-21.
[10]	张娅妹, 周林, 陈辰, 等. 瑞利衰落信道中SC-LDPC码滑窗译码算法[J]. 西安电子科技大学学报, 2020, 47(6):78-83.
	ZHANG Yamei, ZHOU Lin, CHEN Chen, et al. Sliding Window Decoding of the Spatially Coupled LDPC Code over Rayleigh Fading Channels[J]. Journal of Xidian University, 2020, 47(6):78-83.
[11]	张娅妹, 周林, 陈辰, 等. 窗口可变的空间耦合LDPC码滑窗译码算法[J]. 西安电子科技大学学报, 2020, 47(3):128-134.
	ZHANG Yamei, ZHOU Lin, CHEN Chen, et al. Sliding Window Decoding Algorithm for Spatially Coupled LDPC Codes with a Variable Window[J]. Journal of Xidian University, 2020, 47(3):128-134.
[12]	HAGIWARA M, KASAI K, IMAI H, et al. Spatially Coupled Quasi-Cyclic Quantum LDPC Codes[C]//2011 IEEE International Symposium on Information Theory Proceedings. Piscataway:IEEE, 2011:638-642.
[13]	WANG Y J, SANDERS B C, BAI B M, et al. Enhanced Feedback Iterative Decoding of Sparse Quantum Codes[J]. IEEE Transactions on Information Theory, 2012, 58(2):1231-1241. doi: 10.1109/TIT.2011.2169534
[14]	POULIN D, CHUNG Y. On the Iterative Decoding of Sparse Quantum Codes[J]. Quantum Information & Computation, 2008, 8(10):987-1000.
[15]	RIGBY A, OLIVIER J C, JARVIS P. Modified Belief Propagation Decoders for Quantum Low-Density Parity-Check Codes[J]. Physical Review A, 2019, 100(1):012330. doi: 10.1103/PhysRevA.100.012330
[16]	LIU Y H, POULIN D. Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes[J]. Physical Review Letters, 2019, 122(20):200501. doi: 10.1103/PhysRevLett.122.200501
[17]	ROFFE J, WHITE D R, BURTON S, et al. Decoding Across the Quantum Low-Density Parity-Check Code Landscape[J]. Physical Review Research, 2020, 2(4):043423. doi: 10.1103/PhysRevResearch.2.043423
[18]	IYENGAR A R, PAPALEO M, SIEGEL P H, et al. Windowed Decoding of Photograph-Based LDPC Convolutional Codes over Erasure Channels[J]. IEEE Transactions on Information Theory, 2011, 58(4):2303-2320. doi: 10.1109/TIT.2011.2177439
[19]	NIELSEN M A, CHUANG I L. Quantum Computation and Quantum Information[M]. 10th Anniversary Edition.Cambridge: Cambridge University Press, 2010:425-527.

参数	数值
耦合长度	6
耦合宽度	2
码长	1 116
校验矩阵行数	496
最小窗口	3
最大窗口	5
信道模型	退极化信道
最小退极化概率	0.010
最大退极化概率	0.018
最大迭代次数	50
行重	18
列重	3

空间耦合量子LDPC码的双窗口滑动译码

Double windows sliding decoding of spatially-coupled quantum LDPC codes

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