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Complete MDP convolutional codes


Lieb, Julia (2019). Complete MDP convolutional codes. Journal of Algebra and its Applications, 18(06):1950105.

Abstract

Maximum distance profile (MDP) convolutional codes have the property that their column distances are as large as possible. It has been shown that, transmitting over an erasure channel, these codes have optimal recovery rate for windows of a certain length. Reverse MDP convolutional codes have the additional advantage that they are suitable for forward and backward decoding algorithms. Beyond that the subclass of complete MDP convolutional codes has the ability to reduce the waiting time during decoding. The first main result of this paper is to show the existence and genericity of (n,k,δ) complete MDP convolutional codes for all code parameters with (n−k)|δ as well as that complete MDP convolutional codes cannot exist if (n−k)∤δ. The second main contribution is the presentation of two concrete construction techniques to obtain complete MDP convolutional codes. These constructions work for all code parameters with (n−k)|δ but require that the size of the underlying base field is (sufficiently) large.

Abstract

Maximum distance profile (MDP) convolutional codes have the property that their column distances are as large as possible. It has been shown that, transmitting over an erasure channel, these codes have optimal recovery rate for windows of a certain length. Reverse MDP convolutional codes have the additional advantage that they are suitable for forward and backward decoding algorithms. Beyond that the subclass of complete MDP convolutional codes has the ability to reduce the waiting time during decoding. The first main result of this paper is to show the existence and genericity of (n,k,δ) complete MDP convolutional codes for all code parameters with (n−k)|δ as well as that complete MDP convolutional codes cannot exist if (n−k)∤δ. The second main contribution is the presentation of two concrete construction techniques to obtain complete MDP convolutional codes. These constructions work for all code parameters with (n−k)|δ but require that the size of the underlying base field is (sufficiently) large.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Algebra and Number Theory
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Applied Mathematics, Algebra and Number Theory
Language:English
Date:1 June 2019
Deposited On:10 Nov 2021 15:16
Last Modified:26 Apr 2024 01:36
Publisher:World Scientific Publishing
ISSN:0219-4988
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1142/s0219498819501056