Abstract
In this paper we give a self-contained overview of known distance measures for convolutional codes and of upper and lower bounds on the free distance. The upper bounds are valid for general trellis codes and for convolutional codes, respectively. The lower bound is valid for time-varying convolutional codes. We also present a new lower bound on the distance profile for fixed convolutional codes.
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Cedervall, M. and Johannesson, R. (1988), A FAST algorithm for computing distance spectrum of convolutional codes. Submitted to IEEE Trans. Inform. Theory. May 1988.
Chevillat, P. R. and Costello, D. J., Jr. (1976), Distance and computing in sequential decoding. IEEE Trans. Commun., COM-24:440–447.
Costello, D. J., Jr. (1969), A construction technique for random-error-correcting convolutional codes. IEEE Trans. Inform. Theory, IT-19:631–636.
Costello, D. J., Jr. (1974), Free distance bounds for convolutional codes. IEEE Trans. Inform. Theory, IT-20:356–365.
Forney, G. D., Jr. (1967), Review of random tree codes (NASA Ames. Res. Cen., Contract NAS2-3637, NASA CR 73176, Final Rep.;Appx A). See also Forney, G. D., Jr. (1974), Convolutional codes II. Maximumlikelihood decoding and convolutional codes III: Sequential decoding. Inform Contr., 25:222–297.
Forney, G. D., Jr. (1970), Convolutional codes I: Algebraic structure. IEEE Trans. Inform. Theory, IT-16:720–738.
Golomb, S. W. (1967), Shift Register Sequences, Holden-Day, San Fransisco, 1967. Revised ed., Aegean Park Press, Laguna Hills, Cal., 1982.
Griesmer, J. H. (1960), A bound for error-correcting codes. IBM J. Res. Develop., 4:532–542.
Heller, J. A. (1968), Short constraint length convolutional codes. Jet Propulsion Lab., California Inst. Technol., Pasadena, Space Programs Summary 37–54, 3:171–177.
Johannesson, R. (1975), Robustly optimal rate one-half binary convolutional codes. IEEE Trans. Inform. Theory, IT-21:464–468.
Layland, J. and McEliece, R. (1970), An upper bound on the free distance of a tree code. Jet Propulsion Lab., California Inst. Technol., Pasadena, Space Programs Summery 37–62, 3:63–64.
Massey, J. L. and Costello, D. J., Jr. (1971), Nonsystematic convolutional codes for sequential decoding in space applications. IEEE Trans. Commun. Technol., COM-19:806–813.
Massey, J. L. (1975), Error bounds for tree codes, trellis codes, and convolutional codes with encoding and decoding procedures, in G. Longo (ed.), Coding and Complexity—CISM Courses and Lectures No. 216, Springer Verlag, Wien.
Massey, J. L. and Sain, M. K. (1968), Inverses of linear sequential circuits. IEEE Trans. Comput., C-17:330–337.
Viterbi, A. J. (1971), Convolutional codes and their performance in communication systems. IEEE Trans. Commun. Technol., COM-19:751–772.
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© 1989 Springer-Verlag
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Johannesson, R., Zigangirov, K.S. (1989). Distances and distance bounds for convolutional codes—an overview. In: Einarsson, G., Ericson, T., Ingemarsson, I., Johannesson, R., Zigangirov, K., Sundberg, C.E. (eds) Topics in Coding Theory. Lecture Notes in Control and Information Sciences, vol 128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042069
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DOI: https://doi.org/10.1007/BFb0042069
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