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Minimal and canonical rational generator matrices for convolutional codes

Forney, Jr., G David; Johannesson, Rolf LU and Wan, Zhe-Xian LU (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:
author
organization
publishing date
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
2008-04-11 13:45:03
date last changed
2016-10-13 04:23:41
@misc{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    = {ARRAY(0xa5aab88)},
  series       = {IEEE Transactions on Information Theory},
  title        = {Minimal and canonical rational generator matrices for convolutional codes},
  url          = {http://dx.doi.org/10.1109/18.556681},
  volume       = {42},
  year         = {1996},
}