Minimal realizations of syndrome formers of a special class of 2D codes

Abstract

In this paper we consider a special class of 2D convolutional codes (composition codes) with encoders G(d1;d2) that can be decomposed as the product of two 1D encoders, i.e., G(d1;d2) = G2(d2)G1(d1). In case that G1(d1) and G2(d2) are prime we provide constructions of syndrome formers of the code, directly from G1(d1) and G2(d2). Moreover we investigate the minimality of 2D state-space realization by means of a separable Roesser model of syndrome formers of composition codes, where G2(d2) is a quasi-systematic encoder.