On Minimality of Convolutional Ring Encoders
Margreta Kuijper, Raquel Pinto
IEEE TRANSACTIONS ON INFORMATION THEORY | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC | Published : 2009
Convolutional codes are considered with code sequences modeled as semi-infinite Laurent series. It is well known that a convolutional code C over a finite group G has a minimal trellis representation that can be derived from code sequences. It is also well known that, for the case that G is a finite field, any polynomial encoder of C can be algebraically manipulated to yield a minimal polynomial encoder whose controller canonical realization is a minimal trellis. In this paper we seek to extend this result to the finite ring case G = ℤp r by introducing a so-called "p-encoder". We show how to manipulate a polynomial encoding scheme of a noncatastrophic convolutional code over ℤpr to produce ..View full abstract
The work of M. Kuijper was supported in part by the Australian Research Council. The work of R. Pinto was supported in part by the Portuguese Science Foundation (FCT) through the Unidade de Investigacao Matematica e Aplicacoes of the University of Aveiro, Portugal and by Fundacao Calouste Gulbenkian.