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

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

7 Citations (Scopus)

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.

Original language	English
Title of host publication	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
Publisher	IEEE
Pages	19-24
Number of pages	6
ISBN (Electronic)	9781728164328
DOIs	https://doi.org/10.1109/ISIT44484.2020.9174384
Publication status	Published - Jun 2020
MoE publication type	A4 Conference publication
Event	IEEE International Symposium on Information Theory - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Publisher	IEEE
Volume	2020-June
ISSN (Print)	2157-8095

Conference

Conference	IEEE International Symposium on Information Theory
Abbreviated title	ISIT
Country/Territory	United States
City	Los Angeles
Period	21/07/2020 → 26/07/2020

Access to Document

10.1109/ISIT44484.2020.9174384

https://arxiv.org/abs/2001.04800

Cite this

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. In 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings (pp. 19-24). Article 9174384 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June). IEEE. https://doi.org/10.1109/ISIT44484.2020.9174384

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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",

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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. in 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings., 9174384, IEEE International Symposium on Information Theory - Proceedings, vol. 2020-June, IEEE, pp. 19-24, IEEE International Symposium on Information Theory, Los Angeles, California, United States, 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. p. 19-24 9174384 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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

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

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Number-theoretic and combinatorial tools for private and secure cloud services

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

Abstract

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Number-theoretic and combinatorial tools for private and secure cloud services

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