中国物理B ›› 2009, Vol. 18 ›› Issue (10): 4154-4160.doi: 10.1088/1674-1056/18/10/014

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Quantum quasi-cyclic low-density parity-check error-correcting codes

李渊1, 曾贵华1, Moon Ho Lee2   

  1. (1)Institute of Information & Communication, Department of Information & Communication Engineering, Chonbuk National University, Chonju 561-756, Korea; (2)Laboratory of Coding and Communication Security, Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai 200240, China
  • 收稿日期:2007-09-03 修回日期:2008-10-14 出版日期:2009-10-20 发布日期:2009-10-20
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Grant Nos 60773085 and 60801051), and the NSFC-KOSEF International Collaborative Research Funds (Grant Nos 60811140346 and F01-2008-000-10021-0).

Quantum quasi-cyclic low-density parity-check error-correcting codes

Li Yuan(李渊)a)†, Zeng Gui-Hua(曾贵华)a), and Moon Ho Leeb)   

  1. a Laboratory of Coding and Communication Security, Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai 200240, China; b Institute of Information & Communication, Department of Information & Communication Engineering, Chonbuk National University, Chonju 561-756, Korea
  • Received:2007-09-03 Revised:2008-10-14 Online:2009-10-20 Published:2009-10-20
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Grant Nos 60773085 and 60801051), and the NSFC-KOSEF International Collaborative Research Funds (Grant Nos 60811140346 and F01-2008-000-10021-0).

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摘要：

Due to the fault of the author(s) of the article entitled “Quantum quasi-cyclic low-density parity-check error-correcting codes”, published in Chinese Physics B, 2009, Vol. 18, Issue 10, pp 4154--4160, has been found to partly copy from the article arXiv:quant-ph/0701020v2 on the arXiv preprint. So the above article in Chinese Physics B has been withdrawn from the publication.  [2 February 2010]

In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasi-cyclic (QC) low-density parity-check (LDPC) codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.

Abstract:

In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasi-cyclic (QC) low-density parity-check (LDPC) codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.

Key words: quantum LDPC code, quasi-cyclic, circulant permutation matrix, CSS code

中图分类号:  (Telecommunications: signal transmission and processing; communication satellites)

  • 84.40.Ua
03.67.Pp (Quantum error correction and other methods for protection against decoherence)