Symbol Erasure Correction in Random Networks with Spread Codes

Heide Gluesing-Luerssen; Anna Lena Horlemann-Trautmann

doi:10.1109/TIT.2018.2880767

Symbol Erasure Correction in Random Networks with Spread Codes

Heide Gluesing-Luerssen, Anna Lena Horlemann-Trautmann

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider data transmission over a network where each edge is an erasure channel and the inner nodes transmit the random linear combinations of their incoming information. We distinguish two channel models in this setting: the row and the column erasure channel model. For both models, we investigate spread codes and determine their symbol erasure correction capability and the probability of decoding success. We also compare the performance of spread codes to other known codes suitable for those models. Furthermore, we explain how to decode these codes in the two channel models and compare the decoding complexities. The results show that depending on the application and the to-be-optimized aspect, any combination of codes and channel models can be the best choice.

Original language	English
Article number	8531739
Pages (from-to)	2075-2091
Number of pages	17
Journal	IEEE Transactions on Information Theory
Volume	65
Issue number	4
DOIs	https://doi.org/10.1109/TIT.2018.2880767
State	Published - Apr 2019

Bibliographical note

Funding Information:
Manuscript received November 16, 2017; revised July 9, 2018; accepted October 14, 2018. Date of publication November 12, 2018; date of current version March 15, 2019. H. Gluesing-Luerssen was supported by the Simons Foundation under Grant 422479. H. Gluesing-Luerssen is with the Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027 USA. A.-L. Horlemann-Trautmann is with the Faculty of Mathematics and Statistics, University of St. Gallen, St. Gallen 9000, Switzerland (e-mail: anna-lena.horlemann@unisg.ch). Communicated by F. Oggier, Associate Editor for Coding Theory. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2018.2880767

Publisher Copyright:
© 2018 IEEE.

Keywords

Network coding
constant dimension codes
finite spreads
row and column erasures
subspace codes
symbol erasures

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2018.2880767

Cite this

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abstract = "We consider data transmission over a network where each edge is an erasure channel and the inner nodes transmit the random linear combinations of their incoming information. We distinguish two channel models in this setting: the row and the column erasure channel model. For both models, we investigate spread codes and determine their symbol erasure correction capability and the probability of decoding success. We also compare the performance of spread codes to other known codes suitable for those models. Furthermore, we explain how to decode these codes in the two channel models and compare the decoding complexities. The results show that depending on the application and the to-be-optimized aspect, any combination of codes and channel models can be the best choice.",

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note = "Funding Information: Manuscript received November 16, 2017; revised July 9, 2018; accepted October 14, 2018. Date of publication November 12, 2018; date of current version March 15, 2019. H. Gluesing-Luerssen was supported by the Simons Foundation under Grant 422479. H. Gluesing-Luerssen is with the Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027 USA. A.-L. Horlemann-Trautmann is with the Faculty of Mathematics and Statistics, University of St. Gallen, St. Gallen 9000, Switzerland (e-mail: anna-lena.horlemann@unisg.ch). Communicated by F. Oggier, Associate Editor for Coding Theory. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2018.2880767 Publisher Copyright: {\textcopyright} 2018 IEEE.",

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Symbol Erasure Correction in Random Networks with Spread Codes

Abstract

Bibliographical note

Keywords

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