Duality analysis of 2D convolutional codes

The behavioral approach, developed by J.C. Willems (1989) for the analysis of dynamical systems provides an appropriate framework for investigating convolutional codes. In the two-dimensional (2D) case, this approach is very effective, as it allows to avoid a priori assumptions on the ordering of two dimensional data and artificial notions of causality in Z×Z. Moreover, no restriction on the support of the signals is needed, and the only reasonable constraint one might introduce on 2D sequences is that of having finite support, as extra requirements on their shape seem questionable in many practical applications. We analyse the algebraic structure of 2D convolutional codes over finite fields, and discuss how 2D finite support convolutional codes are related to infinite support codes via algebraic duality