Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

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)
Please use this url to cite or link to this publication:
author
; and
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
2016-04-04 09:19:28
date last changed
2022-02-13 08:45:32
@article{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    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Information Theory}},
  title        = {{Some structural properties of convolutional codes over rings}},
  url          = {{https://lup.lub.lu.se/search/files/5293556/1058660.pdf}},
  doi          = {{10.1109/18.661532}},
  volume       = {{44}},
  year         = {{1998}},
}