On a family of circulant matrices for quasi-cyclic low-density generator matrix codes

IEEE Transactions on Information Theory

Volumn 57, Issue 9, 2011, Pages 6052-6067

  Baldi, Marco ^a   Bambozzi, Federico ^b   Chiaraluce, Franco ^a  

^a UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Low density generator matrix (LDGM) codes; low density parity check (LDPC) codes; quasi cyclic (QC) codes; sparse circulant matrices

Indexed keywords

CIRCULANT MATRIX; ELEMENTARY OPERATIONS; ERROR FLOOR; GENERATOR MATRIX; INNER STRUCTURE; LOW-DENSITY GENERATOR MATRIX CODES; LOW-DENSITY PARITY-CHECK CODES; MINIMUM DISTANCE; PERMUTATION MATRIX; QUASI-CYCLIC; QUASICYCLIC CODES; SPARSE CIRCULANT MATRICES;

BAR CODES; CODING ERRORS;

MATRIX ALGEBRA;

EID: 80052376646     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2161953     Document Type: Article

References (32)

1. 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.
2. G. Wiechman and I. Sason, "Parity-check density versus performance of binary linear block codes: New bounds and applications", IEEE Trans. Inf. Theory, vol. 53, no. 2, pp. 550-579, Feb. 2007.
3. T. Richardson and R. Urbanke, "Efficient encoding of low-density parity-check codes", IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 638-656, Feb. 2001.
4. S. Freundlich, D. Burshtein, and S. Litsyn, "Approximately lower triangular ensembles of LDPC codes with linear encoding complexity", IEEE Trans. Inf. Theory, vol. 53, no. 4, pp. 1484-1494, Apr. 2007.
5. D. Haley, A. Grant, and J. Buetefuer, "Iterative encoding of low-density parity-check codes", in Proc. IEEE Global Telecommunications Conf. (GLOBECOM'02), Taipei, Taiwan, R. O. C., Nov. 2002, vol. 2, pp. 1289-1293.
6. D. Haley and A. Grant, "Improved reversible LDPC codes", in Proc. IEEE Int. Symp. Information Theory (ISIT 2005), Adelaide, Australia, Sep. 2005, pp. 1367-1371.
7. J. F. Cheng and R. J. McEliece, "Some high-rate near capacity codecs for the Gaussian channel", in Proc. 34th Allerton Conf. Communications, Control and Computing, Allerton, IL, Oct. 1996.
8. J. Garcia-Frias and W. Zhong, "Approaching Shannon performance by iterative decoding of linear codes with low-density generator matrix", IEEE Commun. Lett., vol. 7, no. 6, pp. 266-268, Jun. 2003.
9. M. González-López, F. J. Vázquez-Araújo, L. Castedo, and J. Garcia-Frias, "Serially-concatenated low-density generator matrix (SCLDGM) codes for transmission over AWGN and Rayleigh fading channels", IEEE Trans. Wireless Commun., vol. 6, no. 8, pp. 2753-2758, Aug. 2007.
10. J.-S. Kim and H.-Y. Song, "Concatenated LDGM codes with single decoder", IEEE Commun. Lett., vol. 10, no. 4, pp. 287-289, Apr. 2006.
11. T. R. Oenning and J. Moon, "A low-density generator matrix interpretation of parallel concatenated single bit parity codes", IEEE Trans. Magn., vol. 37, no. 2, pp. 737-741, Mar. 2001.
12. C.-H. Hsu and A. Anastasopoulos, "Asymptotic weight distributions of irregular repeat-accumulate codes", in Proc. IEEE Global Telecommunications Conf. (GLOBECOM'05), Saint Louis, MO, Nov. 2005, pp. 1147-1151.
13. H. Jin, A. Khandekar, and R. McEliece, "Irregular repeat-accumulate codes", in Proc. 2nd Int. Symp. Turbo Codes, Brest, France, Sep. 2000, pp. 1-8.
14. A. Abbasfar, D. Divsalar, and K. Yao, "Accumulate repeat accumulate codes", in Proc. IEEE Global Telecommunications Conf. (GLOBECOM'04), Dallas, TX, Nov. 2004, pp. 509-513.
15. H. D. Pfister and I. Sason, "Accumulate-repeat-accumulate codes: Capacity-achieving ensembles of systematic codes for the erasure channel with bounded complexity", IEEE Trans. Inf. Theory, vol. 53, no. 2, pp. 2088-2115, Jun. 2007.
16. Z. Li, L. 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.
17. M. P. C. Fossorier, "Quasi-cyclic low-density parity-check codes from circulant permutation matrices", IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1788-1793, Aug. 2004.
18. IEEE Standard for Local and Metropolitan Area Networks - Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems - Amendment for Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands, IEEE Std. 802.16e 2005, Dec. 2005.
19. C. Yoon, E. Choi, M. Cheong, and S.-K. Lee, "Arbitrary bit generation and correction technique for encoding QC-LDPC codes with dual-diagonal parity structure", in Proc. IEEE WCNC 2007, Hong Kong, Mar. 2007, pp. 663-667.
20. S. Myung, K. Yang, and J. Kim, "Quasi-cyclic LDPC codes for fast encoding", IEEE Trans. Inf. Theory, vol. 51, no. 8, pp. 2894-2901, Aug. 2005.
21. Tech. Rep. Orange Book CCSDS. Washington, DC, USA, Consultative Committee for Space Data Systems (CCSDS), "Low Density Parity Check Codes for Use in Near-Earth and Deep Space Applications", 2007.
22. S. J. Johnson and S. R. Weller, "A family of irregular LDPC codes with low encoding complexity", IEEE Commun. Lett., vol. 7, no. 2, pp. 79-81, Feb. 2003.
23. T. Xia and B. Xia, "Quasi-cyclic codes from extended difference families", in Proc. IEEE Wireless Commun. Networking Conf, New Orleans, LA, Mar. 2005, vol. 2, pp. 1036-1040.
24. F. MacWilliams, "Orthogonal circulant matrices over finite fields, and how to find them", J. Comb. Theory Ser. A, vol. 10, pp. 1-17, 1971.
25. Z. Zhang, "Construction of the Orthogonal Groups of n × n Circulant Matrices over Finite Fields", Ph. D. dissertation, Concordia Univ., Montreal, QC, Canada, 1997.
26. m", Math. Comput., vol. 70, pp. 1169-1182, 2001.
27. PARI/GP, 2009 [Online]. Available: http://pari.math.u-bordeaux.fr/
28. J. Hagenauer, E. Offer, and L. Papke, "Iterative decoding of binary block and convolutional codes", IEEE Trans. Inf. Theory, vol. 42, no. 2, pp. 429-445, Mar. 1996.
29. N. Kamiya, "High-rate quasi-cyclic low-density parity-check codes derived from finite affine planes", IEEE Trans. Inf. Theory, vol. 53, no. 4, pp. 1444-1459, Apr. 2007.
30. Digital Video Broadcasting (DVB); Interaction Channel for Satellite Distribution Systems, ETSI EN Std. 301 790(v1.4.1), Sep. 2005.
31. T. Lestable, E. Zimmerman, M.-H. Hamon, and S. Stiglmayr, "Block-LDPC codes vs duo-binary turbo-codes for european next generation wireless systems", in Proc. IEEE VTC-2006 Fall, Montreal, QC, Canada, Sep. 2006, pp. 1-5.
32. M. Baldi, G. Cancellieri, and F. Chiaraluce, "Finite-precision analysis of demappers and decoders for LDPC-coded M-QAM-systems", IEEE Trans. Broadcast., vol. 55, no. 2, pp. 239-250, Jun. 2009.