Some structural properties of convolutional codes over rings
(1998) In IEEE Transactions on Information Theory 44(2). p.839845 Abstract
 Convolutional codes over rings have been motivated by phasemodulated 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 phasemodulated 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:
http://lup.lub.lu.se/record/1056636
 author
 Johannesson, Rolf ^{LU} ; Wan, ZheXian ^{LU} and Wittenmark, Emma
 organization
 publishing date
 1998
 type
 Contribution to journal
 publication status
 published
 subject
 in
 IEEE Transactions on Information Theory
 volume
 44
 issue
 2
 pages
 839  845
 publisher
 IEEEInstitute of Electrical and Electronics Engineers Inc.
 external identifiers

 scopus:0032023713
 ISSN
 00189448
 DOI
 10.1109/18.661532
 language
 English
 LU publication?
 yes
 id
 6e6661c96742411bac71ab6164ee679d (old id 1056636)
 date added to LUP
 20080416 15:16:37
 date last changed
 20180617 04:59:56
@article{6e6661c96742411bac71ab6164ee679d, abstract = {Convolutional codes over rings have been motivated by phasemodulated 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, ZheXian and Wittenmark, Emma}, issn = {00189448}, language = {eng}, number = {2}, pages = {839845}, publisher = {IEEEInstitute of Electrical and Electronics Engineers Inc.}, 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}, }