메뉴 건너뛰기




Volumn 27, Issue 6, 2009, Pages 831-845

Geometrically-structured maximum-girth LDPC block and convolutional codes

Author keywords

Circulant matrices; LDPC codes; LDPC convolutional codes; Maximum girth; QC codes; Slope

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONVOLUTION; CONVOLUTIONAL CODES; FORWARD ERROR CORRECTION; SATELLITE COMMUNICATION SYSTEMS; TURBO CODES;

EID: 70350610434     PISSN: 07338716     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSAC.2009.090802     Document Type: Article
Times cited : (23)

References (52)
  • 1
    • 84925405668 scopus 로고
    • Low-density parity-check codes
    • Jan.
    • R.G. Gallager, "Low-density parity-check codes, "IRE Trans. Info. Theory, vol. IT-18, pp. 21-28, Jan. 1962.
    • (1962) IRE Trans. Info. Theory , vol.IT-18 , pp. 21-28
    • Gallager, R.G.1
  • 3
    • 0035504019 scopus 로고    scopus 로고
    • Low-density parity-check codes based on finite geometries: A rediscovery and new results
    • Nov.
    • Y. Kou, S. Lin, M.P.C 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.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , Issue.7 , pp. 2711-2736
    • Kou, Y.1    Lin, S.2    Fossorier, M.P.C.3
  • 4
    • 0033099611 scopus 로고    scopus 로고
    • Good error-correcting codes based on very sparse matrices
    • Mar.
    • D.J.C. Mackay, "Good error-correcting codes based on very sparse matrices, " IEEE Trans. Info. Theory, vol. 45, no. 2, pp. 399-431, Mar. 1999.
    • (1999) IEEE Trans. Info. Theory , vol.45 , Issue.2 , pp. 399-431
    • MacKay, D.J.C.1
  • 5
    • 0030219216 scopus 로고    scopus 로고
    • Near Shannon limit performance of lowdensity parity-check codes
    • Aug.
    • D.J.C. Mackay, R.M. Neal, "Near Shannon limit performance of lowdensity parity-check codes, "Electron. Lett., vol. 32, no.18, pp. 1645-1646, Aug. 1996.
    • (1996) Electron . Lett. , vol.32 , Issue.18 , pp. 1645-1646
    • MacKay, D.J.C.1    Neal, R.M.2
  • 6
    • 0035246127 scopus 로고    scopus 로고
    • Design of capacityapproaching irregular low-density parity-check codes
    • Feb.
    • T.J. Richardson, M.A. Shokrolahi, R.L. Urbanke, "Design of capacityapproaching irregular low-density parity-check codes, "IEEE Trans. Info. Theory, vol. 47, no. 2 pp. 619-637, Feb. 2001.
    • (2001) IEEE Trans. Info. Theory , vol.47 , Issue.2 , pp. 619-637
    • Richardson, T.J.1    Shokrolahi, M.A.2    Urbanke, R.L.3
  • 7
    • 46649117661 scopus 로고    scopus 로고
    • A novel approach to generating long LDPC codes using two configurations
    • April
    • M. Esmaeili and M.H. Tadayon, "A novel approach to generating long LDPC codes using two configurations, "IET Communications, vol. 2, no. 4, pp. 587-597, April 2008.
    • (2008) IET Communications , vol.2 , Issue.4 , pp. 587-597
    • Esmaeili, M.1    Tadayon, M.H.2
  • 8
    • 85043040943 scopus 로고    scopus 로고
    • A lattice-based systematic recursive construction of QC LDPC Codes
    • Accepted
    • M. Esmaeili and M.H. Tadayon, "A lattice-based systematic recursive construction of QC LDPC Codes, " IEEE Trans. Commun., Accepted.
    • IEEE Trans. Commun
    • Esmaeili, M.1    Tadayon, M.H.2
  • 9
    • 39049138902 scopus 로고    scopus 로고
    • Generalized construction of Quasi-Cyclic regular LDPC codes based on permutation matrices
    • July
    • E. Gabidulin, A. Moinian, B. Honary, "Generalized construction of Quasi-Cyclic regular LDPC codes based on permutation matrices, " in Proc. IEEE Int. Symp. Info. Theory, July 2006, pp. 679-683.
    • (2006) Proc. IEEE Int. Symp. Info. Theory , pp. 679-683
    • Gabidulin, E.1    Moinian, A.2    Honary, B.3
  • 10
    • 3943064364 scopus 로고    scopus 로고
    • Quasi-cyclic low-density parity-check codes from circulant permutation matrices
    • Aug.
    • M.P.C. Fossorier, "Quasi-cyclic low-density parity-check codes from circulant permutation matrices, "IEEE Trans. Inform. Theory, vol. 50, no. 8, pp. 1788-1793, Aug. 2004.
    • (2004) IEEE Trans. Inform. Theory , vol.50 , Issue.8 , pp. 1788-1793
    • Fossorier, M.P.C.1
  • 11
    • 84938915656 scopus 로고    scopus 로고
    • Regular low-density parity-check codes from combinatorial designs
    • Cairns, Australia, Sept.
    • S.J. Johanson, S.R.Weller, "Regular low-density parity-check codes from combinatorial designs, " in Proc. IEEE Information Theory Workshop, Cairns, Australia, Sept. 2001, pp. 90-92.
    • (2001) Proc. IEEE Information Theory Workshop , pp. 90-92
    • Johanson, S.J.1    Weller, S.R.2
  • 12
    • 31744435016 scopus 로고    scopus 로고
    • Algebraic construction of sparse matrices with large girth
    • Feb.
    • M.E. O'Sullivan, "Algebraic construction of sparse matrices with large girth, "IEEE Trans. Inform. Theory, vol. 52, no. 2, pp. 718-727, Feb. 2006.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.2 , pp. 718-727
    • O'sullivan, M.E.1
  • 13
    • 2942640145 scopus 로고    scopus 로고
    • On algebraic construction of Gallager and circulant low-density parity-check codes
    • Jun.
    • H. Tang, J. Xu, Y. Kou, S. Lin, K. Abdel-Ghaffar, "On algebraic construction of Gallager and circulant low-density parity-check codes, "IEEE Trans. Inform. Theory, vol. 50, no. 6, pp. 1269-1279, Jun. 2004.
    • (2004) IEEE Trans. Inform. Theory , vol.50 , Issue.6 , pp. 1269-1279
    • Tang, H.1    Xu, J.2    Kou, Y.3    Lin, S.4    Abdel-Ghaffar, K.5
  • 17
    • 2942659753 scopus 로고    scopus 로고
    • Combinatorial constructions of low-density parity-check codes for iterative decoding
    • Jun.
    • B. Vasic, O. Milenkovic, "Combinatorial constructions of low-density parity-check codes for iterative decoding, "IEEE Trans. Inform. Theory, vol. 50, no. 6, pp. 1156-1176, Jun. 2004.
    • (2004) IEEE Trans. Inform. Theory , vol.50 , Issue.6 , pp. 1156-1176
    • Vasic, B.1    Milenkovic, O.2
  • 18
    • 4444307239 scopus 로고    scopus 로고
    • High-rate girth-eight low-density parity-check codes on rectangular integer lattices
    • Aug.
    • B. Vasic, K. Pedagani, M. Ivkovic, "High-rate girth-eight low-density parity-check codes on rectangular integer lattices, "IEEE Trans. Commun., vol. 52, no. 8, pp. 1248-1252, Aug. 2004.
    • (2004) IEEE Trans. Commun. , vol.52 , Issue.8 , pp. 1248-1252
    • Vasic, B.1    Pedagani, K.2    Ivkovic, M.3
  • 19
    • 0034206426 scopus 로고    scopus 로고
    • Iterative decoding of onestep majority logic decodable codes based on belief propagation
    • Jun.
    • R. Lucas, M.P.C Fossorier, Y. Kou, S. Lin, "Iterative decoding of onestep majority logic decodable codes based on belief propagation, "IEEE Trans. Commun., vol. 48, no.6, pp. 931-937, Jun. 2000.
    • (2000) IEEE Trans. Commun. , vol.48 , Issue.6 , pp. 931-937
    • Lucas, R.1    Fossorier, M.P.C.2    Kou, Y.3    Lin, S.4
  • 20
    • 3543037365 scopus 로고    scopus 로고
    • Near-Shannon-limit quasi-cyclic low-density parity-check Codes
    • Jul.
    • L. Chen, J. Xu, I. Djurdjevic, S. Lin, "Near-Shannon-limit quasi-cyclic low-density parity-check Codes, "IEEE Trans. Commun., vol. 52, no. 7, pp. 1038-1042, Jul. 2004.
    • (2004) IEEE Trans. Commun. , vol.52 , Issue.7 , pp. 1038-1042
    • Chen, L.1    Xu, J.2    Djurdjevic, I.3    Lin, S.4
  • 21
    • 0001813506 scopus 로고    scopus 로고
    • Array codes as low-density parity-check codes
    • Brest, France, Sep.
    • J.L. Fan, "Array codes as low-density parity-check codes, "in Proc. 2nd Int. Symp. Turbo Codes, Brest, France, Sep. 2000, pp. 543-546.
    • (2000) Proc. 2nd Int. Symp. Turbo Codes , pp. 543-546
    • Fan, J.L.1
  • 22
    • 29144467075 scopus 로고    scopus 로고
    • Some classes of quasi-cyclic LDPC codes: Properties and efficient encoding method
    • Dec.
    • H. Fujita, K. Sakaniwa, "Some classes of quasi-cyclic LDPC codes: Properties and efficient encoding method, "IEICE Trans. Fundamentals, vol. E88-A, no. 12, pp. 3627-3635, Dec. 2005.
    • (2005) IEICE Trans. Fundamentals , vol.E88-A , Issue.12 , pp. 3627-3635
    • Fujita, H.1    Sakaniwa, K.2
  • 24
    • 33749437278 scopus 로고    scopus 로고
    • Constructions of quasi-cyclic LDPC codes for the AWGN and binary erasure channels based on finite fields and affine mappings
    • 4-9 Sept.
    • L. Lan, L.-Q. Zeng, Y.Y. Tai, S. Lin, K. Abdel-Ghaffar, "Constructions of quasi-cyclic LDPC codes for the AWGN and binary erasure channels based on finite fields and affine mappings, " in Proc. Int. Symp. Information Theory, 4-9 Sept. 2005, pp. 2285-2289.
    • (2005) Proc. Int. Symp. Information Theory , pp. 2285-2289
    • Lan, L.1    Zeng, L.-Q.2    Tai, Y.Y.3    Lin, S.4    Abdel-Ghaffar, K.5
  • 25
    • 0842267569 scopus 로고    scopus 로고
    • Efficient encoding for a family of quasi-cyclic LDPC codes
    • 1-5 Dec.
    • D.E. Hocevar, "Efficient encoding for a family of quasi-cyclic LDPC codes, " in Proc. IEEE Global Telecommunications Conf., 1-5 Dec. 2003, vol. 7, pp. 3996-4000.
    • (2003) Proc. IEEE Global Telecommunications Conf. , vol.7 , pp. 3996-4000
    • Hocevar, D.E.1
  • 27
    • 23844550376 scopus 로고    scopus 로고
    • Quasi-Cyclic LDPC codes for fast encoding
    • Aug.
    • S. Myung, K. Yang, J. Kim, "Quasi-Cyclic LDPC codes for fast encoding, " IEEE Trans. Inform. Theory, vol. 51, no. 8 , pp. 2894-2901, Aug. 2005.
    • (2005) IEEE Trans. Inform. Theory , vol.51 , Issue.8 , pp. 2894-2901
    • Myung, S.1    Yang, K.2    Kim, J.3
  • 29
    • 33847730317 scopus 로고    scopus 로고
    • Low-complexity high-speed decoder design for quasicyclic LDPC codes
    • Jan.
    • Z. Wang, Z. Cui, "Low-complexity high-speed decoder design for quasicyclic LDPC codes, " IEEE Trans. Very Large Scale Integration(VLSI) Systems, vol. 15, no. 1, pp. 104-114, Jan. 2007.
    • (2007) IEEE Trans. Very Large Scale Integration(VLSI) Systems , vol.15 , Issue.1 , pp. 104-114
    • Wang, Z.1    Cui, Z.2
  • 30
    • 0842332219 scopus 로고    scopus 로고
    • Low complexity LDPC codes for magnetic recording
    • Taipei, Taiwan, R.O.C., Nov. 2002
    • H. Song, J. Liu, B.V.K.V. Kumar, "Low complexity LDPC codes for magnetic recording, " in IEEE Globecom 2002, Taipei, Taiwan, R.O.C., Nov. 2002.
    • (2002) IEEE Globecom
    • Song, H.1    Liu, J.2    Kumar, B.V.K.V.3
  • 31
    • 0036967455 scopus 로고    scopus 로고
    • Low complexity LDPC codes for partial response channels
    • Taipei, Taiwan, Nov. 2002
    • H. Song, J. Liu, B.V.K.V. Kumar, "Low complexity LDPC codes for partial response channels, " in IEEE Globecom 2002, vol. 2, pp. 1294-1299, Taipei, Taiwan, Nov. 2002.
    • (2002) IEEE Globecom , vol.2 , pp. 1294-1299
    • Song, H.1    Liu, J.2    Kumar, B.V.K.V.3
  • 32
    • 4444350397 scopus 로고    scopus 로고
    • Large girth cycle codes for partial response channels
    • H. Song, J. Liu, B.V.K.V. Kumar, "Large girth cycle codes for partial response channels, " IEEE Trans. Magn., vol. 40, no. 4, part 2, pp. 3084-3086, 2004.
    • (2004) IEEE Trans. Magn. , vol.40 , Issue.4 PART 2 , pp. 3084-3086
    • Song, H.1    Liu, J.2    Kumar, B.V.K.V.3
  • 33
    • 84944673133 scopus 로고    scopus 로고
    • Large-girth LDPC codes based on graphical models
    • Rome, Italy, Jun.
    • H. Zhang, J.M.F. Moura, "Large-girth LDPC codes based on graphical models, " in Proc.IEEE SPAWC, Rome, Italy, Jun. 2003, pp. 100-104.
    • (2003) Proc. IEEE SPAWC , pp. 100-104
    • Zhang, H.1    Moura, J.M.F.2
  • 34
    • 0842310780 scopus 로고    scopus 로고
    • The design of structured regular LDPC codes with large girth
    • San Francisco, CA, Dec
    • H. Zhang, J.M.F. Moura, "The design of structured regular LDPC codes with large girth, " in Proc. IEEE Globecom, San Francisco, CA, Dec 2003, pp. 4022-4026.
    • (2003) Proc. IEEE Globecom , pp. 4022-4026
    • Zhang, H.1    Moura, J.M.F.2
  • 35
    • 0019608335 scopus 로고
    • A recursive approach to low complexity codes
    • Sep.
    • R.M. Tanner, "A recursive approach to low complexity codes, "IEEE Trans. Inform. Theory, vol. 27, no.5, pp. 533-547, Sep. 1981.
    • (1981) IEEE Trans. Inform. Theory , vol.27 , Issue.5 , pp. 533-547
    • Tanner, R.M.1
  • 36
    • 84947615743 scopus 로고    scopus 로고
    • http://mathworld.wolfram.com/CageGraph.html
  • 37
    • 58149527911 scopus 로고    scopus 로고
    • Design of cages with a randomized progressive edge-growth algorithm
    • April
    • A. Venkiah, D. Declercq, C. Poulliat, "Design of cages with a randomized progressive edge-growth algorithm, "IEEE Commun. Letters, vol. 12, no.4, pp. 301-303, April 2008.
    • (2008) IEEE Commun. Letters , vol.12 , Issue.4 , pp. 301-303
    • Venkiah, A.1    Declercq, D.2    Poulliat, C.3
  • 38
    • 84947617021 scopus 로고    scopus 로고
    • http://perso-etis.ensea.fr/declercq/graphs.php.
  • 39
    • 0032099205 scopus 로고    scopus 로고
    • Low-density parity check codes over GF(q)
    • June
    • M.C. Davey, D. MacKay, "Low-density parity check codes over GF(q), "IEEE Commun. Lett., vol. 2, pp. 165-167, June 1998.
    • (1998) IEEE Commun. Lett. , vol.2 , pp. 165-167
    • Davey, M.C.1    MacKay, D.2
  • 40
    • 4143097079 scopus 로고    scopus 로고
    • Binary representation of cycle Tanner graph GF(2b) codes
    • Paris, France, June
    • X.-Y. Hu, E. Eleftheriou, "Binary representation of cycle Tanner graph GF(2b) codes, "Proc. IEEE Int. Conf. on Communications, Paris, France, June 2004, pp. 528-532.
    • (2004) Proc. IEEE Int. Conf. on Communications , pp. 528-532
    • Hu, X.-Y.1    Eleftheriou, E.2
  • 41
    • 12544253129 scopus 로고    scopus 로고
    • Regular and irregular progressive edge-growth Tanner graphs
    • Jan.
    • X.-Y. Hu, E. Eleftheriou, D.M. Arnold, "Regular and irregular progressive edge-growth Tanner graphs, "IEEE Trans. Info. Theory, vol. 51, no. 1, pp. 386-398, Jan. 2005.
    • (2005) IEEE Trans. Info. Theory , vol.51 , Issue.1 , pp. 386-398
    • Hu, X.-Y.1    Eleftheriou, E.2    Arnold, D.M.3
  • 43
    • 35448979822 scopus 로고    scopus 로고
    • Structured non-binary LDPC codes with large girth
    • Oct.
    • X. Ge, S.-T. Xia, "Structured non-binary LDPC codes with large girth", IET Electronics Lett., vol. 43, no. 22, Oct. 2007.
    • (2007) IET Electronics Lett. , vol.43 , Issue.22
    • Ge, X.1    Xia, S.-T.2
  • 44
    • 54949083457 scopus 로고    scopus 로고
    • Design of regular (2, dc)-LDPC codes over GF(q) using their binary images
    • Oct.
    • C. Poulliat, M. Fossorier and D. Declercq, "Design of regular (2, dc)-LDPC codes over GF(q) using their binary images, "IEEE Trans. Commun., vol. 56, pp. 1626-1635, Oct. 2008.
    • (2008) IEEE Trans. Commun. , vol.56 , pp. 1626-1635
    • Poulliat, C.1    Fossorier, M.2    Declercq, D.3
  • 46
    • 84947612288 scopus 로고    scopus 로고
    • http://www.cs.utoronto.ca/-radford/ldpc.software.html.
  • 47
    • 0036612281 scopus 로고    scopus 로고
    • Finite-length analysis of low-density parity-check codes on the binary erasure channel
    • June
    • C. Di, D. Proietti, I. E. Teletar, T. Richardson, R. Urbanke, "Finite-length analysis of low-density parity-check codes on the binary erasure channel, "IEEE Trans. Info. Theory, vol. 48, pp. 1570-1579, June 2002.
    • (2002) IEEE Trans. Info. Theory , vol.48 , pp. 1570-1579
    • Di, C.1    Proietti, D.2    Teletar, I.E.3    Richardson, T.4    Urbanke, R.5
  • 50
    • 0018530717 scopus 로고    scopus 로고
    • A connection between block codes and convolutional codes
    • G. Solomon, H.C.A. van Tilborg, "A connection between block codes and convolutional codes, "SIAM J. Appl. Math., vol. 37, pp. 358-369, 2004.
    • (2004) SIAM J. Appl. Math. , vol.37 , pp. 358-369
    • Solomon, G.1    Van Tilborg, H.C.A.2
  • 51
    • 0004239530 scopus 로고
    • Convolutional codes from quasi-cyclic codes: A link between the theories of block and convolutional codes
    • R.M. Tanner, "Convolutional codes from quasi-cyclic codes: A link between the theories of block and convolutional codes, " Univ. Calif. Canta Cruz, Tech. Rep., 1987.
    • (1987) Univ. Calif. Canta Cruz, Tech. Rep.
    • Tanner, R.M.1
  • 52
    • 85043062581 scopus 로고    scopus 로고
    • Structured QC LDPC codes with girth 18 and column-weight J ≥ 3
    • Accepted
    • M. Esmaeili and M. Gholami, "Structured QC LDPC codes with girth 18 and column-weight J ≥ 3, " Int J Electron Commun. (AEUE), Accepted.
    • Int J Electron Commun. (AEUE)
    • Esmaeili, M.1    Gholami, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.