COMPOSITION CODES

Abstract

In this paper we introduce a special class of 2D convolutional codes, called composition codes, which admit encoders G(d(1),d(2)) that can be decomposed as the product of two 1D encoders, i.e., G(d(1), d(2)) = G(2) (d(2))G(1)(d(1))" Taking into account this decomposition, we obtain syndrome formers of the code directly from G(1)(d(1)) and G(2)(d(2)), in case G(1)(d(1)) and G(2)(d(2)) 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(d(1),d(2)) = G(2)(d(2))G(1)(d(1)) with G(2)(d(2)) a systematic 1D encoder. Finally, we investigate the minimality of 2D separable Roesser state-space realizations for syndrome formers of these codes.