메뉴 건너뛰기




Volumn 50, Issue 12, 2004, Pages 3026-3036

A new upper bound on the ML decoding error probability of linear binary block codes in AWGN interference

Author keywords

Additive white Gaussian noise (AWGN) channel; Block codes; Bounds; Decoding error probability; Distance spectrum; Gallager bounds; Linear binary block codes; Maximum likelihood (ML) decoding; Probability of error; Union bound; Upper bounds

Indexed keywords

BINARY CODES; BLOCK CODES; COMPUTATIONAL COMPLEXITY; DECODING; ERROR ANALYSIS; MAXIMUM LIKELIHOOD ESTIMATION; OPTIMIZATION; PHASE SHIFT KEYING; PROBABILITY; SIGNAL INTERFERENCE; SIGNAL TO NOISE RATIO; WHITE NOISE;

EID: 10644237202     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.838091     Document Type: Article
Times cited : (37)

References (42)
  • 1
    • 84907062399 scopus 로고
    • "Probability of error for optimal codes in Gaussian channel"
    • C. E. Shannon, "Probability of error for optimal codes in Gaussian channel," Bell Syst. Tech. J., vol. 38, pp. 611-656, 1959.
    • (1959) Bell Syst. Tech. J. , vol.38 , pp. 611-656
    • Shannon, C.E.1
  • 3
    • 0034317794 scopus 로고    scopus 로고
    • "Tight error bounds for nonuniform signaling over AWGN channels"
    • Nov
    • H. Kuai, F. Alajaji, and G. Takahara, "Tight error bounds for nonuniform signaling over AWGN channels," IEEE Trans. Inform. Theory vol. 46, pp. 2712-2718, Nov. 2000.
    • (2000) IEEE Trans. Inform. Theory , vol.46 , pp. 2712-2718
    • Kuai, H.1    Alajaji, F.2    Takahara, G.3
  • 4
    • 1442337676 scopus 로고    scopus 로고
    • "Lower bounds on the error probability of block codes based on improvements on de Caen's inequlaity"
    • Feb
    • A. Cohen and N. Merhav, "Lower bounds on the error probability of block codes based on improvements on de Caen's inequlaity," IEEE Trans. Inform. Theory, vol. 50, pp. 290-310, Feb. 2004.
    • (2004) IEEE Trans. Inform. Theory , vol.50 , pp. 290-310
    • Cohen, A.1    Merhav, N.2
  • 5
    • 0003964093 scopus 로고    scopus 로고
    • "Upper bounds on maximum-likelihood decoding error probability for block codes and turbo-like codes"
    • Ph.D. dissertation, Dept. Elec. Eng., Technion-Israel Inst. Technol., Haifa, Israel
    • I. Sason, "Upper bounds on maximum-likelihood decoding error probability for block codes and turbo-like codes," Ph.D. dissertation, Dept. Elec. Eng., Technion-Israel Inst. Technol., Haifa, Israel, 2001.
    • (2001)
    • Sason, I.1
  • 6
    • 10644264847 scopus 로고    scopus 로고
    • "Bounds on the performance of maximum-likelihood decoded binary block codes in AWGN interference"
    • Ph.D. dissertation, Dept. Elec. Comput. Eng., Univ. Waterloo, Waterloo, ON, Canada
    • S. Yousefi, "Bounds on the performance of maximum-likelihood decoded binary block codes in AWGN interference," Ph.D. dissertation, Dept. Elec. Comput. Eng., Univ. Waterloo, Waterloo, ON, Canada, 2002.
    • (2002)
    • Yousefi, S.1
  • 7
    • 0027297425 scopus 로고
    • "Near Shannon limit error correcting coding and decoding: Turbo codes"
    • Geneva, Switzerland
    • C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error correcting coding and decoding: Turbo codes," in Proc. 1993 IEEE Int. Conf. Communications, Geneva, Switzerland, 1993, pp. 1064-1070.
    • (1993) Proc. 1993 IEEE Int. Conf. Communications , pp. 1064-1070
    • Berrou, C.1    Glavieux, A.2    Thitimajshima, P.3
  • 8
    • 0001585514 scopus 로고    scopus 로고
    • "Coding theorems for 'Turbolike' codes"
    • Monticello, IL, Sept. 23-25
    • D. Divsalar, H. Jin, and R. J. McEliece, "Coding theorems for 'Turbolike' codes," in Proc. 1998 Allerton Conf., Monticello, IL, Sept. 23-25, 1998.
    • (1998) Proc. 1998 Allerton Conf.
    • Divsalar, D.1    Jin, H.2    McEliece, R.J.3
  • 10
    • 0030219216 scopus 로고    scopus 로고
    • "Near Shannon limit performance of low density parity check codes"
    • Aug
    • 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, Aug. 1996.
    • (1996) Electron. Lett. , vol.32 , pp. 1645-1646
    • MacKay, D.J.C.1    Neal, R.M.2
  • 12
    • 0032097155 scopus 로고    scopus 로고
    • "New performance bounds for Turbo codes"
    • June
    • T. M. Duman and M. Salehi, "New performance bounds for Turbo codes," IEEE Trans. Commun., vol. 46, pp. 717-723, June 1998.
    • (1998) IEEE Trans. Commun. , vol.46 , pp. 717-723
    • Duman, T.M.1    Salehi, M.2
  • 13
    • 0032675342 scopus 로고    scopus 로고
    • "Performance bounds for turbo-coded modulation systems"
    • Apr
    • T. M. Duman and M. Salehi, "Performance bounds for turbo-coded modulation systems," IEEE Trans. Commun., vol. 47, pp. 511-521, Apr. 1999.
    • (1999) IEEE Trans. Commun. , vol.47 , pp. 511-521
    • Duman, T.M.1    Salehi, M.2
  • 14
    • 0033316878 scopus 로고    scopus 로고
    • "The union bound for Turbo-coded modulation systems over fading channels"
    • Oct
    • T. M. Duman and M. Salehi, "The union bound for Turbo-coded modulation systems over fading channels," IEEE Trans. Commun., vol. 47, pp. 1495-1502, Oct. 1999.
    • (1999) IEEE Trans. Commun. , vol.47 , pp. 1495-1502
    • Duman, T.M.1    Salehi, M.2
  • 15
    • 0033899913 scopus 로고    scopus 로고
    • "Improved upper bounds on the decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum"
    • Jan
    • I. Sason and S. Shamai (Shitz), "Improved upper bounds on the decoding error probability of parallel and serial concatenated turbo codes via their ensemble distance spectrum," IEEE Trans. Inform. Theory, vol. 46, pp. 1-23, Jan. 2000.
    • (2000) IEEE Trans. Inform. Theory , vol.46 , pp. 1-23
    • Sason, I.1    Shamai, S.2
  • 16
    • 0033890903 scopus 로고    scopus 로고
    • "Improved upper bounds on the ensemble performance of ML decoded low density parallel check codes"
    • Mar
    • I. Sason and S. Shamai (Shitz), "Improved upper bounds on the ensemble performance of ML decoded low density parallel check codes," IEEE Commun. Lett., vol. 4, pp. 89-91, Mar. 2000.
    • (2000) IEEE Commun. Lett. , vol.4 , pp. 89-91
    • Sason, I.1    Shamai, S.2
  • 17
    • 0035442510 scopus 로고    scopus 로고
    • "On improved bounds on the decoding error probability of block codes over interleaved fading channels, with applications to turbo-like codes"
    • Nov
    • I. Sason and S. Shamai (Shitz), "On improved bounds on the decoding error probability of block codes over interleaved fading channels, with applications to turbo-like codes," IEEE Trans. Inform. Theory, vol. 47, pp. 2275-2299, Nov. 2001.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 2275-2299
    • Sason, I.1    Shamai, S.2
  • 18
    • 8144221312 scopus 로고
    • "Properties of error-correcting codes at low signal-to-noise ratios"
    • July
    • E. C. Posner, "Properties of error-correcting codes at low signal-to-noise ratios," SIAM J. Appl. Math., vol. 15, pp. 775-798, July 1967.
    • (1967) SIAM J. Appl. Math. , vol.15 , pp. 775-798
    • Posner, E.C.1
  • 19
  • 20
    • 0026045314 scopus 로고
    • "On the error probability of signals in additive white Gaussian noise"
    • Jan
    • B. Hughes, "On the error probability of signals in additive white Gaussian noise," IEEE Trans. Inform. Theory, vol. 37, pp. 151-155, Jan. 1991.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 151-155
    • Hughes, B.1
  • 21
    • 0001597243 scopus 로고
    • "A class of binary signaling alphabets"
    • Jan
    • D. Slepian, "A class of binary signaling alphabets," Bell Syst. Tech. J., vol. 35, pp. 203-234, Jan. 1956.
    • (1956) Bell Syst. Tech. J. , vol.35 , pp. 203-234
    • Slepian, D.1
  • 22
    • 80054814722 scopus 로고
    • "Group codes for the Gaussian channel"
    • Apr
    • D. Slepian, "Group codes for the Gaussian channel," Bell Syst. Tech. J., vol. 47, no. 4, pp. 572-602, Apr. 1968.
    • (1968) Bell Syst. Tech. J. , vol.47 , Issue.4 , pp. 572-602
    • Slepian, D.1
  • 23
    • 0026220377 scopus 로고
    • "Geometrically uniform codes"
    • Sept
    • G. D. Forney, Jr., "Geometrically uniform codes," IEEE Trans. Inform. Theory, vol. 37, pp. 1241-1260, Sept. 1991.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1241-1260
    • Forney Jr., G.D.1
  • 24
    • 0028427577 scopus 로고
    • "Techniques of bounding the probability of decoding error for block-coded modulation structures"
    • May
    • H. Herzberg and G. Poltyrev, "Techniques of bounding the probability of decoding error for block-coded modulation structures," IEEE Trans. Inform. Theory, vol. 40, pp. 903-911, May 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 903-911
    • Herzberg, H.1    Poltyrev, G.2
  • 25
    • 0030129868 scopus 로고    scopus 로고
    • "The error probability of M-ary PSK block-coded modulation schemes"
    • Apr
    • H. Herzberg and G. Poltyrev, "The error probability of M-ary PSK block-coded modulation schemes," IEEE Trans. Commun., vol. 44, pp. 427-433, Apr. 1996.
    • (1996) IEEE Trans. Commun. , vol.44 , pp. 427-433
    • Herzberg, H.1    Poltyrev, G.2
  • 26
    • 0028462704 scopus 로고
    • "Bounds on the decoding error probability of binary linear codes via their spectra"
    • July
    • G. Poltyrev, "Bounds on the decoding error probability of binary linear codes via their spectra," IEEE Trans. Inform. Theory, vol. 40, pp. 1284-1292, July 1994.
    • (1994) IEEE Trans. Inform. Theory , vol.40 , pp. 1284-1292
    • Poltyrev, G.1
  • 27
    • 0003811543 scopus 로고    scopus 로고
    • "A simple tight bound on error probability of block codes with application to turbo codes"
    • NASA, JPL, Pasadena, CA, TMO Progr. Rep. 42-139
    • D. Divsalar, "A simple tight bound on error probability of block codes with application to turbo codes," NASA, JPL, Pasadena, CA, TMO Progr. Rep. 42-139, 1999.
    • (1999)
    • Divsalar, D.1
  • 28
    • 0019021257 scopus 로고
    • "The technology of error-correcting codes"
    • May
    • E. R. Berlekamp, "The technology of error-correcting codes," Proc. IEEE, vol. 68, pp. 564-593, May 1980.
    • (1980) Proc. IEEE , vol.68 , pp. 564-593
    • Berlekamp, E.R.1
  • 29
    • 0036912818 scopus 로고    scopus 로고
    • "Variations on the Gallager bounds, connections and applications"
    • Dec
    • I. Sason and S. Shamai (Shitz), "Variations on the Gallager bounds, connections and applications," IEEE Trans. Inform. Theory, vol. 48, pp. 3029-3051, Dec. 2002.
    • (2002) IEEE Trans. Inform. Theory , vol.48 , pp. 3029-3051
    • Sason, I.1    Shamai, S.2
  • 30
    • 8144229647 scopus 로고    scopus 로고
    • "Generalized tangential sphere bound on the ML decoding error probability of linear binary block codes in AWGN interference"
    • Nov
    • S. Yousefi and A. K. Khandani, "Generalized tangential sphere bound on the ML decoding error probability of linear binary block codes in AWGN interference," IEEE Trans. Inform. Theory, vol. 50, pp. 2810-2815, Nov. 2004.
    • (2004) IEEE Trans. Inform. Theory , vol.50 , pp. 2810-2815
    • Yousefi, S.1    Khandani, A.K.2
  • 33
    • 0000850549 scopus 로고
    • "An upper bound for the probability of a union"
    • D. Hunter, "An upper bound for the probability of a union," J. Appl. Probab., vol. 13, pp. 597-603, 1976.
    • (1976) J. Appl. Probab. , vol.13 , pp. 597-603
    • Hunter, D.1
  • 34
    • 0003677229 scopus 로고    scopus 로고
    • New York: Springer-Verlag
    • R. Diestel, Graph Theory. New York: Springer-Verlag, 1997.
    • (1997) Graph Theory
    • Diestel, R.1
  • 35
    • 70350674995 scopus 로고
    • "On the shortest spanning tree of a graph and the traveling salesman problem"
    • J. B. Kruskal, "On the shortest spanning tree of a graph and the traveling salesman problem," Proc. Amer. Math. Soc., no. 7, pp. 48-50, 1956.
    • (1956) Proc. Amer. Math. Soc. , Issue.7 , pp. 48-50
    • Kruskal, J.B.1
  • 36
    • 84911584312 scopus 로고
    • "Shortest connection networks and some generalizations"
    • R. C. Prim, "Shortest connection networks and some generalizations," Bell Syst. Tech. J., no. 36, pp. 1389-1401, 1957.
    • (1957) Bell Syst. Tech. J. , Issue.36 , pp. 1389-1401
    • Prim, R.C.1
  • 37
    • 0002726668 scopus 로고
    • "On the history of the minimum spanning tree problem"
    • R. L. Graham and P. Hell, "On the history of the minimum spanning tree problem," Ann. History of Comput., vol. 7, no. 1, pp. 43-57, 1985.
    • (1985) Ann. History of Comput. , vol.7 , Issue.1 , pp. 43-57
    • Graham, R.L.1    Hell, P.2
  • 39
    • 0032202120 scopus 로고    scopus 로고
    • "A lower bound on the error probability for signals in white Gaussian noise"
    • Nov
    • G. E. Séguin, "A lower bound on the error probability for signals in white Gaussian noise," IEEE Trans. Inform. Theory, vol. 44, pp. 3168-3175, Nov. 1998.
    • (1998) IEEE Trans. Inform. Theory , vol.44 , pp. 3168-3175
    • Séguin, G.E.1
  • 41
    • 0029307577 scopus 로고
    • "A lower bound on the error probability for signals in white Gaussian noise"
    • May
    • P. F. Swaszek, "A lower bound on the error probability for signals in white Gaussian noise," IEEE Trans. Inform. Theory, vol. 41, pp. 837-841, May 1995.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 837-841
    • Swaszek, P.F.1
  • 42
    • 0003549770 scopus 로고    scopus 로고
    • "Turbo codes and turbo-coded modulation systems: Analysis and performance bounds"
    • Ph.D. dissertation, Dept. Elec. Comput. Eng., Northeastern Univ., Boston, MA
    • T. M. Duman, "Turbo codes and turbo-coded modulation systems: Analysis and performance bounds," Ph.D. dissertation, Dept. Elec. Comput. Eng., Northeastern Univ., Boston, MA, 1998.
    • (1998)
    • Duman, T.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.