Algebraic aspects of 2D convolutional codes

Two-dimensional (2D) codes are introduced as linear shift-invariant spaces of admissible signals on the discrete plane. Convolutional and, in particular, basic codes are characterized both in terms of their internal properties and by means of their input-output representations. The algebraic structure of the class of all encoders that correspond to a given convolutional code is investigated and the possibility of obtaining 2D decoders, free from catastrophic errors, as,veil as efficient syndrome decoders is considered. Some aspects of the state space implementation of 2D encoders and decoders via (finite memory) 2D system are discussed