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Some structural properties of convolutional codes over rings

Johannesson, Rolf LU ; Wan, Zhe-Xian LU and Wittenmark, Emma (1998) In IEEE Transactions on Information Theory 44(2). p.839-845
Abstract
Convolutional codes over rings have been motivated by phase-modulated signals. Some structural properties of the generator matrices of such codes are presented. Successively stronger notions of the invertibility of generator matrices are studied, and a new condition for a convolutional code over a ring to be systematic is given and shown to be equivalent to a condition given by Massey and Mittelholzer (1990). It is shown that a generator matrix that can be decomposed into a direct sum is basic, minimal, and noncatastrophic if and only if all generator matrices for the constituent codes are basic, minimal, and noncatastrophic, respectively. It is also shown that if a systematic generator matrix can be decomposed into a direct sum, then all... (More)
Convolutional codes over rings have been motivated by phase-modulated signals. Some structural properties of the generator matrices of such codes are presented. Successively stronger notions of the invertibility of generator matrices are studied, and a new condition for a convolutional code over a ring to be systematic is given and shown to be equivalent to a condition given by Massey and Mittelholzer (1990). It is shown that a generator matrix that can be decomposed into a direct sum is basic, minimal, and noncatastrophic if and only if all generator matrices for the constituent codes are basic, minimal, and noncatastrophic, respectively. It is also shown that if a systematic generator matrix can be decomposed into a direct sum, then all generator matrices of the constituent codes are systematic, but that the converse does not hold. Some results on convolutional codes over Z(pe) are obtained (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
IEEE Transactions on Information Theory
volume
44
issue
2
pages
839 - 845
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • Scopus:0032023713
ISSN
0018-9448
DOI
10.1109/18.661532
language
English
LU publication?
yes
id
6e6661c9-6742-411b-ac71-ab6164ee679d (old id 1056636)
date added to LUP
2008-04-16 15:16:37
date last changed
2016-10-13 04:28:24
@misc{6e6661c9-6742-411b-ac71-ab6164ee679d,
  abstract     = {Convolutional codes over rings have been motivated by phase-modulated signals. Some structural properties of the generator matrices of such codes are presented. Successively stronger notions of the invertibility of generator matrices are studied, and a new condition for a convolutional code over a ring to be systematic is given and shown to be equivalent to a condition given by Massey and Mittelholzer (1990). It is shown that a generator matrix that can be decomposed into a direct sum is basic, minimal, and noncatastrophic if and only if all generator matrices for the constituent codes are basic, minimal, and noncatastrophic, respectively. It is also shown that if a systematic generator matrix can be decomposed into a direct sum, then all generator matrices of the constituent codes are systematic, but that the converse does not hold. Some results on convolutional codes over Z(pe) are obtained},
  author       = {Johannesson, Rolf and Wan, Zhe-Xian and Wittenmark, Emma},
  issn         = {0018-9448},
  language     = {eng},
  number       = {2},
  pages        = {839--845},
  publisher    = {ARRAY(0x7efc2b0)},
  series       = {IEEE Transactions on Information Theory},
  title        = {Some structural properties of convolutional codes over rings},
  url          = {http://dx.doi.org/10.1109/18.661532},
  volume       = {44},
  year         = {1998},
}