多元量子LDPC码的构造与译码

doi:10.3969/j.issn.1001-2400.2010.06.005

J4 ›› 2010, Vol. 37 ›› Issue (6): 1005-1010.doi: 10.3969/j.issn.1001-2400.2010.06.005

多元量子LDPC码的构造与译码

邵军虎;白宝明;林伟;周林

(西安电子科技大学综合业务网理论及关键技术国家重点实验室，陕西西安 710071)

收稿日期:2009-11-10 出版日期:2010-12-20 发布日期:2011-01-22
通讯作者: 邵军虎
作者简介:邵军虎(1980-)，西安电子科技大学博士研究生，E-mail: jhshao@mail.xidian.edu.cn．
基金资助:
国家自然科学基金资助项目(60972046);国家部委预研基金资助项目

Construction and decoding of nonbinary quantum LDPC codes

SHAO Jun-hu;BAI Bao-ming;LIN Wei;ZHOU Lin

(State Key Lab. of Integrated Service Networks, Xidian Univ., Xi'an 710071， China)

Received:2009-11-10 Online:2010-12-20 Published:2011-01-22
Contact: SHAO Jun-hu

摘要/Abstract

摘要：

基于多元稳定子理论，提出一类有限域上多元量子LDPC码的构造方法，在退极化信道模型下对多元量子码的BP译码算法进行了描述．举例构造了一类CSS结构、码率为1/2和1/4的四元量子LDPC码，并对其纠错性能进行了Monte Carlo仿真．与现有同等参数的二元量子LDPC码相比，误帧率10-5时的信道转移概率阈值由0.016提高到0.025．

关键词: 量子信息, LDPC码, 量子LDPC码, BP算法

Abstract:

Nonbinary quantum codes are more suitable for error-correction in multi-level quantum systems. Based on stabilizer formalism over the finite field, a class of nonbinary quantum LDPC codes is presented in this paper. And the BP iterative decoding algorithm for these codes is described under the quantum depolarizing channel with the Monte Carlo simulation method. For example, a class of CSS structure 4-ary quantum LDPC codes is given with code rates 1/2 and 1/4. Compared with the present binary quantum LDPC codes of equivalent codelength, the channel threshold with 10-5FER is improved from 0.016 to 0.025.

Key words: quantum information, LDPC code, quantum LDPC code, BP algorithm

邵军虎周林白宝明林伟. 多元量子LDPC码的构造与译码[J]. J4, 2010, 37(6): 1005-1010.

SHAO Jun-hu;BAI Bao-ming;LIN Wei;ZHOU Lin. Construction and decoding of nonbinary quantum LDPC codes[J]. J4, 2010, 37(6): 1005-1010.

参考文献

[1] Shor P W. Scheme for Reducing Decoherence in Quantum Computer Memory[J]. Phys Rev A, 1995, 52(4): 2493-2496.
[2] 李卓,刑丽娟,王新梅. 量子常数循环码[J]. 西安电子科技大学学报,2009,36(1):48-51.
Li Zhuo,Xing Lijuan,Wang Xinmei. Quantum Constacyclic Codes[J]. Journal of Xidian University,2009,36(1):48-51.
[3] 李卓,刑丽娟,王新梅. 一类量子循环码的构造方法[J]. 西安电子科技大学学报,2007,34(2):187-189.
Li Zhuo,Xing Lijuan,Wang Xinmei. Encoding and Decoding of a Family of Quantum Stabilizer Codes[J]. Journal of Xidian University, 2007, 34(2): 187-189.
[4] Calderbank A R, Shor P W. Good Quantum Error-correcting Codes Exist[J]. Phys Rev A, 1996, 54(2): 1098-1105.
[5] MacKay D. Good Eoor-Correcting Codes Base on very Sparse Matrix[J]. IEEE Trans on Information Theory, 1999, 45(5): 399-431.
[6] MacKay D, Mitchison G, McFadden P. Sparse-graph Codes for Quantum Error Correction[J]. IEEE Trans on Information Theory, 2004, 50(10): 2315-2330.
[7] Aly S A. A Class of Quantum LDPC Codes Constructed From Finite Geometries[C]//IEEE Globecom. New Orleans: IEEE, 2008: 1097-2101.
[8] Tan Peiyu, Li Jing. New Classes of LDPC Stabilizer Codes Using Ideas from Matrix Scrambling[C]//IEEE International Conference on Communications. Beijing: IEEE, 2008: 1166-1170.
[9] Leifer M, Poulin D. Quantum Graphical Models and Belief Propagation[J]. Ann Phys, 2008, 323(8): 1899-1946.
[10] Poulin D, Chung Yeojin. On the Iterative Decoding of Sparse Quantum Codes[J]. International Journal of Quantum Information and computation, 2008, 8(10): 987-995.
[11] Ashikhmin A, Knill E. Nonbinary Quantum Stabilizer Codes[J]. IEEE Trans on Information Theory, 2001, 47(7): 3065-3072.
[12] Rains E M. Nonbinary Quantum Codes[J]. IEEE Trans on Information Theory, 1999, 45(6): 1827-1832.
[13] Ketkar A, Klappenecker A, Kumar S, et al. Nonbinary Stabilizer Codes over Finite Fields[J]. IEEE Trans on Information Theory, 2006, 52 (11): 4892-4914.
[14] Sundeep B, Thangaraj A. Self-orthogonality of q-ary Images of q^m Codes and Quantum code[J]. IEEE Trans on Information Theory, 2007, 53(7): 2480-2489.

[1]	刘景美;王延丽;梁斌;赵森林. 相关准循环码字集方法攻击McEliece密码体制[J]. J4, 2014, 41(2): 15-19+50.
[2]	王静怡;李颖;孙岳. 适用于网络LDPC码的速率兼容算法[J]. J4, 2013, 40(2): 13-17+47.
[3]	林伟;白宝明;王雪鹏. 多元LDPC码的动态扩展最小和译码算法[J]. J4, 2012, 39(2): 59-65.
[4]	肖鹤玲;蔡宁;王骁. 量子LDPC码在量子密钥分配中的应用[J]. J4, 2012, 39(2): 8-11+23.
[5]	何光华;白宝明;李博;林伟. 采用EMS算法的多元LDPC译码器的FPGA实现[J]. J4, 2011, 38(5): 27-33.
[6]	张国华；王新梅. 一类围长至少为6的QC-LDPC码的存在性[J]. J4, 2011, 38(3): 136-139+149.
[7]	胡树楷;王新梅. 一种简化的GF(q)-LDPC码译码算法[J]. J4, 2011, 38(2): 8-12+196.
[8]	周林;白宝明;邵军虎;林伟. 多元LDPC码的速率兼容技术研究[J]. J4, 2011, 38(1): 147-152.
[9]	杨洋;陈超;白宝明;王新梅. LDPC码串行译码策略的收敛速度分析[J]. J4, 2010, 37(5): 795-800.
[10]	慕建君;焦晓鹏;曹训志. 一类逼近容量LDPC纠删码的二部图构造算法[J]. J4, 2010, 37(4): 705-709.
[11]	崔俊云;白宝明;郭旭东. 一种改进的准循环LDPC码环消除算法[J]. J4, 2010, 37(4): 700-704.
[12]	寇小明;刘上乾;洪鸣;汪大宝. 一种自适应红外图像增强技术[J]. J4, 2009, 36(6): 1070-1074.
[13]	刘原华;王新梅;胡树楷;陈汝伟. 一种改进的卷积LDPC码置信传播译码算法[J]. J4, 2009, 36(3): 424-447.
[14]	李卓;邢莉娟;王新梅. 一类量子稳定子码的编译码方法 [J]. J4, 2008, 35(5): 834-837.
[15]	吴晓丽1;2;葛建华1;王勇1. OFDM系统的非二进制级联码性能分析 [J]. J4, 2008, 35(3): 459-463.

多元量子LDPC码的构造与译码

Construction and decoding of nonbinary quantum LDPC codes

PDF (PC)

赞

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10