A linear algebra approach to minimal convolutional encoders
(1993) In IEEE Transactions on Information Theory 39(4). p.12191233 Abstract
 The authors review the work of G.D. Forney, Jr., on the algebraic structure of convolutional encoders upon which some new results regarding minimal convolutional encoders rest. An example is given of a basic convolutional encoding matrix whose number of abstract states is minimal over all equivalent encoding matrices. However, this encoding matrix can be realized with a minimal number of memory elements neither in controller canonical form nor in observer canonical form. Thus, this encoding matrix is not minimal according to Forney's definition of a minimal encoder. To resolve this difficulty, the following three minimality criteria are introduced: minimalbasic encoding matrix, minimal encoding matrix, and minimal encoder. It is shown... (More)
 The authors review the work of G.D. Forney, Jr., on the algebraic structure of convolutional encoders upon which some new results regarding minimal convolutional encoders rest. An example is given of a basic convolutional encoding matrix whose number of abstract states is minimal over all equivalent encoding matrices. However, this encoding matrix can be realized with a minimal number of memory elements neither in controller canonical form nor in observer canonical form. Thus, this encoding matrix is not minimal according to Forney's definition of a minimal encoder. To resolve this difficulty, the following three minimality criteria are introduced: minimalbasic encoding matrix, minimal encoding matrix, and minimal encoder. It is shown that all minimalbasic encoding matrices are minimal and that there exist minimal encoding matrices that are not minimalbasic. Several equivalent conditions are given for an encoding matrix to be minimal. It is proven that the constraint lengths of two equivalent minimalbasic encoding matrices are equal one by one up to a rearrangement. All results are proven using only elementary linear algebra (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1056840
 author
 Johannesson, Rolf ^{LU} and Wan, ZheXian ^{LU}
 organization
 publishing date
 1993
 type
 Contribution to journal
 publication status
 published
 subject
 in
 IEEE Transactions on Information Theory
 volume
 39
 issue
 4
 pages
 1219  1233
 publisher
 IEEEInstitute of Electrical and Electronics Engineers Inc.
 external identifiers

 scopus:0027634632
 ISSN
 00189448
 DOI
 10.1109/18.243440
 language
 English
 LU publication?
 yes
 id
 160cecfb634a4cf1af71ed8cee898f26 (old id 1056840)
 alternative location
 http://ieeexplore.ieee.org/iel1/18/6268/00243440.pdf
 date added to LUP
 20080411 13:53:48
 date last changed
 20180107 10:12:36
@article{160cecfb634a4cf1af71ed8cee898f26, abstract = {The authors review the work of G.D. Forney, Jr., on the algebraic structure of convolutional encoders upon which some new results regarding minimal convolutional encoders rest. An example is given of a basic convolutional encoding matrix whose number of abstract states is minimal over all equivalent encoding matrices. However, this encoding matrix can be realized with a minimal number of memory elements neither in controller canonical form nor in observer canonical form. Thus, this encoding matrix is not minimal according to Forney's definition of a minimal encoder. To resolve this difficulty, the following three minimality criteria are introduced: minimalbasic encoding matrix, minimal encoding matrix, and minimal encoder. It is shown that all minimalbasic encoding matrices are minimal and that there exist minimal encoding matrices that are not minimalbasic. Several equivalent conditions are given for an encoding matrix to be minimal. It is proven that the constraint lengths of two equivalent minimalbasic encoding matrices are equal one by one up to a rearrangement. All results are proven using only elementary linear algebra}, author = {Johannesson, Rolf and Wan, ZheXian}, issn = {00189448}, language = {eng}, number = {4}, pages = {12191233}, publisher = {IEEEInstitute of Electrical and Electronics Engineers Inc.}, series = {IEEE Transactions on Information Theory}, title = {A linear algebra approach to minimal convolutional encoders}, url = {http://dx.doi.org/10.1109/18.243440}, volume = {39}, year = {1993}, }