Non-binary quasi-cyclic quantum LDPC codes

IEEE International Symposium on Information Theory - Proceedings

Volumn , Issue , 2011, Pages 653-657

  Kasai, Kenta ^a   Hagiwara, Manabu ^b   Imai, Hideki ^b,c   Sakaniwa, Kohichi ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

^c CHUO UNIVERSITY   (Japan)

Author keywords

belief propagation; CSS codes; Galois field; iterative decoding; LDPC code; non binary LDPC codes; quantum error correcting codes

Indexed keywords

BELIEF PROPAGATION; CSS CODES; GALOIS FIELDS; LDPC CODES; NON-BINARY LDPC CODES; QUANTUM ERROR CORRECTING CODES;

CODING ERRORS; ERROR CORRECTION; ITERATIVE DECODING; QUANTUM COMPUTERS; QUANTUM THEORY;

CODES (SYMBOLS);

EID: 80054822666     PISSN: 21578104     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2011.6034212     Document Type: Conference Paper

References (15)

1. R. G. Gallager, Low Density Parity Check Codes. in Research Monograph series, MIT Press, Cambridge, 1963.
2. T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes", IEEE Trans. Inf. Theory, vol. 47, pp. 619-637, Feb. 2001.
3. M. Davey and D. MacKay, "Low-density parity check codes over GF (q)", IEEE Commun. Lett., vol. 2, no. 6, pp. 165-167, Jun. 1998.
4. A. R. Calderbank and P. W. Shor, "Good quantum error-correcting codes exist", Phys. Rev. A, vol. 54, no. 2, pp. 1098-1105, Aug. 1996.
5. A. M. Steane, "Error correcting codes in quantum theory", Phys. Rev. Lett., vol. 77, no. 5, pp. 793-797, Jul. 1996.
6. D. Gottesman, "Class of quantum error-correcting codes saturating the quantum Hamming bound", Phys. Rev. A, vol. 54, no. 3, pp. 1862-1868, Sep. 1996.
7. M. S. Postol, "A proposed quantum low density parity check code", 2001. [Online]. Available: http://arxiv.org/abs/quant-ph/0108131v1
8. D. MacKay, G. Mitchison, and P. McFadden, "Sparse-graph codes for quantum error correction", IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2315-2330, Oct. 2004.
9. D. J. C. MacKay, A. Shokrollahi, O. Stegle, and G. Mitchison, "More sparse-graph codes for quantum error-correction", Jun. 2007, preprint available from http://www.inference.phy.cam.ac.uk/mackay/QECC.html.
10. D. Poulin, J.-P. Tillich, and H. Ollivier, "Quantum serial turbo codes", IEEE Trans. Inf. Theory, vol. 55, no. 6, pp. 2776-2798, Jun. 2009.
11. M. Hagiwara and H. Imai, "Quantum quasi-cyclic LDPC codes", in Proc. 2007 IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2007, pp. 806-810.
12. -, "Quantum quasi-cyclic LDPC codes", 2007. [Online]. Available: http://arxiv.org/abs/quant-ph/0701020
13. 1/2", in Proc. 2009 IEEE Int. Symp. Inf. Theory (ISIT), Jul. 2009, pp. 799-803.
14. c) - LDPC codes over GF (q) using their binary images", IEEE Trans. Commun., vol. 56, no. 10, pp. 1626-1635, Oct. 2008.
15. M. Davey and D. MacKay, "Low density parity check codes over GF (q)", in Information Theory Workshop, 1998, Jun. 1998, pp. 70-71.