On the existence of non-catastrophic p-encoders of (2,1) convolutional codes over ℤp2

Abstract

In this work, we analyze the problem of catastrophicity of encoders of convolutional codes over the Laurent series with coefficients in [Formula: see text], [Formula: see text]. Kuijper and Pinto proved in [M. Kuijper and R. Pinto, On minimality of convolutional ring encoders, IEEE Trans. Autom. Control 55(11) (2009) 4890–4897] that, contrary to what happens for codes over [Formula: see text], where [Formula: see text] is a field, when dealing with [Formula: see text] there are convolutional codes that do not admit non-catastrophic encoders. Nevertheless it was conjectured that any catastrophic convolutional code admits another type of non-catastrophic encoder called [Formula: see text]-encoder. In this paper we solve this conjecture for a class of [Formula: see text] convolutional codes over [Formula: see text] and show that, in fact, these codes always admit a non-catastrophic [Formula: see text]-encoder. We also describe a constructive procedure that allows us to obtain a non-catastrophic [Formula: see text]-encoder.