Minimal and canonical rational generator matrices for convolutional codes

Summary, in English

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.

• Author: G David Forney, Jr.; Rolf Johannesson; Zhe-Xian Wan
• Department/s: Department of Electrical and Information Technology
• Publishing year: 1996
• Language: English
• Pages: 1865-1880
• Publication/Series: IEEE Transactions on Information Theory
• Volume: 42
• Issue: 6, Part 1
• Full text: - 2 MB; Download statistics
• Links: http://ieeexplore.ieee.org/iel1/18/12144/00556681.pdf; http://dx.doi.org/10.1109/18.556681
• Document type: Journal article
• Publisher: IEEE - Institute of Electrical and Electronics Engineers Inc.
• Topic: Electrical Engineering, Electronic Engineering, Information Engineering
• Status: Published
• ISBN/ISSN/Other: ISSN: 0018-9448