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

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Abstract
In this work, we analyze the problem of catastrophicity of encoders of convolutional codes over the Laurent series with coefficients in [ ], [ ]. 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 [ ], where [ ] is a field, when dealing with [ ] 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 [ ]-encoder. In this paper we solve this conjecture for a class of [ ] convolutional codes over [ ] and show that, in fact, these codes always admit a non-catastrophic p-encoder. We also describe a constructive procedure that allows us to obtain a non-catastrophic [ ]-encoder.
Funding Information
  • Portuguese Foundation for Science and Technology (UIDB/04106/2020)
  • Portuguese Foundation for Science and Technology (UIDP/04106/2020)
  • Spanish I+D+i (PID2022-142159OB-I00, AICO 2023 with reference CIAICO/2022/167)

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