International Journal of applied mathematics and computer science

online read us now

Paper details

Number 3 - September 2019
Volume 29 - 2019

Realization of 2D (2,2)-periodic encoders by means of 2D periodic separable Roesser models

Diego Napp, Ricardo Pereira, Raquel Pinto, Paula Rocha

in the implementation of convolutional codes is to obtain a minimal state representation of the code. Compared with the literature on one-dimensional (1D) time-invariant convolutional codes, there exist relatively few results on the realization problem for time-varying 1D convolutional codes and even fewer if the convolutional codes are two-dimensional (2D). In this paper we consider 2D periodic convolutional codes and address the minimal state space realization problem for this class of codes. This is, in general, a highly nontrivial problem. Here, we focus on separable Roesser models and show that in this case it is possible to derive, under weak conditions, concrete formulas for obtaining a 2D Roesser state space representation. Moreover, we study minimality and present necessary conditions for these representations to be minimal. Our results immediately lead to constructive algorithms to build these representations.

periodic 2D systems, convolutional codes, realizations