Quaternary Convolutional Codes from Linear Block Codes over Galois Rings

Solé, Patrick; Sison, Virgilio P.

doi:10.1109/isit.2007.4557617

Cited by 2 publications

(5 citation statements)

References 16 publications

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“…Remark 2 Conform [1,15,21,27,30] we have decided to define our codes as finite support convolutional codes. There exists however a considerable body of literature in which code sequences are semi-infinite Laurent series [7,11,18,23,24].…”

Section: Convolutional Codesmentioning

confidence: 99%

“…In particular, the properties of noncatastrophic, right invertible, basic and systematic ring convolutional encoders were thoroughly discussed. The problem of deriving minimal encoders (left prime and row-reduced) was posed in [6,30]. This problem was solved in [17,16] using the concept of minimal p-encoder, which is an extension of the concept of p-basis introduced in [31] to the polynomial context.…”

Section: Introductionmentioning

confidence: 99%

“…In [12] two 16-state trellis codes of rate 2 4 , again over Z 4 , were found by computer search. However, in contrast to the block code case [10,25] little is known about distance properties and constructions of convolutional codes over large rings, see for instance [30].…”

Section: Introductionmentioning

confidence: 99%

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On MDS convolutional codes over $${\mathbb {Z}}_{p^{r}}$$ Z p r

Napp

Pinto

Toste

2016

Des. Codes Cryptogr.

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Resumo Maximum Distance Separable (MDS) convolutional codes are characterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Z p r was recently discovered in [26] via the Hensel lift of a cyclic code. In this paper we further investigate this important class of convolutional codes over Z p r from a new perspective. We introduce the notions of p-standard form and roptimal parameters to derive a novel upper bound of Singleton type on the free distance. Moreover, we present a constructive method for building general (non necessarily free) MDS convolutional codes over Z p r for any given set of parameters.

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Section: Convolutional Codesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On MDS convolutional codes over $${\mathbb {Z}}_{p^{r}}$$ Z p r

Napp

Pinto

Toste

2016

Des. Codes Cryptogr.

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“…In this paper we seek to extend this result to the finite ring case G = Z p r , where r is a positive integer and p is a prime integer. The open problem that we solve is also mentioned in the 2007 paper [23]. We first tailor the concept of encoder to the Z p r case, making use of the specific algebraic finite chain structure of Z p r .…”

Section: Introductionmentioning

confidence: 99%

“…A more recent approach [22] (see also [7], [23]) to convolutional codes focuses on so-called "finite support convolutional codes" in which the input sequence u corresponds to a polynomial. Thus the natural time axis is Z + and both input sequences and code sequences have finite support.…”

Section: Introductionmentioning

confidence: 99%

On Minimality of Convolutional Ring Encoders

Kuijper

Pinto

2009

IEEE Trans. Inform. Theory

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Convolutional codes are considered with code sequences modelled as semi-infinite Laurent series. It is wellknown 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 wellknown 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 = Zpr by introducing a socalled "p-encoder". We show how to manipulate a polynomial encoding of a noncatastrophic convolutional code over Zpr 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 Zpr 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 Zpr admits a noncatastrophic p-encoder.

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Quaternary Convolutional Codes from Linear Block Codes over Galois Rings

Cited by 2 publications

References 16 publications

On MDS convolutional codes over $${\mathbb {Z}}_{p^{r}}$$ Z p r

On MDS convolutional codes over $${\mathbb {Z}}_{p^{r}}$$ Z p r

On Minimality of Convolutional Ring Encoders

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