一种基于BIBD的量子LDPC码构造新方法

赵生妹; 朱修利; 肖宇

doi:10.3724/SP.J.1146.2009.01482

一种基于BIBD的量子LDPC码构造新方法

doi: 10.3724/SP.J.1146.2009.01482

赵生妹^{* 朱修利肖宇,},
朱修利,
肖宇

基金项目:

国家自然科学基金 (60672133)，江苏省青蓝工程(TJ207006)和教育部博士点专项科研基金(20060293003)资助课题

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出版历程
- 收稿日期: 2009-11-20
- 修回日期: 2010-09-28
- 刊出日期: 2011-01-19

A Novel Construction of Quantum LDPC Codes Based on Balanced Incomplete Block Designs

Zhao Sheng-Mei^{* 朱修利肖宇
,},
Zhu Xiu-Li,
Xiao Yu

摘要

摘要: 利用均衡不完全区组设计(Balance Imcomplete Block Designs，BIBD)的半结构化低密度奇偶校验(Low Density Parity Check，LDPC)码设计方法，该文提出了一种获得自对偶CSS(Calderbank-Shor-Steane)式的量子LDPC码的校验矩阵的新构造方法。由于构造出的量子码校验矩阵稀疏，有且仅有一个4环(girth 4)，在置信传播迭代译码算法下可获得良好的性能。数值计算结果表明，对于该构造方法得到的GF(6t+1)和GF(12t+1)量子LDPC码，比基于BIBD的其他构造方法所得到的量子码的码长更长、量子校验矩阵更加稀疏、性能也更加优越。
- 低密度奇偶校验码 /
- 量子低密度奇偶校验码 /
- 量子校验矩阵 /
- 均衡不完全区组设计
Abstract: Making use of the advantage of classical Low Density Parity Check (LDPC) codes based on Balance Incomplete Block Designs (BIBD), a novel construction of quantum LDPC codes is proposed in this paper. The constructed check matrix satisfies the requirement of self-dual quantum code with sparse 1 element and has only one 4 girth in every two rows. The simulation results show that the quantum LDPC codes constructed by this method, such as GF(6t+1), GF(12t+1) have longer code length, more sparse check matrix and good performance than that of other method based on BIBDs.
- Low Density Parity Check (LDPC) code /
- Quantum LDPC code /
- Quantum check matrix /
- Balanced Incomplete Block Design (BIBD)

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参考文献(1)

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