An Encounter with Convolutional Codes over Rings
(1998) Abstract
 Convolutional codes is one possibility when there is a need for errorcorrecting codes in communication systems. Using convolutional codes over rings is a relatively new approach. When coding is used in combination with, for example, phaseshift keying, codes over rings constitue a natural choice as the symbols in the code alphabet have a natural signal point interpretation. This thesis reports on fundamental questions regarding convolutional codes over rings.
A careful definition of convolutional codes over rings is presented. It is interesting to note that properties as systematicity, right invertibility, and minimality of generator matrices are code properties. In the case of convolutional codes over fields, these are... (More)  Convolutional codes is one possibility when there is a need for errorcorrecting codes in communication systems. Using convolutional codes over rings is a relatively new approach. When coding is used in combination with, for example, phaseshift keying, codes over rings constitue a natural choice as the symbols in the code alphabet have a natural signal point interpretation. This thesis reports on fundamental questions regarding convolutional codes over rings.
A careful definition of convolutional codes over rings is presented. It is interesting to note that properties as systematicity, right invertibility, and minimality of generator matrices are code properties. In the case of convolutional codes over fields, these are properties connected to the chosen generator matrix only.
The choice of generator matrix for a specific convolutional code is important for the behavior of the code. Structural properties as minimality, systematicity, the predictable degree property, right invertibility, catastrophicity, and basic and minimalbasic generator matrices are studied and reported on in the thesis.
The direct sum decomposition of rings that satisfy the descending chain condition is used to further study generator matrix properties and code properties.
Code search results for rate1/2 convolutional codes over the ring of integers modulo 4 up to memory m=5 have been conducted. The obtained codes are compared with rate1/2 convolutional codes over the binary field. Furthermore, an algorithm for constructing the code state trellis of convolutional codes over rings starting with an arbitrary generator matrix is presented. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/18752
 author
 Wittenmark, Emma ^{LU}
 opponent

 Dr. Loeliger, HansAndrea, Endora Tech AG, Gartenstrasse 120, CH4052 Basel, Switzerland
 organization
 publishing date
 1998
 type
 Thesis
 publication status
 published
 subject
 keywords
 Telekommunikationsteknik, Data och systemvetenskap, Telecommunication engineering, computer technology, direct sum decomposition of a ring, Systems engineering, minimal trellis, generator matrix properties, code properties, convolutional codes, codes over rings
 pages
 158 pages
 publisher
 Department of Information Technology, Lund Univeristy
 defense location
 Room E:1406, Ebuilding, Lund Institute of Technology
 defense date
 19980522 10:15
 external identifiers

 Other:ISRN LUTEDX/TEIT98/1011SE
 ISBN
 9171670122
 language
 English
 LU publication?
 yes
 id
 d30a939274ae407cbcb71ea5756aa88c (old id 18752)
 date added to LUP
 20070524 12:19:49
 date last changed
 20160919 08:45:03
@misc{d30a939274ae407cbcb71ea5756aa88c, abstract = {Convolutional codes is one possibility when there is a need for errorcorrecting codes in communication systems. Using convolutional codes over rings is a relatively new approach. When coding is used in combination with, for example, phaseshift keying, codes over rings constitue a natural choice as the symbols in the code alphabet have a natural signal point interpretation. This thesis reports on fundamental questions regarding convolutional codes over rings.<br/><br> <br/><br> A careful definition of convolutional codes over rings is presented. It is interesting to note that properties as systematicity, right invertibility, and minimality of generator matrices are code properties. In the case of convolutional codes over fields, these are properties connected to the chosen generator matrix only.<br/><br> <br/><br> The choice of generator matrix for a specific convolutional code is important for the behavior of the code. Structural properties as minimality, systematicity, the predictable degree property, right invertibility, catastrophicity, and basic and minimalbasic generator matrices are studied and reported on in the thesis.<br/><br> <br/><br> The direct sum decomposition of rings that satisfy the descending chain condition is used to further study generator matrix properties and code properties.<br/><br> <br/><br> Code search results for rate1/2 convolutional codes over the ring of integers modulo 4 up to memory m=5 have been conducted. The obtained codes are compared with rate1/2 convolutional codes over the binary field. Furthermore, an algorithm for constructing the code state trellis of convolutional codes over rings starting with an arbitrary generator matrix is presented.}, author = {Wittenmark, Emma}, isbn = {9171670122}, keyword = {Telekommunikationsteknik,Data och systemvetenskap,Telecommunication engineering,computer technology,direct sum decomposition of a ring,Systems engineering,minimal trellis,generator matrix properties,code properties,convolutional codes,codes over rings}, language = {eng}, pages = {158}, publisher = {ARRAY(0x83bab28)}, title = {An Encounter with Convolutional Codes over Rings}, year = {1998}, }