메뉴 건너뛰기




Volumn 50, Issue 6, 2004, Pages 1269-1279

On algebraic construction of Gallager and circulant low-density parity-check codes

Author keywords

Cyclic code; Euclidean geometry; Projective geometry; Quasi cyclic code; Sum product algorithm (SPA)

Indexed keywords

ALGEBRA; ALGORITHMS; ELECTRIC NETWORK ANALYSIS; GEOMETRY;

EID: 2942640145     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.828088     Document Type: Letter
Times cited : (94)

References (35)
  • 1
    • 84925405668 scopus 로고
    • Low-density parity-check codes
    • Jan.
    • R. G. Gallager, "Low-density parity-check codes," IRE Trans. Inform. Theory, vol. IT-18, pp. 21-28, Jan. 1962.
    • (1962) IRE Trans. Inform. Theory , vol.IT-18 , pp. 21-28
    • Gallager, R.G.1
  • 3
    • 0030219216 scopus 로고    scopus 로고
    • Near Shannon limit performance of low density parity check codes
    • D. J. C. MacKay and R. M. Neal, "Near Shannon limit performance of low density parity check codes," Electron. Lett., vol. 32, pp. 1645-1646, 1996.
    • (1996) Electron. Lett. , vol.32 , pp. 1645-1646
    • MacKay, D.J.C.1    Neal, R.M.2
  • 5
    • 0030283874 scopus 로고    scopus 로고
    • Linear-time encodable error-correctable codes
    • Nov.
    • D. Spielman, "Linear-time encodable error-correctable codes," IEEE Trans. Inform. Theory, vol. 42, pp. 1723-1731, Nov. 1996.
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 1723-1731
    • Spielman, D.1
  • 6
    • 0032099205 scopus 로고    scopus 로고
    • Low density parity check codes over GF (q)
    • June
    • M. C. Davey and D. J. C. 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.J.C.2
  • 7
    • 0035246580 scopus 로고    scopus 로고
    • Improved low-density parity-check codes using irregular graphs and belief propagation
    • Feb.
    • M. G. Luby, M. Mitzenmacher, M. A. Shokrollahi, and D. A. Spielman, "Improved low-density parity-check codes using irregular graphs and belief propagation," IEEE Trans. Inform. Theory, vol. 47, pp. 585-598, Feb. 2001.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 585-598
    • Luby, M.G.1    Mitzenmacher, M.2    Shokrollahi, M.A.3    Spielman, D.A.4
  • 9
    • 0033099611 scopus 로고    scopus 로고
    • Good error-correcting codes based on very sparse matrices
    • Mar.
    • ____, "Good error-correcting codes based on very sparse matrices," IEEE Trans. Inform. Theory, vol. 45, pp. 399-432, Mar. 1999.
    • (1999) IEEE Trans. Inform. Theory , vol.45 , pp. 399-432
    • MacKay, D.J.C.1
  • 10
    • 0035248618 scopus 로고    scopus 로고
    • On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit
    • Feb.
    • S. Y. Chung, G. D. Forney, Jr., T. J. Richardson, and R. Urbanke, "On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit," IEEE Commun. Lett., vol. 5, pp. 58-60, Feb. 2001.
    • (2001) IEEE Commun. Lett. , vol.5 , pp. 58-60
    • Chung, S.Y.1    Forney Jr., G.D.2    Richardson, T.J.3    Urbanke, R.4
  • 11
    • 0035246307 scopus 로고    scopus 로고
    • The capacity of low-density parity-check codes under massage-passing decoding
    • Feb.
    • T. J. Richardson and R. Urbanke, "The capacity of low-density parity-check codes under massage-passing decoding," IEEE Trans. Inform. Theory, vol. 47, pp. 599-618, Feb. 2001.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 599-618
    • Richardson, T.J.1    Urbanke, R.2
  • 12
    • 0035246127 scopus 로고    scopus 로고
    • Design of capacity-approaching irregular low-density parity-check codes
    • Feb.
    • T. J. Richardson, M. A. Shokrollahi, and R. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, Feb. 2001.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 619-637
    • Richardson, T.J.1    Shokrollahi, M.A.2    Urbanke, R.3
  • 13
    • 0035504019 scopus 로고    scopus 로고
    • Low-density parity-check codes based on finite geometries: A rediscovery and new results
    • Nov.
    • 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, pp. 2711-2736, Nov. 2001.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 2711-2736
    • Kou, Y.1    Lin, S.2    Fossorier, M.3
  • 16
    • 0032001728 scopus 로고    scopus 로고
    • Turbo decoding as an instance of Pearl's belief propagation algorithm
    • Feb.
    • R. J. McEliece, D. J. C. MacKay, and J.-F. Cheng, "Turbo decoding as an instance of Pearl's belief propagation algorithm," IEEE J. Select. Areas Commun., vol. 16, pp. 140-152, Feb. 1998.
    • (1998) IEEE J. Select. Areas Commun. , vol.16 , pp. 140-152
    • McEliece, R.J.1    MacKay, D.J.C.2    Cheng, J.-F.3
  • 17
    • 0034206426 scopus 로고    scopus 로고
    • Iterative decoding of one-step majority logic decodable codes based on belief propagation
    • Jun.
    • R. Lucas, M. Fossorier, Y. Kou, and S. Lin, "Iterative decoding of one-step majority logic decodable codes based on belief propagation," IEEE Trans. Commun., vol. 48, pp. 931-937, Jun. 2000.
    • (2000) IEEE Trans. Commun. , vol.48 , pp. 931-937
    • Lucas, R.1    Fossorier, M.2    Kou, Y.3    Lin, S.4
  • 20
    • 0038397549 scopus 로고    scopus 로고
    • Graph-theoretic construction of low density parity check codes
    • Apr.
    • I. Djurdjevic, S. Lin, and K. Abdel-Ghaffar, "Graph-theoretic construction of low density parity check codes," IEEE Commun. Lett., vol. 7, pp. 171-173, Apr. 2003.
    • (2003) IEEE Commun. Lett. , vol.7 , pp. 171-173
    • Djurdjevic, I.1    Lin, S.2    Abdel-Ghaffar, K.3
  • 25
    • 2942661950 scopus 로고    scopus 로고
    • Construction of low-density parity-check codes based on balanced incomplete block designs
    • June
    • B. Ammar, B. Honary, Y. Kou, J. Xu, and S. Lin, "Construction of low-density parity-check codes based on balanced incomplete block designs," IEEE Trans. Inform. Theory, vol. 50, pp. 1257-1268, June 2004.
    • (2004) IEEE Trans. Inform. Theory , vol.50 , pp. 1257-1268
    • Ammar, B.1    Honary, B.2    Kou, Y.3    Xu, J.4    Lin, S.5
  • 26
    • 2942659753 scopus 로고    scopus 로고
    • Combinatorial construction of low-density parity-check codes for iterative decoding
    • June
    • B. Vasić, "Combinatorial construction of low-density parity-check codes for iterative decoding," IEEE Trans. Inform. Theory, vol. 50, pp. 1156-1176, June 2004.
    • (2004) IEEE Trans. Inform. Theory , vol.50 , pp. 1156-1176
    • Vasić, B.1
  • 28
    • 0019608335 scopus 로고
    • A recursive approach to low complexity codes
    • R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inform. Theory, vol. IT-27, pp. 533-547, 1981.
    • (1981) IEEE Trans. Inform. Theory , vol.IT-27 , pp. 533-547
    • Tanner, R.M.1
  • 34
    • 2942644348 scopus 로고    scopus 로고
    • private communication
    • D. J. C. MacKay, private communication.
    • MacKay, D.J.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.