Decoding of $2$D convolutional codes over an erasure channel

Joan-Josep  Climent; Diego  Napp; Raquel  Pinto; Rita  Simões

doi:10.3934/amc.2016.10.179

Article Contents

2016, Volume 10, Issue 1: 179-193. Doi: 10.3934/amc.2016.10.179

This issue Previous Article Composition codes Next Article Algorithms for the minimum weight of linear codes

Decoding of $2$D convolutional codes over an erasure channel

1.
Departament de Matemàtiques, Universitat d'Alacant, Ap. Correus 99, E-03080, Alacant
2.
CIDMA - Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro

Received: November 30, 2014

Revised: August 31, 2015

Published: January 2016

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Abstract

In this paper we address the problem of decoding $2$D convolutional codes over an erasure channel. To this end we introduce the notion of neighbors around a set of erasures which can be considered an analogue of the notion of sliding window in the context of $1$D convolutional codes. The main idea is to reduce the decoding problem of $2$D convolutional codes to a problem of decoding a set of associated $1$D convolutional codes. We first show how to recover sets of erasures that are distributed on vertical, horizontal and diagonal lines. Finally we outline some ideas to treat any set of erasures distributed randomly on the $2$D plane.

Keywords:

$1$D finite support convolutional codes,
$2$D finite support convolutional codes,
erasure channel.

Mathematics Subject Classification: Primary: 94B10; Secondary: 94B20.

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