메뉴 건너뛰기




Volumn 41, Issue 6, 1995, Pages 1938-1954

Lower Bounds on Trellis Complexity of Block Codes

Author keywords

block codes; dynamics of codes; generalized Hamming weight hierarchy; maximum likelihood decoding; Trellis complexity

Indexed keywords

COMPUTATIONAL COMPLEXITY; DECODING; HIERARCHICAL SYSTEMS; TRELLIS CODES;

EID: 0029409022     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.476318     Document Type: Article
Times cited : (47)

References (43)
  • 1
    • 0016037512 scopus 로고
    • Optimal decoding of linear codes for minimizing symbol error rate
    • L. R. Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 284–287, 1974.
    • (1974) IEEE Trans. Inform. Theory , vol.IT-20 , pp. 284-287
    • Bahl, L.R.1    Cocke, J.2    Jelinek, F.3    Raviv, J.4
  • 2
    • 0005654225 scopus 로고
    • Concatenated decoding algorithms with partial enumeration of code vectors
    • (in Russian)
    • A. M. Barg and I. I. Dumer, “Concatenated decoding algorithms with partial enumeration of code vectors,” Probl. Peredachi Inform., vol. 22, pp. 3–10, 1986 (in Russian).
    • (1986) Probl. Peredachi Inform. , vol.22 , pp. 3-10
    • Barg, A.M.1    Dumer, I.I.2
  • 5
    • 0027555114 scopus 로고
    • An updated table of minimum-distance bounds for binary linear codes
    • A. E. Brouwer and T. Verhoeff, “An updated table of minimum-distance bounds for binary linear codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 662–677, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 662-677
    • Brouwer, A.E.1    Verhoeff, T.2
  • 6
    • 0028550249 scopus 로고
    • Upper bounds on generalized distances
    • G. Cohen, S. Litsyn, and G. Zémor, “Upper bounds on generalized distances,” IEEE Trans. Inform. Theory, vol. 40, pp. 2090–2092, 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 2090-2092
    • Cohen, G.1    Litsyn, S.2    Zémor, G.3
  • 9
    • 0015600423 scopus 로고
    • The Viterbi algorithm
    • G. D. Forney, Jr., “The Viterbi algorithm,” Proc. IEEE, vol. 61, pp. 268–278, 1973.
    • (1973) Proc. IEEE , vol.61 , pp. 268-278
    • Forney, G.D.1
  • 10
    • 84941860379 scopus 로고
    • Coset codes II: Binary lattices and related codes
    • —, “Coset codes II: Binary lattices and related codes,” IEEE Trans. Inform. Theory, vol. 34, pp. 1152–1187, 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1152-1187
    • Forney, G.D.1
  • 11
    • 0028547151 scopus 로고
    • Dimension/length profiles and trellis complexity of linear block codes
    • —, “Dimension/length profiles and trellis complexity of linear block codes,” IEEE Trans. Inform. Theory, vol. 40, pp. 1741–1752, 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1741-1752
    • Forney, G.D.1
  • 12
    • 0028547248 scopus 로고
    • Density/length profiles and trellis complexity of lattices
    • —, “Density/length profiles and trellis complexity of lattices,” IEEE Trans. Inform. Theory, vol. 40, pp. 1752–1772, 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1752-1772
    • Forney, G.D.1
  • 13
    • 0027668052 scopus 로고
    • The dynamics of group codes: State spaces, trellis diagrams and canonical encoders
    • G. D. Forney, Jr. and M. D. Trott, “The dynamics of group codes: State spaces, trellis diagrams and canonical encoders,” IEEE Trans. Inform. Theory, vol. 39, pp. 1491–1513, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 1491-1513
    • Forney, G.D.1    Trott, M.D.2
  • 14
    • 84938013072 scopus 로고    scopus 로고
    • The state complexity of trellis diagrams for a class of generalized concatenated codes
    • preprint
    • T. Fujiwara, T. Kasami, R. Morelos-Zaragoza, and S. Lin, “The state complexity of trellis diagrams for a class of generalized concatenated codes,” preprint.
    • Fujiwara, T.1    Kasami, T.2    Morelos-Zaragoza, R.3    Lin, S.4
  • 15
    • 3943098596 scopus 로고
    • Bounds for codes
    • (in Russian)
    • V. D. Goppa, “Bounds for codes,” Dokl. Akad. Nauk, vol. 333, p. 423, 1993 (in Russian).
    • (1993) Dokl. Akad. Nauk , vol.333 , pp. 423
    • Goppa, V.D.1
  • 16
    • 0000085073 scopus 로고
    • The weight distribution of irreducible cyclic codes
    • T. Helleseth, T. Kløve, and J. Mykkelveit, “The weight distribution of irreducible cyclic codes,” Discr. Math., vol. 18, pp. 179–211, 1977.
    • (1977) Discr. Math. , vol.18 , pp. 179-211
    • Helleseth, T.1    Kløve, T.2    Mykkelveit, J.3
  • 18
    • 84944989005 scopus 로고
    • On complexity of trellis structure of linear block codes
    • presented at the IEEE Int. Symp. Inform. Theory, Budapest, Hungary
    • T. Kasami, T. Takata, T. Fujiwara, and S. Lin, “On complexity of trellis structure of linear block codes,” presented at the IEEE Int. Symp. Inform. Theory, Budapest, Hungary, 1991.
    • (1991)
    • Kasami, T.1    Takata, T.2    Fujiwara, T.3    Lin, S.4
  • 19
    • 0027257044 scopus 로고
    • On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes
    • —, “On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 242–243, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 242-243
    • Kasami, T.1    Takata, T.2    Fujiwara, T.3    Lin, S.4
  • 21
  • 22
    • 0029407106 scopus 로고    scopus 로고
    • On the trellis structure of block codes
    • this issue
    • F. R. Kschischang and V. Sorokine, “On the trellis structure of block codes,” this issue, pp. 1924–1937.
    • Kschischang, F.R.1    Sorokine, V.2
  • 23
    • 0008241387 scopus 로고
    • Block codes from convolutional codes
    • (in Russian)
    • B. D. Kudryashov and T.G. Zakharova, “Block codes from convolutional codes,” Probl. Peredachi Inform., vol. 25, pp. 98–102, 1989 (in Russian).
    • (1989) Probl. Peredachi Inform. , vol.25 , pp. 98-102
    • Kudryashov, B.D.1    Zakharova, T.G.2
  • 25
    • 0029276653 scopus 로고
    • Asymptotically good codes have infinite trellis complexity
    • —, “Asymptotically good codes have infinite trellis complexity,” IEEE Trans. Inform. Theory, vol. 41, pp. 555–559, 1995.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 555-559
    • Lafourcade, A.1    Vardy, A.2
  • 26
    • 0022665432 scopus 로고
    • On tail biting convolutional codes
    • H. H. Ma and J. K. Wolf, “On tail biting convolutional codes,” IEEE Trans. Commun., vol. COM-34, pp. 104–111, 1986.
    • (1986) IEEE Trans. Commun. , vol.COM-34 , pp. 104-111
    • Ma, H.H.1    Wolf, J.K.2
  • 29
    • 33747468142 scopus 로고
    • The Viterbi decoding complexity of linear block codes
    • presented at the IEEE Int. Symp. Inform. Theory, Trondheim, Norway
    • R. J. McEliece, “The Viterbi decoding complexity of linear block codes,” presented at the IEEE Int. Symp. Inform. Theory, Trondheim, Norway, 1994.
    • (1994)
    • McEliece, R.J.1
  • 30
    • 34648824756 scopus 로고    scopus 로고
    • On the BCJR trellis for linear block codes
    • submitted for publication
    • —, “On the BCJR trellis for linear block codes,” IEEE Trans. Inform. Theory, submitted for publication.
    • IEEE Trans. Inform. Theory
    • McEliece, R.J.1
  • 31
    • 0017468074 scopus 로고
    • New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities
    • R. J. McEliece, E. R. Rodemich, H. C. Rumsey, and L. R. Welch, “New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities,” IEEE Trans. Inform. Theory, vol. IT-23, pp. 157–166, 1977.
    • (1977) IEEE Trans. Inform. Theory , vol.IT-23 , pp. 157-166
    • McEliece, R.J.1    Rodemich, E.R.2    Rumsey, H.C.3    Welch, L.R.4
  • 32
    • 0024078703 scopus 로고
    • Minimal trellises for block codes
    • D. J. Muder, “Minimal trellises for block codes,” IEEE Trans. Inform. Theory, vol. 34, pp. 1049–1053, 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1049-1053
    • Muder, D.J.1
  • 33
    • 84938007287 scopus 로고
    • Shearer, personal communication
    • J. B. Shearer, personal communication, 1994.
    • (1994)
    • Shearer, J.B.1
  • 34
    • 84938020469 scopus 로고    scopus 로고
    • Decoding complexity versus coding gain of lattices
    • submitted for publication
    • V. Tarokh and I. F. Blake, “Decoding complexity versus coding gain of lattices,” IEEE Trans. Inform. Theory, submitted for publication.
    • IEEE Trans. Inform. Theory
    • Tarokh, V.1    Blake, I.F.2
  • 35
    • 84938013498 scopus 로고
    • Dynamical structure of block codes
    • presented at the IEEE Int. Workshop on Coding, System Theory, and Symbolic Dynamics, Mansfield, MA, Oct.
    • A. Vardy, “Dynamical structure of block codes,” presented at the IEEE Int. Workshop on Coding, System Theory, and Symbolic Dynamics, Mansfield, MA, Oct. 1993.
    • (1993)
    • Vardy, A.1
  • 36
    • 0028514913 scopus 로고
    • The Nordstrom-Robinson code: Representation over GF(4) and efficient decoding
    • —, “The Nordstrom-Robinson code: Representation over GF(4) and efficient decoding,” IEEE Trans. Inform. Theory, vol. 40, pp. 1686–1693, 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1686-1693
    • Vardy, A.1
  • 37
    • 0028388409 scopus 로고
    • Maximum-likelihood soft decision decoding of BCH codes
    • A. Vardy and Y. Be'ery, “Maximum-likelihood soft decision decoding of BCH codes,” IEEE Trans. Inform. Theory, vol. 40, pp. 546–554, 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 546-554
    • Vardy, A.1    Be'ery, Y.2
  • 38
    • 0026219389 scopus 로고
    • Generalized Hamming weights for linear codes
    • V. K. Wei, “Generalized Hamming weights for linear codes,” IEEE Trans. Inform. Theory, vol. 37, pp. 1412–1418, 1991.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1412-1418
    • Wei, V.K.1
  • 39
    • 84938009877 scopus 로고
    • A survey of results on generalized Hamming weights for linear codes
    • presented at the IEEE Inform. Theory Workshop, Sunoso, Japan
    • —, “A survey of results on generalized Hamming weights for linear codes,” presented at the IEEE Inform. Theory Workshop, Sunoso, Japan, 1993.
    • (1993)
    • Wei, V.K.1
  • 40
    • 0017922440 scopus 로고
    • Efficient maximum-likelihood decoding of linear block codes using a trellis
    • J. K. Wolf, “Efficient maximum-likelihood decoding of linear block codes using a trellis,” IEEE Trans. Inform. Theory, vol. IT-24, pp. 76–80, 1978.
    • (1978) IEEE Trans. Inform. Theory , vol.IT-24 , pp. 76-80
    • Wolf, J.K.1
  • 41
    • 0029271967 scopus 로고
    • On the trellis complexity of certain binary linear block codes
    • Ø. Ytrehus, “On the trellis complexity of certain binary linear block codes,” IEEE Trans. Inform. Theory, vol. 41, pp. 559–560, 1995.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 559-560
    • Ytrehus, Ø.1
  • 42
    • 0027629275 scopus 로고
    • Bounds on complexity of trellis decoding of linear block codes
    • (in Russian)
    • V. V. Zyablov and V. R. Sidorenko, “Bounds on complexity of trellis decoding of linear block codes,” Probl. Peredachi Inform., vol. 29, pp. 3–9, 1993 (in Russian).
    • (1993) Probl. Peredachi Inform. , vol.29 , pp. 3-9
    • Zyablov, V.V.1    Sidorenko, V.R.2
  • 43
    • 84938020456 scopus 로고
    • On complexity of maximum likelihood decoding of the best concatenated codes
    • (Moscow-Kuibushev), (in Russian)
    • I. I. Dumer, “On complexity of maximum likelihood decoding of the best concatenated codes,” in Proc. 8th All-Union Conf. on Coding Theory and Information Theory (Moscow-Kuibushev, 1981), pp. 66–69 (in Russian).
    • (1981) Proc. 8th All-Union Conf. on Coding Theory and Information Theory , pp. 66-69
    • Dumer, I.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.