On the Construction of Jointly Superregular Lower Triangular Toeplitz Matrices

Jonas Hansen, Jan Østergaard, Johnny Kudahl, John Madsen

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

3 Citations (Scopus)

Abstract

Superregular matrices have the property that all of their submatrices, which can be full rank are so. Lower triangular superregular matrices are useful for e.g., maximum distance separable convolutional codes as well as for (sequential) network codes. In this work, we provide an explicit design for all superregular lower triangular Toeplitz matrices in GF(2p) for the case of matrices with dimensions less than or equal to 5 × 5. For higher dimensional matrices, we present a greedy algorithm that find a solution provided the field size is sufficiently high. We also introduce the notions of jointly superregular and product preserving jointly superregular matrices, and extend our explicit constructions of superregular matrices to these cases. Jointly superregular matrices are necessary to achieve optimal decoding capabilities for the case of codes with a rate lower than 1/2, and the product preserving property is necessary for optimal decoding capabilities in network recoding.
Original languageEnglish
Title of host publication2016 IEEE International Symposium on Information Theory (ISIT)
PublisherIEEE
Publication dateJul 2016
Pages1954-1958
ISBN (Print)978-1-5090-1807-9
ISBN (Electronic)978-1-5090-1806-2
DOIs
Publication statusPublished - Jul 2016
Event2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain
Duration: 10 Jul 201615 Jul 2016

Conference

Conference2016 IEEE International Symposium on Information Theory, ISIT 2016
CountrySpain
CityBarcelona
Period10/07/201615/07/2016
Sponsoret al., Gobierno de Espana-Ministerio de Economia y Competitividad, Huawei, NSF, Qualcomm, Universitat Pompeu Fabra (UPF)
SeriesI E E E International Symposium on Information Theory. Proceedings
ISSN2157-8095

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