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Title: Composition codes
Author: Fornasini, Ettore
Pinho, Telma
Pinto, Raquel
Rocha, Paula
Keywords: Encoders and syndrome formers
2D composition codes
Minimal 2D state-space models
Issue Date: 1-Jan-2017
Publisher: American Institute of Mathematical Sciences
Abstract: In this paper we introduce a special class of 2D convolutional codes, called composition codes, which admit encoders G(d1,d2) that can be decomposed as the product of two 1D encoders, i.e., G(d1,d2)=G2(d2)G1(d1). Taking into account this decomposition, we obtain syndrome formers of the code directly from G1(d1) andG2(d2), in case G1(d1) andG2(d2) are right prime. Moreover we consider 2D state-space realizations by means of a separable Roesser model of the encoders and syndrome formers of a composition code and we investigate the minimality of such realizations. In particular, we obtain minimal realizations for composition codes which admit an encoder G(d1,d2)=G2(d2)G1(d1) withG2(d2) a systematic 1D encoder. Finally, we investigate the minimality of 2D separable Roesser state-space realizations for syndrome formers of these codes.
Peer review: yes
DOI: DOI:10.3934/amc.2016.10.163
ISSN: 1930-5346
Appears in Collections:CIDMA - Artigos

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