Periodic state-space representations of periodic convolutional codes

• Type: Article in International Scientific Journal
• Date: 2019

Authors

Diego Napp (Author) Other; Ricardo Pereira (Author) Other; Raquel Pinto (Author) Other; Paula Rocha (Author) FEUP

Journal

Title: Cryptography and Communications

Vol. 11 No. 4

Pages: 585-595

ISSN: 1936-2447

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 7 Citations

Other information

Authenticus ID: P-00P-GEM

DOI: 10.1007/s12095-018-0313-6

Abstract (EN): In this paper we study the representation of periodically time-varying convolutional codes by means of periodic input-state-output models. In particular, we focus on period two and investigate under which conditions a given two-periodic convolutional code (obtained by alternating two time-invariant encoders) can be represented by a periodic input-state-output system. We first show that one cannot expect, in general, to obtain a periodic input-state-output representation of a periodic convolutional code by means of the individual realizations of each of the associated time-invariant codes. We, however, provide sufficient conditions for this to hold in terms of the column degrees of the associated column reduced generator matrices. Moreover, we derive a sufficient condition to obtain a periodic state-space realization that is minimal. Finally, examples to illustrate the results are presented.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 11