A Survey of Error-Control Codes

  • P. G. Farrell
Part of the International Centre for Mechanical Sciences book series (CISM)


In order to introduce error-control coding, it is convenient initially to consider coding in a wider context. In general, coding is a form of mapping; that is, the conversion of a given sequence, stream or set of digits or symbols into another sequence or set of digits.


Linear Code Block Code Parity Check Code Word Cyclic Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    F.M. Peza, An introduction to information theory, McGraw-Hill, 1961.Google Scholar
  2. 2.
    R.G. Gallager, Information theory and relia to comnunication, Wiley, 1968.Google Scholar
  3. 3.
    T. Berger, Rate distortion theory — A mathematical basis for data compression, Prentice-Hall, 1971.Google Scholar
  4. 4.
    D.A. Huffman, A method for the construction of minimum redundancy codes, Proc. IRE, 40, 1098, Sept. 1952.CrossRefGoogle Scholar
  5. 5.
    G. Longo, Source coding theory, Lecture notes, CISM, Udine, 1970.Google Scholar
  6. 6.
    B.P. Tunstall, Synthesis of Noiseless compression codes, Ph.D. Dissertation, Georgia Inst. Tech., Atlanta, 1968.Google Scholar
  7. 7.
    D.W. Davies & D.L.A. Barber, Communication networks for computers, Wiley, 1973.Google Scholar
  8. 8.
    J. Salz & B.R. Saltzberg, Double error rates in differentially coherent phase systems, IEEE Trans, COM-12, 202, June, 1964.CrossRefGoogle Scholar
  9. 9.
    P.G. Farrell, Coding for noisy data links, Ph.D. Dissertation, Universtiy of Cambridge, 1969.Google Scholar
  10. 10.
    J.L. Massey, Joint source and channel coding, Proc. NATO ASI on Cormm. Systs and Random Process Theory, North-Holland, 1978.Google Scholar
  11. 11.
    K.W. Cattermole, Principles of pulse code modulation, Iliffe, 1969.Google Scholar
  12. 12.
    W.W. Peterson & E.J. Weldon, Error-correcting codes, MIT Press, 1972.zbMATHGoogle Scholar
  13. 13.
    Shu Lin, An introduction to error-correcting codes, Prentice-Hall, 1970.Google Scholar
  14. 14.
    F.J. Macwilliams & N.J.A. Sloane, The theory of error-correcting codes, Vols. I & II, North-Holland, 1977.Google Scholar
  15. 15.
    E.R. Berlekamp, Algebraic coding theory, McGraw-Hill, 1968.zbMATHGoogle Scholar
  16. 16.
    I.F. Blake & R.C. Mullin, The nathematic theory of coding, Academic Press, 1975.Google Scholar
  17. 17.
    H.B. Mann (Ed.), Error correcting codes, Wiley, 1968.Google Scholar
  18. 18.
    E.G. Search, Performance of Multilevel error control codes, M.Sc. Dissertation, University of Kent at Canterbury, 1977.Google Scholar
  19. 19.
    D. Slepian, Some further theory of group codes, BSTJ, 39, 5, 1219, Sept. 1960.MathSciNetGoogle Scholar
  20. 20.
    N. Tokura et al., A search procedure for finding optimum group codes for the binary symmetric channel, IEEE Trans, IT-13, 4, 587, Oct. 1967.Google Scholar
  21. 21.
    J.L. Massey & M.K. Sain, Inverses of linear sequential machines, IEEE Trans, C-17, 330, April 1968.zbMATHGoogle Scholar
  22. 22.
    D.J. Costello, A streng lower bound on free distance for periodic convolutional codes, Proc. IEEE Int. Symp. on Info. Theory, Noordwijk, 1970.Google Scholar
  23. 23.
    R.W. Haimting, Error detecting and error correcting codes, BSTJ, 26, 2, 147, April 1950.Google Scholar
  24. 24.
    D. Slepian, A class of binary signalling alphabets, BSTJ, 35, 203, Jan. 1956.MathSciNetGoogle Scholar
  25. 25.
    D. Slepian, Group codes for the Gaussian channel, BSTJ, 47, 575, 1968.MathSciNetzbMATHGoogle Scholar
  26. 26.
    D. Slepian, Permutation modulation, Proc. IEEE, 53, 3, 228, March 1965.CrossRefGoogle Scholar
  27. 27.
    S.I. Samoylenko, Binoid error-correcting codes, IEEE Trans, IT-19, 95, Jan. 1973.MathSciNetzbMATHGoogle Scholar
  28. 28.
    G.D. Forney, Burst-correcting codes for the classic bursty channel, IEEE Trans, CQM-19, 5, 772, Oct. 1971, Part II.CrossRefGoogle Scholar
  29. 29.
    D.W. Hagelbarger, Recurrent codes — easily mechanised burst- correcting, binary codes, BSTJ, 38, 4, 969, July 1959.MathSciNetGoogle Scholar
  30. 30.
    A.D. Wyner & R.B. Ash, Analysis of Recurrent Codes, IEEE Trans, IT-9, 3, 143, July 1963.MathSciNetzbMATHGoogle Scholar
  31. 31.
    A. Kohlenberg & G.D. Forney, Convoluticnal coding for channels with memory, IEEE Trans, IT-14, 5, 618, Sept. 1968.Google Scholar
  32. 32.
    C.E. Shannon, A Mathematical Theory of Camunicaticn, BSTJ, 27, July p 379, Oct. p 623, 1948 (also Univ. of Illinois Press, 1963).MathSciNetzbMATHGoogle Scholar
  33. 33.
    M.J.E. Golay, Notes on Digital Coding, Proc IRE, 37, 6, 657, Jan. 1949.Google Scholar
  34. 34.
    M.J.E. Golay, Binary coding, IRE Trans, IT-4, 23, Sept. 1954.Google Scholar
  35. 35.
    D.A. Huffman, The synthesis of linear sequential coding networks, 3rd London Synp. on Info. Theory, Sept. 1955; Ed. Cherry, 1956.Google Scholar
  36. 36.
    D.A. Huffman, A linear circuit viewpoint on error-correcting codes, IRE Trans, IT-2, 3, 20, Dec. 1956.MathSciNetGoogle Scholar
  37. 37.
    B. Elspas, The theory of Autonomous linear networks, IRE Trans, CT-6, 1, 45, March 1959.MathSciNetGoogle Scholar
  38. 38.
    J.J. Stiffler, Theory of synchronous communications, Prentice-Hall, 1971.Google Scholar
  39. 39.
    H.C.A. Van Durren, Typendruktelegraphie over Radioverbindigen, Tydschrift van het Netherlands Radio Genootschap, 16, 53, March 1951.Google Scholar
  40. 40.
    H.C.A. Van Durren, Error probability and transmission speed on circuits using error detection and automatic repetition of signals, IRE Trans, CS-9, 1, 38, March 1961.CrossRefGoogle Scholar
  41. 41.
    R.J. Benice & A.H. Frey, Improvements in the Design of Retransmission Systems, IEEE Trans, CCM-15, 3, 463, June 1967.CrossRefGoogle Scholar
  42. 42.
    A.R.J. Sastry, Improving ARQ performance on satellite channels under high error rate conditions, IEEE Trans, CCM-23, 4, 436, April 1975.CrossRefGoogle Scholar
  43. 43.
    J.P.M. Schalkwijk & T. Kailath, A coding scheme for additive noise channels with feedback — Part i: No bandwidth constraint, IEEE Trans, IT-12, 2, 172, April 1966; Part II: Band-limited signals, 183.MathSciNetzbMATHGoogle Scholar
  44. 44.
    A.J. Kramer, Use of Orthogonal signalling in sequential decision feedback, Info. & Control, 10, 509, May 1967.CrossRefzbMATHGoogle Scholar
  45. 45.
    K. Brayer, ARQ and Hybrid FEC-ARQ system design to meet tight performance constraints, Proc. NIC DAllas, II, 24.6–1/6–5, Nov.-Dec. 1976.Google Scholar
  46. 46.
    E.Y. Rocher & R.L. Pickholtz, An analysis of the effectiveness of hybrid transmission schemes, IBM Jour Res Dev, 426, July 1970.Google Scholar
  47. 47.
    D.M. Mandelbaum, An adaptive feedback coding scheme using incremented redundancy, IEEE Trans, IT-20, 3, 388, May 1974.zbMATHGoogle Scholar
  48. 48.
    P.S. Sindhu, Retransmission error control with memory, IEEE Trans, CQM-25, 5, 473, May 1977.CrossRefzbMATHGoogle Scholar
  49. 49.
    R.L. Kirlin, Variable Block length and transmission efficiency, IEEE Trans, COM-17, 3, 350, June 1969.CrossRefGoogle Scholar
  50. 50.
    R.M.F. Goodman & P.G. Farrell, Data transmission with variable redundancy error control over a high-frequency channel, Proc. IEE, 122, 2, 113, Feb. 1975.Google Scholar
  51. 51.
    G. Neri, et al., A reliable protocol for high-speed packet transmission, IEEE Trans, COM-25, 10, 1203, Oct. 1977.CrossRefGoogle Scholar
  52. 52.
    P. Elias, Error-free coding, IRE Trans, IT-4, 29, Sept. 1954.MathSciNetGoogle Scholar
  53. 53.
    J.M. Wozencraft, Sequential decoding for reliable catmunication, IRE Nat. Com. Reo., Pt 2, p 11, 1957.Google Scholar
  54. 54.
    Z. Kiyasu, Res. and Dev. Data No 4, Elec. Cornu Lab., Nippon Tele. Corp., Tokyo.Google Scholar
  55. 55.
    G. Forney & E.K. Bower, A high-speed sequential decoder, IEEE Trans, COM-19, 5, Pt. II, 821, Oct. 1971.CrossRefGoogle Scholar
  56. 56.
    J.E. Meggitt, Error correcting codes and their implementation for data transmission systems, IEEE Trans, IT-7, 4, 234, Oct. 1960.MathSciNetGoogle Scholar
  57. 57.
    V.C. Rocha, Versatile error-control coding systems, Ph.D. Dissertation, Univ. of Kent at Canterbury, 1976.Google Scholar
  58. 58.
    F.J. Macwillianis, Permutation decoding of systematic codes, BSTJ, 43, 485.Google Scholar
  59. 59.
    J.J. Metzner, VAriable-length block codes with internal sequential decoding and retransmission strategies, Proc. NTC Dallas, II, 24.2–1/3–5, Dec. 1976.Google Scholar
  60. 60.
    J.L. Katz, A feedback cannunication system using convolutional codes, Ph.D. Dissertation, Purdue Univ. 1971.Google Scholar
  61. 61.
    R.W. Lucky, J. Salz & E.J. Weldon, Principles of aata communication, McGraw-Hill, 1968.Google Scholar
  62. 62.
    R.L. Tcwnsend & E.J. Weldon, Self-orthogonal quasi-cyclic codes, IEEE Trans, IT-13, 2, 183, April 1967.Google Scholar
  63. 63.
    L.D. Rudolph & CR.P. Hartmann, Decoding by sequential code reduction, IEEE Trans, IT-19, 4, 549, July 1973.MathSciNetzbMATHGoogle Scholar
  64. 64.
    L.E. Wright & L.F. Turner, Simplified decoders for projective-gecmetry codes, Proc IEE, 125, 5, 365, May 1978.Google Scholar
  65. 65.
    L.D. Rudolph, Threshold decoding of cyclic codes, IEEE Trans, IT-15, 3, 414, May 1969.MathSciNetzbMATHGoogle Scholar
  66. 66.
    J.L. Massey, Threshold decoding, MIT Press, 1963.Google Scholar
  67. 67.
    I.M. Jacobs & E.R. Berlekamp, A lower bound to the distribution of ocnputation for sequential decoding, IEEE Trans, IT-13, 2, 167, April 1967.Google Scholar
  68. 68.
    J.E. Savage, The distribxition of sequential decoding computation time, IEEE Trans, IT-12, 143.Google Scholar
  69. 69.
    J.M. Wbzencraft & M. Horstein, Coding for two-way channels, Proc. 4th London Symp. on Info. Theory, Ed. C. Cherry, p 11, 1961.Google Scholar
  70. 70.
    R.M. Fano, A heuristic discussion of probabilistic decoding, IEEE Trans, IT-9, 2, 64, April 1963.MathSciNetGoogle Scholar
  71. 71.
    W.H. Ng & R.M.F. Goodman, An efficient minimumrdistance decoding algorithm for convoluticnal error-correcting codes, Proa IEE, 125, 2, 97, Feb. 1978.Google Scholar
  72. 72.
  73. 73.
    J. Hagenauer, Sequential decoding for burst-error-channels, Proc. NATO ASI on Comm. Systems and Random Processes, North-Holland, 1978.Google Scholar
  74. 74.
    A.J. Viterbi, Error bounds for convolutional codes and an Asymptotically optimum decoding algorithm, IEEE Trans, IT-13, 2, 260, April 1967.zbMATHGoogle Scholar
  75. 75.
    J.G. Proakis, Performance capabilities of the Viterbi Algorithm for catibatting intersymbol interference on fading multipath channels, Proc. NATO ASI on Comm. Systs and Random Processes, North-Holland, 1978.Google Scholar
  76. 76.
    F. Heirmati & D.J. Costello, Truncation error probability in Viterbi decoding, IEEE Trans, COM-25, 5, 530, May 1977.CrossRefGoogle Scholar
  77. 77.
    P.S. Moharir, Totally selective convolutional decoding, Elec. Letters, 12, 7, 161, 1st April 1976.CrossRefGoogle Scholar
  78. 78.
    F. Jelinek, A fast sequential decoding algorithm using a stack, IBM Jour. Res. Dev., 13, 675, Nov. 1969.MathSciNetCrossRefzbMATHGoogle Scholar
  79. 79.
    D. Haccoun & M.J. Ferguson, Genralised stack algorithms for decoding convolutional codes, IEEE Trans, IT-21, 6, 638, Nov. 1975.zbMATHGoogle Scholar
  80. 80.
    P.R. Chevillat & D.J. Costello, A multiple stack algorithm for erasure free decoding of convolutional codes, IEEE Trans, CGM-25, 12, 1460, Dec. 1977.CrossRefzbMATHGoogle Scholar
  81. 81.
    J.P.M. Schalkwijk & A.J. Vinck, Syndrome decoding of convolutional codes, IEEE Trans, COM-23, 789, July 1975.CrossRefzbMATHGoogle Scholar
  82. 82.
    J.P.M. Schalkwijk, On the performance of a maximum likelihood decoder for convolutional codes, AGARD Symp. on Dig. Cairns in Avionics, Munich, June 1978, pp 13–1/13–6 (AGARD Conf. Preprint No. 239).Google Scholar
  83. 83.
    J.K. Wolf, Efficient maximum likelihood decoding of linear block codes using a trellis, IEEE Trans, 3T-24, 1, 76, Jan. 1978.Google Scholar
  84. 84.
    J.M. Wozencraft & R.S. Kennedy, Modulation and demodulation for probabilistic decoding, IEEE Trans, IT-12, 4, 291, July 1966.Google Scholar
  85. 85.
    M. BAlser & R.A. Silverman, Coding for constant-data-rate systems, Part I, Proc IRE, 42, 9, 1428, Sept. 1954; Part II, Proc IRE, 43, 6, 728, June 1955.CrossRefGoogle Scholar
  86. 86.
    C.R. Cahn, Binary decoding extended to Nonbiliary demodulation of phase shift keying, IEE Trans, COM-17, 5, 583, Oct. 1969.CrossRefGoogle Scholar
  87. 87.
    P.G. Farrell, E. Munday & N. Kalligeros, Digital cemnunicaticns using soft-decision detection techniques, AGARD Synp. on Dig. Cairns in Avionics, Munich, June 1978, p 14.1/9.Google Scholar
  88. 88.
    K.L. Jordan, The performance of sequential decoding in conjunction with efficient modulation, IEEE Trans, CCM-14, 3, 283, June 1966.CrossRefGoogle Scholar
  89. 89.
    R.M.F. Goodman & W.H. Ng, Soft-decision threshold decoding of convolutional codes, Proc 1ERE on Digital processing of signals in communications, 37, 535, Loughborough, Qigland, 1977.Google Scholar
  90. 90.
    C.E. Sundberg, Asymptotically optimum soft-decision decoding algorithms for Hanming codes, Elec Letters, 13, 2, 38, 20th Jan. 1977.MathSciNetCrossRefGoogle Scholar
  91. 91.
    C.N. Harrison, Application of soft decision techniques to block codes, Proc 1ERE Conf. on Digital processing of signals in communications, 37, 331, Loughborough, Bigland, 1977.Google Scholar
  92. 92.
    G. Forney, Genralised minimum distance decoding, IEEE Trans, IT-12, 2 (April), 125, and in “Concatenated codes”, MIT Res. Memo. 37, 1966.MathSciNetzbMATHGoogle Scholar
  93. 93.
    S.M. Reddy & J.P. Robinson, Random error and burst correction by iterated codes, IEEE Trans, IT-18, 182, 1972.MathSciNetzbMATHGoogle Scholar
  94. 94.
    G. Einarsson & C.E. Sundberg, A note en soft-decision decoding with successive erasures, IEEE Trans, IT-22, 1 (Jan.), 88, 1976.MathSciNetzbMATHGoogle Scholar
  95. 95.
    R.M.F. Goodman & A.D. Green, Microprocessor controlled soft-decision decoding of error-correcting block codes. Proc. IERE Conf. on Digital processing of signals in communieations, 37, 37, Loughborough, England, 1977.Google Scholar
  96. 96.
    E.J. Weldon, Decoding binary block codes on Q-ary output channels, IEEE Trans, IT-17, 6 (Nov.), 713, 1971.MathSciNetzbMATHGoogle Scholar
  97. 97.
    C.E. Sundberg, One-step majority logic decoidng with symbol reliability information, IEE Trans, IT-21, 2 (March), 236, 1975.MathSciNetzbMATHGoogle Scholar
  98. 98.
    C.R.P. Hartmann & L.D. Rudolph, An optiirrum syrribol-by-synibol decoding rule for linear codes, IEEE Trans, IT-22, 5 (Sept), 514, 1976.MathSciNetzbMATHGoogle Scholar
  99. 99.
    B. Dorsch, A decoding algorithm for binary block codes and J-ary Output channels, IEE Trans, IT-20, 3 (May), 391, 1974.zbMATHGoogle Scholar
  100. 100.
    P.G. Farrell, Soft-decision minimum-distance decoding, Proo NATO ASI on Communications systems and random process theory, Darlington, England, Aug. 1977; North-Holland, 1978.Google Scholar
  101. 101.
    P.G. Farrell & E. Munday, Variable-redundancy HF digital ccorrunications with adaptive soft-decision minimum-distance decoding, Final Rep. Res. Study Contract AT/2099/05/ASWE MOD, May 1978.Google Scholar
  102. 102.
    D. McQuilton & M.E. Woodward, Pseudostep orthogonalisation — an algorithm for improving Reed-Massey threshold codes, Elec Letters, 14, 12, 355, 8th June 1978.CrossRefGoogle Scholar
  103. 103.
    Barry Research Corp, Time-diversity modem, Palo Alto, Calif. USA, 1974.Google Scholar
  104. 104.
    G. Andjargholi, Spread-spectrum data transmission at HF, Ph.D. Thesis, University of Kent at Canterbury, 1976.Google Scholar
  105. 105.
    P.G. Farrell & G. Andjargholi, A spread-spectrum digital transmission system for reliable communication in the HF band, Proo IEE Colloq. on HF Communication systems, London, Feb. 1976.Google Scholar
  106. 106.
    P.R. Keller, An automatic error correction system for uniderectional HF teleprinter circuits, Point-to-Point Telecoms, 7, 3, 1, June 1963.Google Scholar
  107. 107.
    M. Tcmlinson & B. H. Davies, Low error rate correction coding for channels with pahse jitter, Report No.77004, RSRE, Feb. 1977.Google Scholar
  108. 108.
    J. Pieper, et al., The use of constant weight block codes for the underwater channel, Proc IEEE EASCON.Sept. 1977, Arlington, U.S.A., p 36.Google Scholar
  109. 109.
    J.B. Moore, US Patent 2,183,147, 1934.Google Scholar
  110. 110.
  111. 111.
    The Netherlands, Contribution to data transmission over isochronous systems and to error control, CCnT Blue Book 1964, Supp.17, 169.Google Scholar
  112. 112.
    H.B. Voelcker, Simple codes for fading circuits, IRE Trans, CS-6, 47, Dec. 1958.CrossRefGoogle Scholar
  113. 113.
    R. Treciokas, Application of FEE to a Raleigh fading HF ccmnunication channel, Proo IEE, 125, 3, 173, March 1978.Google Scholar
  114. 114.
    Marconi Ltd., SPBCTOR, A new telegraph error correcting system.Google Scholar
  115. 115.
    M.-Y. Hsiao & J.T. Tou, Application of error-correcting codes in ccmputer reliability studies, IEEE Trans, R-18, 3, 108, Aug. 1969.Google Scholar
  116. 116.
    G. Riley, Error control for data multiplex systems, Ph.D. thesis, Univ. of Kent at Canterbury, 1975.Google Scholar
  117. 117.
    M. Goldberg, Easily decoded error-correcting codes and tehcniques for their generation, Ph.D. thesis, Univ. of London, 1971.Google Scholar
  118. 118.
    N.E. Head, A high-speed data transmission system, GEC Jour, 30, 3, 129, 1963.Google Scholar
  119. 119.
    N.J.A. Slcane, A simple description of an error-correcting code for high-density magnetic tape, BSTJ, 55, 2, 157, Feb. 1976.Google Scholar
  120. 120.
    D.T. Brown & F.F. Sellers, Error correction for IBM 800-bit-per-inch magnetic tape, IBM Jour. Res. Dev., 384, July 1970.Google Scholar
  121. 121.
    C.D. Mathers, Digital video recording — some experiments in error protection, BBC Res. Dept. Rep. 1976/1, Jan. 1976.Google Scholar
  122. 122.
    M.E. Kanter, A check digit technology for data preparation (off-line) equipment, M.Sc. dissertation, Univ. of Kent at Canterbury, 1971.Google Scholar
  123. 123.
    J.H. Van Lint, Coding theory, Springer-Verlag, 1971.zbMATHGoogle Scholar
  124. 124.
    Scientific Control Systems Ltd, SPARQ of life for HF.Google Scholar
  125. 125.
    P. Darrington, Wireless World Teletext Decoder, Wireless World, 498, Nov. 1975.Google Scholar
  126. 126.
    R.W. Levell, The application of a Hanming error correcting codes to a standard teletype equipment, Jour. Brit. IRE, 371, Nov. 1961.Google Scholar
  127. 127.
    A.H. Cribbens, et al., An experimental application of microprocessors to railway signalling, Electronics & Power, 209, March 1978.Google Scholar
  128. 128.
    B. Hillam & G.F. Gott, An experimental evaluation of interleaved block coding in aeronautical HF channels, AGARD Symp on Dig. Conns in Avionics, Munich, June 1978.Google Scholar
  129. 129.
    J. Brooks, Error correcting stores for a small computer, New Elec, 30, October 5th, 1976.Google Scholar
  130. 130.
    M.Y. Hsiao, A class of optimal minimum odd-weight-colurm SBC-DED codes, IBM Jour. Res. Dev., 395, July 1970.Google Scholar
  131. 131.
    S.W. Golomb (Ed.), Digital communications with space applications, Prentice-Hall, 1964.zbMATHGoogle Scholar
  132. 132.
    D.C. Bossen, b-Adjacent error correction, IBM Jour. Res. Dev., 402, July 1970.Google Scholar
  133. 133.
    G. Benelli, et al., Generalised Hanming codes for burst-error-correction, Alta Frequenza, 44, Nov. 1975.Google Scholar
  134. 134.
    N.M. Abramson, A class of systematic codes for non-independent errors, IRE Trans, IT-5, 4, 150, Dec. 1959.MathSciNetGoogle Scholar
  135. 135.
    C. Badran, Double adjacent error correction, M.Sc. Dissertation, Univ. of Kent at Canterbury, March 1976.Google Scholar
  136. 136.
    C.R. Telfer, The generation of codes for DPSK channels, Proc. Conf. on Dig. Proc. of Signals in Ccmms, Loughborough, p 403, Sept. 1977.Google Scholar
  137. 137.
    I.S. Reed, A class of multiple-error-correcting codes and the decoding scheme, IEEE Trans, Vol IT-4, 38, 1954.Google Scholar
  138. 138.
    D.E. Muller, Application of Boolean algebra to switching circuit design and to error detection, IEEE Trans, V-3, 6, 1954.Google Scholar
  139. 139.
    J.H. Green & R.L. San Soucie, An error-correcting encoder and decoder of high efficiency, Proc IRE, 46, 7, 1741, Oct. 1958.Google Scholar
  140. 140.
    H.J. Crowley, A field test of error control systems, IEEE Trans. CQM-17, 5, 569, Oct. 1969.CrossRefGoogle Scholar
  141. 141.
    R.C. Dixon, Spread-spectrum systems, Wiley, 1976.Google Scholar
  142. 142.
    E.D. Gibson, Exceptionally cost-effective error control, IEEE Int. Comms. Conf. Digest, June 1976.Google Scholar
  143. 143.
    Linkabit Corp., Error control products. Google Scholar
  144. 144.
    B.E. Sinclair, An error reducing coding system for digital satellite comunication systems, IEE Conf. Pub. No. 39, April 1968.Google Scholar
  145. 145.
    P. McNanamon, R. Jane & S. Tsai, HF ccmnunications performance: Coding and diversity, Telecoms, 27, August 1970.Google Scholar
  146. 146.
    K. Brayer, Error-correction code performance on HF, troposcatter and satellite channels, IEEE Trans, C0M-19, 5, 781, Oct. 1971.CrossRefGoogle Scholar
  147. 147.
    S.-Y. Tong, Burst trapping techniques for a compound channel, IEEE Trans, IT-15, 6, 710, Nov. 1969.zbMATHGoogle Scholar
  148. 148.
    R.C. Bose & D.K. Ray-chaudhuri, On a class of error correcting binary group codes, Info & Control, 3, 68, March 1960 and 279 1960.MathSciNetCrossRefzbMATHGoogle Scholar
  149. 149.
    A.A. Hocquenghem, Codes correcteurs d’erreurs, Chiffres, 2, 147, 1959.MathSciNetzbMATHGoogle Scholar
  150. 150.
    R.L. Townsend & R.N. Watts, Effectiveness of error control in data cotinunication over the switched telephone network, BSTJ, 43, 6, 2611, Nov. 1964.Google Scholar
  151. 151.
    R.F. Steen, Error correction for voice grade data communication using a carmunication processor, IEEE Trans, CCM-22, 10, 1595, Oct. 1974.CrossRefGoogle Scholar
  152. 152.
    F. Schreiber, et al., An error-correcting data transmission system with block-by-block synchronous operation over telephone channels, IEEE Int. Conv. Rec., pt 5, 73, 1964.Google Scholar
  153. 153.
    British Post Office, Error correction for digital transmission of broadcast quality TV signals, June 1977.Google Scholar
  154. 154.
    D.L. Cohn, Performance of selected block and convoluticnal codes on a fading HF channel, IEEE Trans, IT-14, 5, 627, Sept. 1970.Google Scholar
  155. 155.
    J.R. Juroshek, Interleaved block coding tests over VHF and HF channels, IEEE Trans, CQM-19, 5, 709, Oct. 1971.Google Scholar
  156. 156.
    P. Fire, A class of multiple-error-correcting binary codes for non-independent errors, Sylvania Elec. Products Inc., Rpt No. RSL-E12, March 1959.Google Scholar
  157. 157.
    A.H. Frey & R.E. Kavanaugh, Every data bit counts in transmission cleanup, Electronics, 77, Jan. 22nd 1968.Google Scholar
  158. 158.
    A.H. Frey, Adaptive decoding without feedback, IBM Tech. TR 48–67–001, 1967.Google Scholar
  159. 159.
    I.S. Reed & G. Solomon, Polynomial codes over certain finite fields, Jour. Soc. Ind. Applic. Maths, 8, 300.Google Scholar
  160. 160.
    H. Fredricksen, Error correction for deep space network teletype circuits, NASA Jet Prop. Lab, Rep 32–1275, June 1968.Google Scholar
  161. 161.
    G.D. Forney, Concatenated codes, MIT Res. Memo no. 37, 1966.Google Scholar
  162. 162.
    A.M. Walker, High data rate PSK modems for satellite ccmmunications, Mio. Jourr, p27, July 1976.Google Scholar
  163. 163.
    B.H. Batson & G.K. Huth, Convolutional coding at 50 MBPS for the shuttle KU-band return link, Proc. Int. Teleccms. Conf., L.A. Calif. USA, 175, Sept..1976.Google Scholar
  164. 164.
    J.W. Modestino & S.Y. Mui, Performance of convolutionally encoded noncoherent MFSK modem in fading channels, Proc Int. Telecoms Cont. L.A. Calif. USA, 433, Sept. 1976.Google Scholar
  165. 165.
    G.D. Forney & E.K. Bower, A high-speed sequential decoder, IEEE Trans, CQM-19, 5, 821, Oct. 1971.CrossRefGoogle Scholar
  166. 166.
    J.L. Massey & D.J. Costello, Nonsystematic convolutional codes for sequential decoding in space applications, IEEE Trans, COM-19, 5, 806, Oct. 1971.CrossRefGoogle Scholar
  167. 167.
    J.W. Layland & W.A. Lushbaugh, A flexible high-speed sequential decoder for deep space channels, IEEE Trans, CQM-19, 5, 813, Oct. 1971.CrossRefGoogle Scholar
  168. 168.
    J.A. Heller & I.M. Jacobs, Viterbi decoding for satellite and space carmunication, IEEE Trans, CQM-19, 5, 835, Oct. 1971.CrossRefGoogle Scholar
  169. 169.
    G.C. Clark & R.C. Davis, Two recent applications of error-correction coding to conmunications systems design, IEEE Trans, COM-19, 5, 856, Oct. 1971.CrossRefGoogle Scholar
  170. 170.
    J.H. Stott, et al.. Digital video-error-correcting codes and a practical study of a Wyner-Ash error correctior, BBC Res. Dept. Rep. RD 1974/40, Dec. 1974.Google Scholar
  171. 171.
    SPC/PSK and SCPC/PCM/PSK System Specification, Oct. 1976.Google Scholar
  172. 172.
    R.T. Chien, et al., Error correction in a radio-based data ccxtinunicatiais system, IEEE Trans, COM-23, 4, 458, April 1975.CrossRefzbMATHGoogle Scholar
  173. 173.
    W.R. Bennett & F.E. Froehlich, Sane results en the effectiveness of error-control procedures in digital data transmission, IRE Trans, CS-9, 1, 58, March 1961.Google Scholar
  174. 174.
    M.J. Ferguson, “Diffuse” threshold decodable rate 1/2 convolutional codes, IEEE Trans, IT-17, 2, 171, March 1971.MathSciNetzbMATHGoogle Scholar
  175. 175.
  176. 176.
    W.K. Pehlert, Desiqn and evaluation of a generalised burst-trapping error control system, IEEE Trans, CCM-19, 5, 863, Oct. 1971.CrossRefGoogle Scholar
  177. 177.
    B.H. Davies & G. Foley, The implementation of Viterbi decoding on satellite catinunication circuits, Proc Conf on Dig. Proc. of Sigs in Conns, Loughborough, 1ERE Conf. Pub. No. 37, 159, 1977.Google Scholar
  178. 178.
    Codex Corp, 6000 Series intelligent network processor.Google Scholar
  179. 173.
    Hewlett-Packard Ltd., On line/on location data collection, Computer Advances 2, 6, 1977.Google Scholar
  180. 180.
    Int. Data Sciences, Inc., Automatic data error corrector.Google Scholar
  181. 181.
    R. Metcalfe & D.R. Boggs, Ethernet-distributed packet switching for local canputer networks, Comm. ACM, 19, 7, 395, July 1976.Google Scholar
  182. 182.
    J.R. Nielsen & D.S. Kaplan, Data entry and ccmnunication systems have network capabilities, Hewlett Packard Jour,21, March 1978.Google Scholar
  183. 183.
    T.D. Wells, et al., Implementation of an efficient inter-cemputer network for the distribution of multidestination messages, Elec. Letters, 14, 6, 189, 16th March 1978.CrossRefGoogle Scholar
  184. 184.
    Cambridge Consultants Ltd., High speed inter-carputer highway, Elec. & Power, 337, May 1978.Google Scholar
  185. 185.
    Ocitt Special Study Group A, Report on methods of error control, Blue Book 1964, Suppl. 61, 535.Google Scholar
  186. 186.
    Ocitt Special Study Group A, Error control systems for use on the International Telex Network, Blue Book 1964, Suppl. 12, 145.Google Scholar
  187. 187.
    H.O. Burton & D.D. Sullivan, Error and error control, Proc. IEEE, 60, 11, 1293, Nov. 1972.CrossRefGoogle Scholar
  188. 188.
    E.R. Aylott & E.S. Simmonds, Error correction in data transmission systems, Jour. Brit IRE, 141, Aug. 1962.Google Scholar
  189. 189.
    F. Mirshekari, An error control simulator, M.Sc. Dissertation, Univ. of Kent at Canterbury, Dec. 1977.Google Scholar
  190. 190.
    O.O. Olaniyan & L.F. Turner, On the error-correcting capability of optimum linear block codes, Proo. IEE, 123, 1, 26, Jan. 1976.Google Scholar
  191. 191.
    A.M. Michelson, The calculation of post-decoding bit-error probabilities for binary block codes, Nat. Telecoms Conf., Dallas, II, 24.3–1, Nov.-Dec. 1976.Google Scholar
  192. 192.
    A.B. Fontaine & W.W. Peterson, Group code equivalence and optimum codes, Special Supp. IEEE Trans, CT-6, 60, May 1959.Google Scholar
  193. 193.
    C.F. Hobbs, Approximating the performance of a binary goup code, IEEE Trans, IT-11, 142, Jan. 1965.Google Scholar
  194. 194.
    C.R.R. Hartmann, et al., Asymptotic performance of optimum bit-by- fit decoding for the white Gaussian channel, IEEE Trans, IT-23, 4, 520, July 1977.zbMATHGoogle Scholar
  195. 195.
    K.A. Post, Explicit evaluation of Viterbi’s union bounds on con- volutional code performance for the BSC, IEEE Trans,IT-23, 3, 403, May 1977.zbMATHGoogle Scholar
  196. 196.
  197. 197.
    J.A. Gordon, Sane aspects of adaptive multiplexing, Ph.D. Thesis, Hatfield Polytechnic, England, June 1977.Google Scholar
  198. 198.
    J.M. Morris, Throughput performance of data — communication systems using ARQ error-control schemes, US Naval Res. Lab. Re.8140, Sept.1977.Google Scholar
  199. 199.
  200. 200.
    S.H. Lebowitz, High-rate error correction codes, the correlation decoding approach, Nat. Telecoms Conf, Dallas, I, 13.1–1, 1976.Google Scholar
  201. 201.
    A.H. Levesque, Block-error distributions and error control code performance in slew Rayleigh fading, Nat. Telecoms Conf., II, 24.4–1, 1976.Google Scholar
  202. 202.
  203. 203.
    J.P. Odenwalder, Carrier tracking, bit synchronization and coding for S-band oenmunications links, Proc. Int. Telem. Conf, Los Angeles, 467, Oct. 1974.Google Scholar
  204. 204.
    T.H. Abdel-Nabi et al., On interleaving certain block codes, Canadian Comms & Power Conf, 209, 1976.Google Scholar
  205. 205.
    G. Uhgeroeck, Channel coding with multilevel/phase signals, IBM Zurich Res. Rep. May 1977.Google Scholar
  206. 206.
    J.B. Anderson & R. De Buda, Better phase-modulation error performance using trellis phase codes, Elec Letters, 12, 22, 587, 28th Oct. 1976.CrossRefGoogle Scholar
  207. 207.
    I.M. Jacobs, Practical applications of coding, IEEE Trans, IT-20, 3, 305, May 1974.zbMATHGoogle Scholar
  208. 208.
    J. Conan et al., Performance of ARQ, FEC and Hybrid ARQ/FBC error control schemes for high speed data transmission on satellite channels, Canadian Conf. on Ccmms & Power, 216, 1976.Google Scholar
  209. 209.
    B.G. Dorsch & F. Dolainsky, Tehoretical limits on diannel coding under various constraints, AGAFD Synp. on Dig. Cairns in Avionics, Munich, June 1978.Google Scholar
  210. 210.
    A. Sewards, et al., FEC for the aeronautical satellite communications diannel, AGAFD Synp. on Dig. Conns in Avionics, Munich, 9.1, June 1978.Google Scholar

Copyright information

© Springer-Verlag Wien 1979

Authors and Affiliations

  • P. G. Farrell
    • 1
  1. 1.Electronics LaboratoriesThe University of Kent at CanterburyCanterbury, KentEngland

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