State realizations of 2-periodic convolutional codes: a switching system approach

Abstract

In this work we investigate the realization problem of periodic convolutional codes. As convolutional codes are discrete linear systems over a finite field we use systems theory techniques to address our problem. In particular, we aim at deriving and studying state-space realizations of 2-periodic convolutional codes. Although one cannot expect, in general, to obtain a periodic state-space realization of a periodic convolutional code by means of the individual realizations of each of the associated time-invariant codes, we show that one can implement the periodic system switching periodically the output in each state system. Comments on the minimality of this realization are given.