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Title: Periodic state-space representations of periodic convolutional codes
Author: Napp, Diego
Pereira, Ricardo
Pinto, Raquel
Rocha, Paula
Keywords: Convolutional codes
Periodically time-varying codes
Input-state- output representations
Issue Date: Jul-2019
Publisher: Springer Verlag
Abstract: 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.
Peer review: yes
DOI: 10.1007/s12095-018-0313-6
ISSN: 1936-2447
Publisher Version:
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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