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Title: MDS 2D convolutional codes with optimal 1D horizontal projections
Author: Almeida, Paulo J.
Napp, Diego
Pinto, Raquel
Keywords: 2D convolutional codes
Optimal codes
MDS codes
Superregular matrices
Issue Date: Feb-2018
Publisher: Springer
Abstract: Two dimensional (2D) convolutional codes is a class of codes that generalizes standard one-dimensional (1D) convolutional codes in order to treat two dimensional data. In this paper we present a novel and concrete construction of 2D convolutional codes with the particular property that their projection onto the horizontal lines yield optimal [in the sense of Almeida et al. (Linear Algebra Appl 499:1–25, 2016)] 1D convolutional codes with a certain rate and certain Forney indices. Moreover, using this property we show that the proposed constructions are indeed maximum distance separable, i.e., are 2D convolutional codes having the maximum possible distance among all 2D convolutional codes with the same parameters. The key idea is to use a particular type of superregular matrices to build the generator matrix.
Peer review: yes
DOI: 10.1007/s10623-017-0357-1
ISSN: 0925-1022
Appears in Collections:CIDMA - Artigos
AGG - Artigos

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