Minimal and canonical rational generator matrices for convolutional codes
(1996) In IEEE Transactions on Information Theory 42(6, Part 1). p.1865-1880- Abstract
- A full-rank IC x n matrix G(D) over the rational
functions F(D) generates a rate R = k/n convolutional code
C. G(D) is minimal if it can be realized with as few memory
elements as any encoder for C, and G(D) is canonical if it has a minimal realization in controller canonical form. We show that G(D) is minimal if and only if for all rational input sequences p1 (D), the span of U (D) G (D) covers the span of ZL (D). Alternatively, G(D) is minimal if and only if G(D) is globally zero-free, or globally invertible. We show that G(D) is canonical if and only if G(D) is minimal and also globally orthogonal, in the valuation-theoretic sense of Monna.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1056656
- author
- Forney, Jr., G David ; Johannesson, Rolf LU and Wan, Zhe-Xian LU
- organization
- publishing date
- 1996
- type
- Contribution to journal
- publication status
- published
- subject
- in
- IEEE Transactions on Information Theory
- volume
- 42
- issue
- 6, Part 1
- pages
- 1865 - 1880
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:0030290222
- ISSN
- 0018-9448
- DOI
- 10.1109/18.556681
- language
- English
- LU publication?
- yes
- id
- f3e40b67-d2d2-4177-be85-813cdbabad72 (old id 1056656)
- alternative location
- http://ieeexplore.ieee.org/iel1/18/12144/00556681.pdf
- date added to LUP
- 2016-04-04 09:05:20
- date last changed
- 2022-02-28 06:21:32
@article{f3e40b67-d2d2-4177-be85-813cdbabad72, abstract = {{A full-rank IC x n matrix G(D) over the rational<br/><br> functions F(D) generates a rate R = k/n convolutional code<br/><br> C. G(D) is minimal if it can be realized with as few memory<br/><br> elements as any encoder for C, and G(D) is canonical if it has a minimal realization in controller canonical form. We show that G(D) is minimal if and only if for all rational input sequences p1 (D), the span of U (D) G (D) covers the span of ZL (D). Alternatively, G(D) is minimal if and only if G(D) is globally zero-free, or globally invertible. We show that G(D) is canonical if and only if G(D) is minimal and also globally orthogonal, in the valuation-theoretic sense of Monna.}}, author = {{Forney, Jr., G David and Johannesson, Rolf and Wan, Zhe-Xian}}, issn = {{0018-9448}}, language = {{eng}}, number = {{6, Part 1}}, pages = {{1865--1880}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, series = {{IEEE Transactions on Information Theory}}, title = {{Minimal and canonical rational generator matrices for convolutional codes}}, url = {{https://lup.lub.lu.se/search/files/5228446/1058676.pdf}}, doi = {{10.1109/18.556681}}, volume = {{42}}, year = {{1996}}, }