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An Encounter with Convolutional Codes over Rings

Wittenmark, Emma LU (1998)
Abstract
Convolutional codes is one possibility when there is a need for error-correcting codes in communication systems. Using convolutional codes over rings is a relatively new approach. When coding is used in combination with, for example, phase-shift 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 error-correcting codes in communication systems. Using convolutional codes over rings is a relatively new approach. When coding is used in combination with, for example, phase-shift 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 minimal-basic 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 rate-1/2 convolutional codes over the ring of integers modulo 4 up to memory m=5 have been conducted. The obtained codes are compared with rate-1/2 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:
author
opponent
  • Dr. Loeliger, Hans-Andrea, Endora Tech AG, Gartenstrasse 120, CH-4052 Basel, Switzerland
organization
publishing date
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, E-building, Lund Institute of Technology
defense date
1998-05-22 10:15
external identifiers
  • other:ISRN LUTEDX/TEIT-98/1011-SE
ISBN
91-7167-012-2
language
English
LU publication?
yes
id
d30a9392-74ae-407c-bcb7-1ea5756aa88c (old id 18752)
date added to LUP
2007-05-24 12:19:49
date last changed
2016-09-19 08:45:03
@phdthesis{d30a9392-74ae-407c-bcb7-1ea5756aa88c,
  abstract     = {Convolutional codes is one possibility when there is a need for error-correcting codes in communication systems. Using convolutional codes over rings is a relatively new approach. When coding is used in combination with, for example, phase-shift 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 minimal-basic 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 rate-1/2 convolutional codes over the ring of integers modulo 4 up to memory m=5 have been conducted. The obtained codes are compared with rate-1/2 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         = {91-7167-012-2},
  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    = {Department of Information Technology, Lund Univeristy},
  school       = {Lund University},
  title        = {An Encounter with Convolutional Codes over Rings},
  year         = {1998},
}