Quantum error correction beyond the bounded distance decoding limit

IEEE Transactions on Information Theory

Volumn 58, Issue 2, 2012, Pages 1223-1230

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

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Belief propagation; Calderbank; Galois field; Iterative decoding; Low density paritycheck (LDPC) code; Nonbinary LDPC codes; Quantum error correcting codes; Shor; Steane (CSS) codes

Indexed keywords

BELIEF PROPAGATION; CALDERBANK; GALOIS FIELDS; LOW-DENSITY PARITYCHECK (LDPC) CODE; NON-BINARY LDPC CODES; QUANTUM ERROR CORRECTING CODES; SHOR; STEANE (CSS) CODES;

ERROR CORRECTION; ITERATIVE DECODING; QUANTUM COMPUTERS;

CODES (SYMBOLS);

EID: 84856881299     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2167593     Document Type: Article

References (20)

1. K. Kasai, M. Hagiwara, H. Imai, and K. Sakaniwa, "Nonbinary quasicyclic quantum LDPC codes," in Proc. IEEE Int. Symp. Inf. Theory, Jul. 2011, pp. 558-562.
2. R. G. Gallager, Low Density Parity Check Codes, ser. ResearchMonograph. Cambridge, MA: MIT Press, 1963.
3. T. Richardson and R. Urbanke, "The capacity of low-density parity-check codes under message-passing decoding," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 599-618, Feb. 2001.
4. 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, no. 2, pp. 619-637, Feb. 2001.
5. M. Davey and D. MacKay, "Low-density parity check codes over GF ," IEEE Commun. Lett., vol. 2, no. 6, pp. 165-167, Jun. 1998.
6. 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.
7. A. M. Steane, "Error correcting codes in quantum theory," Phys. Rev. Lett., vol. 77, no. 5, pp. 793-797, Jul. 1996.
8. 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.
9. M. S. Postol, "A proposed quantum low density parity check code," 2001 [Online]. Available: http://arxiv.org/abs/quant-ph/0108131v1
10. 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.
11. D. J. C. MacKay, A. Shokrollahi, O. Stegle, and G. Mitchison, "More sparse-graph codes for quantum error-correction," Jun. 2007 [Online]. Available: http://www.inference.phy.cam.ac.uk/mackay/QECC.html
12. 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.
13. M. Hagiwara and H. Imai, "Quantum quasi-cyclic LDPC codes," in Proc. IEEE Int. Symp. Inf. Theory, Jun. 2007, pp. 806-810.
14. J.-P. Tillich and G. Zemor, "Quantum LDPC codes with positive rate and minimum distance proportional to ," in Proc. IEEE Int. Symp. Inf. Theory, Jul. 2009, pp. 799-803.
15. C. Poulliat, M. Fossorier, and D. Declercq, "Design of regular (2, )-LDPC codes over GF using their binary images," IEEE Trans. Commun., vol. 56, no. 10, pp. 1626-1635, Oct. 2008.
16. M. Davey and D. MacKay, "Low density parity check codes over GF ," in Proc. Information Theory Workshop, Jun. 1998, pp. 70-71.
17. M. Hagiwara and H. Imai, "Quantum quasi-cyclic LDPC codes," Jan. 2007 [Online]. Available: http://arxiv.org/abs/quant-ph/0701020v4
18. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: Elsevier, 1977.
19. D. Declercq and M. Fossorier, "Decoding algorithms for nonbinary LDPC codes over GF ," IEEE Trans. Commun., vol. 55, no. 4, pp. 633-643, Apr. 2007.
20. V. Rathi and R. Urbanke, "Density evolution, threshold and the stability condition for nonbinary LDPC codes," IEE Proc. Commun., vol. 152, no. 6, pp. 1069-1074, 2005.