American Institute of Mathematical Sciences

February  2016, 10(1): 179-193. doi: 10.3934/amc.2016.10.179

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, Portugal, Portugal, Portugal

Received  December 2014 Revised  September 2015 Published  March 2016

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.
Citation: Joan-Josep Climent, Diego Napp, Raquel Pinto, Rita Simões. Decoding of $2$D convolutional codes over an erasure channel. Advances in Mathematics of Communications, 2016, 10 (1) : 179-193. doi: 10.3934/amc.2016.10.179
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