Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

Julian Renner; Sven Puchinger; Antonia Wachter-Zeh; Camilla Hollanti; Ragnar Freij-Hollanti

doi:10.1109/ISIT44484.2020.9174384

Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

Julian Renner, Sven Puchinger, Antonia Wachter-Zeh, Camilla Hollanti, Ragnar Freij-Hollanti

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference contribution › Scientific › vertaisarvioitu

3 Sitaatiot (Scopus)

Abstrakti

We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring {{\mathbb{Z}}-{{p^r}}}, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.

Alkuperäiskieli	Englanti
Otsikko	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
Kustantaja	IEEE
Sivut	19-24
Sivumäärä	6
ISBN (elektroninen)	9781728164328
DOI - pysyväislinkit	https://doi.org/10.1109/ISIT44484.2020.9174384
Tila	Julkaistu - kesäk. 2020
OKM-julkaisutyyppi	A4 Artikkeli konferenssijulkaisuussa
Tapahtuma	IEEE International Symposium on Information Theory - Los Angeles, Yhdysvallat Kesto: 21 heinäk. 2020 → 26 heinäk. 2020

Julkaisusarja

Nimi	IEEE International Symposium on Information Theory - Proceedings
Kustantaja	IEEE
Vuosikerta	2020-June
ISSN (painettu)	2157-8095

Conference

Conference	IEEE International Symposium on Information Theory
Lyhennettä	ISIT
Maa/Alue	Yhdysvallat
Kaupunki	Los Angeles
Ajanjakso	21/07/2020 → 26/07/2020

Pääsy asiakirjaan

10.1109/ISIT44484.2020.9174384

https://arxiv.org/abs/2001.04800

OpenUrl-saatavuus

Koko teksti

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Link to publication in Scopus

Lukuteoreettisia ja kombinatorisia työkaluja yksityisiin ja turvallisiin pilvipalveluihin
Hollanti, C., Arabi Kakavandfaramani, M., Grezet, M., Westerbäck, T., Damir, M., Blomqvist, F. & Tajeddine, R.
01/07/2016 → 30/06/2018
Projekti: Academy of Finland: Other research funding

Siteeraa tätä

Renner, J., Puchinger, S., Wachter-Zeh, A., Hollanti, C., & Freij-Hollanti, R. (2020). Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power. teoksessa 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings (Sivut 19-24). [9174384] (IEEE International Symposium on Information Theory - Proceedings; Vuosikerta 2020-June). IEEE. https://doi.org/10.1109/ISIT44484.2020.9174384

@inproceedings{c5a279bbed2d4d27bf0f4cdd1d0040c4,

title = "Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power",

abstract = "We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring {{\mathbb{Z}}-{{p^r}}}, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.",

author = "Julian Renner and Sven Puchinger and Antonia Wachter-Zeh and Camilla Hollanti and Ragnar Freij-Hollanti",

year = "2020",

month = jun,

doi = "10.1109/ISIT44484.2020.9174384",

language = "English",

series = "IEEE International Symposium on Information Theory - Proceedings",

publisher = "IEEE",

pages = "19--24",

booktitle = "2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings",

address = "United States",

note = "IEEE International Symposium on Information Theory, ISIT ; Conference date: 21-07-2020 Through 26-07-2020",

}

Renner, J, Puchinger, S, Wachter-Zeh, A, Hollanti, C & Freij-Hollanti, R 2020, Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power. julkaisussa 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings., 9174384, IEEE International Symposium on Information Theory - Proceedings, Vuosikerta 2020-June, IEEE, Sivut 19-24, IEEE International Symposium on Information Theory, Los Angeles, California, Yhdysvallat, 21/07/2020. https://doi.org/10.1109/ISIT44484.2020.9174384

Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power. / Renner, Julian; Puchinger, Sven; Wachter-Zeh, Antonia et al.
2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. IEEE, 2020. s. 19-24 9174384 (IEEE International Symposium on Information Theory - Proceedings; Vuosikerta 2020-June).

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference contribution › Scientific › vertaisarvioitu

TY - GEN

T1 - Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

AU - Renner, Julian

AU - Puchinger, Sven

AU - Wachter-Zeh, Antonia

AU - Hollanti, Camilla

AU - Freij-Hollanti, Ragnar

PY - 2020/6

Y1 - 2020/6

N2 - We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring {{\mathbb{Z}}-{{p^r}}}, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.

AB - We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring {{\mathbb{Z}}-{{p^r}}}, where p is a prime and r is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.

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U2 - 10.1109/ISIT44484.2020.9174384

DO - 10.1109/ISIT44484.2020.9174384

M3 - Conference contribution

AN - SCOPUS:85090420499

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 19

EP - 24

BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings

PB - IEEE

T2 - IEEE International Symposium on Information Theory

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ER -

Renner J, Puchinger S, Wachter-Zeh A, Hollanti C , Freij-Hollanti R. Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power. julkaisussa 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. IEEE. 2020. s. 19-24. 9174384. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT44484.2020.9174384

Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power

Abstrakti

Julkaisusarja

Conference

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Muut tiedostot ja linkit

Sormenjälki

Projektit

Lukuteoreettisia ja kombinatorisia työkaluja yksityisiin ja turvallisiin pilvipalveluihin

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