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 On minimality of convolutional ring encoders
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/6355

title: On minimality of convolutional ring encoders
authors: Kuijper, M.
Pinto, R.
keywords: Convolutional codes over rings
Minimal polynomial encoder
Minimal trellis
issue date: 2009
abstract: 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 = ℤ_{p^r} by introducing a so-called "p-encoder". We show how to manipulate a polynomial encoding scheme of a noncatastrophic convolutional code over ℤ_{p^r} to produce a particular type of p-encoder ("minimal p-encoder") whose controller canonical realization is a minimal trellis with nonlinear features. The minimum number of trellis states is then expressed as p^γ, where γ is the sum of the row degrees of the minimal p-encoder. In particular, we show that any convolutional code over ℤ_{p^r} admits a delay-free p-encoder which implies the novel result that delay-freeness is not a property of the code but of the encoder, just as in the field case. We conjecture that a similar result holds with respect to catastrophicity, i.e., any catastrophic convolutional code over ℤ_{p^r} admits a noncatastrophic p-encoder. © 2009 IEEE.
URI: http://hdl.handle.net/10773/6355
ISSN: 0018-9448
publisher version/DOI: http://dx.doi.org/10.1109/TIT.2009.2030486
source: IEEE Transactions on Information Theory
appears in collectionsCIDMA - Artigos

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