STATE-SPACE REALIZATIONS OF PERIODIC CONVOLUTIONAL CODES

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Fornasini, E (Author) Other; Napp, D (Author) Other; Pereira, R (Author) Other; Pinto, R (Author) Other; Rocha, P (Author) FEUP

Journal

Title: SIAM Journal on Control and Optimization

Vol. 60

Pages: 2927-2946

ISSN: 0363-0129

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00X-C1Y

DOI: 10.1137/21m1452172

Abstract (EN): Convolutional codes are discrete linear systems over a finite field and can be defined as F[d]-modules, where F[d] is the ring of polynomials with coefficient in a finite field F. In this paper we study the algebraic properties of periodic convolutional codes of period 2 and their representation by means of input-state-output representations. We show that they can be described as F[d2]-modules and present explicit representation of the set of equivalent encoders. We investigate their statespace representation and present two different but equivalent types of state-space realizations for these codes. These novel representations can be implemented by realizing two linear time-invariant systems separately and switching the input (or the output) that is entering (or leaving) the system. We investigate their minimality and provide necessary and also sufficient conditions in terms of the reachability and observability properties of the two linear systems involved. The ideas presented here can be easily generalized for codes with period larger than 2.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20