Maximum Distance Separable Convolutional Codes

Rosenthal, Joachim; Smarandache, Roxana

doi:10.1007/s002000050120

Cited by 144 publications

(192 citation statements)

References 13 publications

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“…Note that this upper-bound does not depend on the degree δ of C in contrast to the generalized Singleton bound for the free distance [20]. Also note that the bound given in (1.8) grows infinitely and in practice one is interested in knowing the values of d r j , 1 ≤ j ≤ J for same given integer J.…”

Section: Bounds and Constructionsmentioning

confidence: 94%

“…In [20] a Singleton bound for convolutional codes was derived (called generalized Singleton bound) and the codes achieving such a bound were called maximum distance separable (MDS). In [23] the first concrete construction of an MDS convolutional code (over the finite field F) of rate k n and degree δ was presented for every given set of parameters (n, k, δ ), (with the characteristic of the finite field F and the length n of the code being coprime).…”

Section: Introductionmentioning

confidence: 99%

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On Optimal Extended Row Distance Profile

Almeida

Napp

Pinto

2017

Springer Proceedings in Mathematics &Amp; Statistics

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In this paper, we investigate extended row distances of Unit Memory (UM) convolutional codes. In particular, we derive upper and lower bounds for these distances and moreover present a concrete construction of a UM convolutional code that almost achieves the derived upper bounds. The generator matrix of these codes is built by means of a particular class of matrices, called superregular matrices. We actually conjecture that the construction presented is optimal with respect to the extended row distances as it achieves the maximum extended row distances possible. This in particular implies that the upper bound derived is not completely tight. The results presented in this paper further develop the line of research devoted to the distance properties of convolutional codes which has been mainly focused on the notions of free distance and column distance. Some open problems are left for further research.

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Section: Bounds and Constructionsmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

On Optimal Extended Row Distance Profile

Almeida

Napp

Pinto

2017

Springer Proceedings in Mathematics &Amp; Statistics

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show abstract

“…Rosenthal and Smarandache [16] showed that the free distance of an (n, k, δ) convolutional code is upper bounded by…”

Section: Convolutional Codesmentioning

confidence: 99%

Column Rank Distances of Rank Metric Convolutional Codes

Napp

Pinto

Rosenthal

et al. 2017

Coding Theory and Applications

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Abstract. In this paper, we deal with the so-called multi-shot network coding, meaning that the network is used several times (shots) to propagate the information. The framework we present is slightly more general than the one which can be found in the literature. We study and introduce the notion of column rank distance of rank metric convolutional codes for any given rate and finite field. Within this new framework we generalize previous results on column distances of Hamming and rank metric convolutional codes [3,8]. This contribution can be considered as a continuation follow-up of the work presented in [11].

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“…Finally, the free distance of an (n, k, δ)-convolutional code C is always upper-bounded (see [34]) by the generalized Singleton bound…”

mentioning

confidence: 99%

“…Moreover, the convolutional code C is called maximum distance separable (MDS) if its free distance is equal to the generalized Singleton bound [34]. Figure 1: Concatenated convolutional code PC (1) Depending on the value of the column distances, we can obtain the following classification of convolutional codes.…”

mentioning

confidence: 99%

Parallel concatenated convolutional codes from linear systems theory viewpoint

Climent

Herranz

Perea

2016

Systems & Control Letters

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The aim of this work is to characterize two models of concatenated convolutional codes based on the theory of linear systems. The problem we consider can be viewed as the study of composite linear system from the classical control theory or as the interconnection from the behavioral system viewpoint. In this paper we provide an input-state-output representation of both models and introduce some conditions for such representations to be both controllable and observable. We also introduce a lower bound on their free distances and the column distances.

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Maximum Distance Separable Convolutional Codes

Cited by 144 publications

References 13 publications

On Optimal Extended Row Distance Profile

On Optimal Extended Row Distance Profile

Column Rank Distances of Rank Metric Convolutional Codes

Parallel concatenated convolutional codes from linear systems theory viewpoint

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