High performance nonbinary quasi-cyclic LDPC codes on Euclidean geometries

Proceedings - IEEE Military Communications Conference MILCOM

Volumn , Issue , 2007, Pages

  Zhou, Bo ^a   Kang, Jingyu ^a   Tai, Ying Y ^a   Huang, Qin ^a   Lin, Shu ^a  

^a University of California Davis   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC METHOD (AM); AWGN CHANNELS; BERLEKAMP-MASSEY ALGORITHMS; CODING GAINS; EUCLIDEAN; FOURIER; LINEAR COMPLEXITY; PUNCTURED LOW DENSITY PARITY CHECK (LDPC) CODES; QUASI-CYCLIC; QUASI-CYCLIC LDPC CODES; REED SOLOMON (RS); SHIFT-REGISTERS; SOME APPLICATIONS; STORAGE SYSTEMS; SUM-PRODUCT ALGORITHM (SPA);

BOOLEAN ALGEBRA; BOOLEAN FUNCTIONS; CODES (STANDARDS); COMMUNICATION CHANNELS (INFORMATION THEORY); COMMUNICATION SYSTEMS; DECODING; FAST FOURIER TRANSFORMS; FOURIER TRANSFORMS; HIGH PERFORMANCE LIQUID CHROMATOGRAPHY; ITERATIVE DECODING; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; MILITARY COMMUNICATIONS; MILITARY OPERATIONS; PROGRAMMING THEORY; REED-SOLOMON CODES;

CODES (SYMBOLS);

EID: 47949084369     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/MILCOM.2007.4454753     Document Type: Conference Paper

References (29)

1. C.E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J., vol. 27, pp. 379-423 and 623-656, July and October, 1948.
2. R.G. Gallager, "Low density parity check codes," IRE Trans. Inform. Theory, vol. IT-8, no. 1, pp. 21-28, Jan. 1962.
3. D.J.C. MacKay and R.M. Neal, "Near Shannon limit performance of low density parity check codes," Electron. Lett., vol. 32, no. 18, pp. 1645-1646, Aug. 1996.
4. D.J.C. MacKay, "Good error-correcting codes based on very sparse matrices," IEEE Trans. Inform. Theory, vol. 45, no. 2, pp. 399-431, Mar. 1999.
5. J. Pearl, Probabilistic Reasoning in Intelligent Systems, Morgan Kaufmann, San Mateo, CA, 1988.
6. F.R. Kschischang, B.J. Frey, and H.-A. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inform. Theory, vol, 47, no, 2, pp. 498-519, Feb, 2001.
7. T. Richardson, A. Shokrollahi, and R, Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inform Theory, vol. 47, no. 2, pp. 619-637, Feb. 2001.
8. S.-Y. Chung, T.J. Richardson, and R.L. Urbanke, "Analysis of sumproduct decoding of low-density parity-check codes using a Gaussian approximation," IEEE Trans. Inform. Theory, vol. 47, no. 2, pp. 657-670, Feb, 2001.
9. Y. Kou, S. Lin, and M. Fossorier, "Low-density parity-check codes based on finite geometries: A rediscovery and new results," IEEE Trans. Inform. Theory, vol. 47, no. 7, pp. 2711-2736, Nov, 2001.
10. M.C. Davey and D J.C. MacKay, "Low-density parity check codes over GF(q)," IEEE Commun. Lett., vol. 2, no. 6, pp. 165-167, June 1998.
11. D.J.C. MacKay and M.C. Davey, "Evaluation of Gallager codes of short block length and high rate applications," Proc. IMA International Conference on Mathematics and Its Applications: Codes, Systems and Graphical Models, pp. 113-130, Springer-Verlag, New York, 2000.
12. q)," in Proc. 2003 IEEE Inform. Theory Workshop, pp. 70-73, Paris, France, Mar, 31-Apr, 4, 2003.
13. D. Decleicq and M. Fossorier, "Decoding Algorithms for Nonbinary LDPC Codes over GF(q)," IEEE Trans. Commun., vol. 54, no. 4, pp. 633-643, Apr. 2007.
14. L. Zeng, L. Lan, Y.Y. Tai, and L. Shu, "Dispersed Reed-Solomon codes for iterative decoding and construction of q-ary LDPC codes," in Proc. IEEE Global Telecommun. Conf., St. Louis, MO, Nov. 28-Dec. 2, 2005, pp. 1193-1198.
15. S. Song, L. Zeng, S. Lin and K. Abdel-Ghaffar, "Algebraic constructions of nonbinary quasi-cyclic LDPC codes," in Proc. IEEE Int. Symp. Inform. Theory, Seattle, WA, Jul. 9-14, 2006, pp. 83-87.
16. B. Zhou, Y.Y. Tai, L. Lan, S. Song, L. Zeng, and S. Lin, "Construction of high performance and efficiently encodable nonbinary quasi-cyclic LDPC codes," in Proc. IEEE Global Telecommun, Conf., San Francisco, CA, Nov, 27-Dec. 1, 2006.
17. V. Rathi and R. Urbanke, "Density evolution, thresholds and the stability condition for non-binary LDPC codes," IEE Proc. Commun., vol. 152, no. 6, pp. 1069-1074, Dec. 2005.
18. A. Bennatan and D. Burshtein, "Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels," IEEE Trans. Inform. Theory, vol. 52, no. 2, pp. 549-583, Feb. 2006.
19. E.R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, New York, NY. 1968.
20. J.L. Massey, "Shift-register synthesis and BCH decoding," IEEE Trans. Inform Theory, vol. 15, no.1, pp. 122-127, Jan. 1969.
21. R. Kötter and A. Vardy, "Algebraic soft-decision decoding of Reed-Solomon codes," IEEE Trans. Inform. Theory, vol. 49, no.11, pp. 2809-2825, Nov. 2003.
22. M. El-Khamy and R. McEliece, "Iterative algebraic soft-decision list decoding of RS codes," IEEE J. Select. Areas Commun., vol. 24, pp. 481-490, Mar. 2006.
23. W.J. Gross, F.R. Kschischang, R. Kötter, and P.G. Gulak, "Applications of algebraic soft-decision decoding of Reed-Solomon codes," IEEE Trans. Commun., vol. 54, no. 7, pp. 1224-1234, Jul. 2006.
24. R.M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inform Theory, vol. 27, no. 5, pp. 533-547, Sep. 1981.
25. S. Lin and D.J. Costello, Jr., Error Control Coding: Fundamentals and Applications, 2nd edition, Prentice Hall, Upper Saddle River. NJ. 2004.
26. Z. Li, I. Chen, L. Zeng, S. Lin, and W. Fong, "Efficient encoding of quasi-cyclic low-density parity-check codes," IEEE Trans. Commun., vol. 54, no. 1, pp. 71-81, Jan. 2006.
27. H.B. Mann, Analysis and Design of Experiments, Dover, New York, NY, 1949.
28. R.D. Carmichael, Introduction to the Theory of Groups of Finite Order, Dover, New York, NY, 1956.
29. J. Xu, L. Chen, I. Djurdjevic, S. Lin, and K. Abdel-Ghaffar, "Construction of regular and irregular LDPC codes: Geometry decomposition and masking," IEEE Trans. Inform. Theory, vol. 53, no. 1, pp. 121-134, Jan. 2007.