Retracted: Quantum Quasi-Cyclic Low-Density Parity-Check Codes

  • Dazu Huang
  • Zhigang Chen
  • Xin Li
  • Ying Guo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5754)

Abstract

In this paper, how to construct quantum quasi-cyclic (QC) low-density parity-check (LDPC) codes is proposed. Using the proposed approach, some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graph are designed. In addition, the presented quantum codes can be efficiently constructed with large codeword length. Finally, we show the decoding of the proposed quantum QC LDPC.

Keywords

Quantum code Quasi-cyclic Low-density Parity-check Codes encoding and decoding CSS code 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, 2493 (1995)CrossRefGoogle Scholar
  2. 2.
    Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)CrossRefGoogle Scholar
  3. 3.
    Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793 (1996)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Gottesman, D.: Stabilizer codes and quantum error correction. PhD thesis, California Institute of Technology, Pasadena, CA (1997)Google Scholar
  5. 5.
    Gallager, R.G.: Low density parity check codes. IRE Trans. Inform.Theory IT-8, 21–28 (1962)Google Scholar
  6. 6.
    MacKay, D.J.C., Neal, R.M.: Near Shannon limit performance of low density parity check codes. Electron. Lett. 32, 1645–1646 (1996)CrossRefGoogle Scholar
  7. 7.
    Wiberg, N.: Codes and decoding on general graphs, Dissertation no. 440, Dept. Elect. Eng. Link?ping Univ., Link?ping, Sweden (1996)Google Scholar
  8. 8.
    MacKay, D.J.C., Mitchison, G., McFadden, P.L.: Sparse graph codes for quantum error-correction. IEEE Trans. Info. The Theory 50(10), 2315–2330 (2004)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Camara, J., Ollivier, H., Tillich, J.P.: (2), 0502086 (2005)Google Scholar
  10. 10.
    Li, Z.W., Chen, L., Lin, S., Fong, W., Yeh, P.S.: Efficientencoding of quasi-cyclic low-density parity-check codes. IEEE Trans. Commun. (2005)Google Scholar
  11. 11.
    Richardson, T.J., Shokrollahi, A., Urbanke, R.: Design of capacityapproaching low desnsity parity-check codes. IEEE Trans. Inform. Theory 47, 619–637 (2001)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Feng, K., Ma, Z.: A finite Gilbert-Varshamov bound for pure stabilizer quantum codes. IEEE Trans. Inf. Theory 50, 3323–3325 (2004)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Hamada, M.: Information Rates Achievable with Algebraic Codes on Quantum Discrete Memoryless Channels. IEEE Transactions on Information Theory 51(12), 4263–4277 (2005)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Dazu Huang
    • 1
    • 2
  • Zhigang Chen
    • 1
  • Xin Li
    • 1
    • 2
  • Ying Guo
    • 1
  1. 1.School of Information Science and EngineeringCentral South UniversityChangshaChina
  2. 2.Department of Information ManagementHunan College of Finance and EconomicsChangshaChina

Personalised recommendations