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Erasure decoding of convolutional codes using first-order representations

It is well known that there is a correspondence between convolutional codes and discrete-time linear systems over finite fields. In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. In thi...

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Autores principales: Lieb, Julia, Rosenthal, Joachim
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer London 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8591787/
https://www.ncbi.nlm.nih.gov/pubmed/34803233
http://dx.doi.org/10.1007/s00498-021-00289-9
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author Lieb, Julia
Rosenthal, Joachim
author_facet Lieb, Julia
Rosenthal, Joachim
author_sort Lieb, Julia
collection PubMed
description It is well known that there is a correspondence between convolutional codes and discrete-time linear systems over finite fields. In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. In this kind of channel, which is important due to its use for data transmission over the Internet, the receiver knows if a received symbol is correct. We study the decoding problem using the state space description of a convolutional code, and this provides in a natural way additional information. With respect to previously known decoding algorithms, our new algorithm has the advantage that it is able to reduce the decoding delay as well as the computational effort in the erasure recovery process. We describe which properties a convolutional code should have in order to obtain a good decoding performance and illustrate it with an example.
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spelling pubmed-85917872021-11-19 Erasure decoding of convolutional codes using first-order representations Lieb, Julia Rosenthal, Joachim Math Control Signal Syst Original Article It is well known that there is a correspondence between convolutional codes and discrete-time linear systems over finite fields. In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. In this kind of channel, which is important due to its use for data transmission over the Internet, the receiver knows if a received symbol is correct. We study the decoding problem using the state space description of a convolutional code, and this provides in a natural way additional information. With respect to previously known decoding algorithms, our new algorithm has the advantage that it is able to reduce the decoding delay as well as the computational effort in the erasure recovery process. We describe which properties a convolutional code should have in order to obtain a good decoding performance and illustrate it with an example. Springer London 2021-06-04 2021 /pmc/articles/PMC8591787/ /pubmed/34803233 http://dx.doi.org/10.1007/s00498-021-00289-9 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Article
Lieb, Julia
Rosenthal, Joachim
Erasure decoding of convolutional codes using first-order representations
title Erasure decoding of convolutional codes using first-order representations
title_full Erasure decoding of convolutional codes using first-order representations
title_fullStr Erasure decoding of convolutional codes using first-order representations
title_full_unstemmed Erasure decoding of convolutional codes using first-order representations
title_short Erasure decoding of convolutional codes using first-order representations
title_sort erasure decoding of convolutional codes using first-order representations
topic Original Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8591787/
https://www.ncbi.nlm.nih.gov/pubmed/34803233
http://dx.doi.org/10.1007/s00498-021-00289-9
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