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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
Abstract
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.
Keywords
periodic 2D systems, convolutional codes, realizations