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On weight enumerators and MacWilliams identity for convolutional codes

Bocharova, Irina LU ; Hug, Florian LU ; Johannesson, Rolf LU and Kudryashov, Boris LU (2010) Information Theory and Applications Workshop (ITA), 2010 In [Host publication title missing]
Abstract
Convolutional codes are defined to be equivalent if their code symbols differ only in how they are ordered and two generator matrices are defined to be weakly equivalent (WE) if they encode equivalent convolutional codes. It is shown that tailbiting convolutional codes encoded by WE minimal-basic generator matrices have the same spectra. Shearer and McEliece showed that MacWilliams identity does not hold for convolutional codes. However, for the spectra of truncated convolutional codes and their duals, MacWilliams identity clearly holds. It is shown that the dual of a truncated convolutional code is not a truncation of a convolutional code but its reversal is. Finally, a recursion for the spectra of truncated convolutional codes is given... (More)
Convolutional codes are defined to be equivalent if their code symbols differ only in how they are ordered and two generator matrices are defined to be weakly equivalent (WE) if they encode equivalent convolutional codes. It is shown that tailbiting convolutional codes encoded by WE minimal-basic generator matrices have the same spectra. Shearer and McEliece showed that MacWilliams identity does not hold for convolutional codes. However, for the spectra of truncated convolutional codes and their duals, MacWilliams identity clearly holds. It is shown that the dual of a truncated convolutional code is not a truncation of a convolutional code but its reversal is. Finally, a recursion for the spectra of truncated convolutional codes is given and the spectral components are related to those for the corresponding dual codes. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
[Host publication title missing]
conference name
Information Theory and Applications Workshop (ITA), 2010
external identifiers
  • scopus:77952727698
DOI
10.1109/ITA.2010.5454120
language
English
LU publication?
yes
id
68a6cbe2-b547-4917-81e2-91fc27f94233 (old id 1539098)
date added to LUP
2010-01-29 11:24:16
date last changed
2017-06-04 04:44:55
@inproceedings{68a6cbe2-b547-4917-81e2-91fc27f94233,
  abstract     = {Convolutional codes are defined to be equivalent if their code symbols differ only in how they are ordered and two generator matrices are defined to be weakly equivalent (WE) if they encode equivalent convolutional codes. It is shown that tailbiting convolutional codes encoded by WE minimal-basic generator matrices have the same spectra. Shearer and McEliece showed that MacWilliams identity does not hold for convolutional codes. However, for the spectra of truncated convolutional codes and their duals, MacWilliams identity clearly holds. It is shown that the dual of a truncated convolutional code is not a truncation of a convolutional code but its reversal is. Finally, a recursion for the spectra of truncated convolutional codes is given and the spectral components are related to those for the corresponding dual codes.},
  author       = {Bocharova, Irina and Hug, Florian and Johannesson, Rolf and Kudryashov, Boris},
  booktitle    = {[Host publication title missing]},
  language     = {eng},
  title        = {On weight enumerators and MacWilliams identity for convolutional codes},
  url          = {http://dx.doi.org/10.1109/ITA.2010.5454120},
  year         = {2010},
}