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 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.
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.
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  1998 May 22 
Publisher  
ISBN (Print)  9171670122 
Publication status  Published  1998 
Bibliographical note
Defence detailsDate: 19980522
Time: 10:15
Place: Room E:1406, Ebuilding, Lund Institute of Technology
External reviewer(s)
Name: Loeliger, HansAndrea
Title: Dr.
Affiliation: Endora Tech AG, Gartenstrasse 120, CH4052 Basel, Switzerland

Subject classification (UKÄ)
 Electrical Engineering, Electronic Engineering, Information Engineering
Free 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