Codes for erasures over directed graphs

Lev Yohananov; Eitan Yaakobi

doi:10.1109/ITW.2017.8277983

Codes for erasures over directed graphs

Lev Yohananov, Eitan Yaakobi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

In this work we continue the study of a new class of codes, called codes over graphs. Here we consider storage systems where the information is stored on the edges of a complete directed graph with n nodes. The failure model we consider is of node failures which are erasures of all edges, both incoming and outgoing, connected to the failed node. It is said that a code over graphs is a ρ-node-erasure-correcting code if it can correct the failure of any ρ nodes in the graphs of the code. While the construction of such optimal codes is an easy task if the field size is O(n²), our main goal in the paper is the construction of codes over smaller fields. In particular, our main result is the construction of optimal binary codes over graphs which correct two node failures with a prime number of nodes.

Original language	English
Title of host publication	2017 IEEE Information Theory Workshop, ITW 2017
Publisher	Institute of Electrical and Electronics Engineers
Pages	116-120
Number of pages	5
ISBN (Electronic)	9781509030972
DOIs	https://doi.org/10.1109/ITW.2017.8277983
State	Published - 2 Jul 2017
Externally published	Yes
Event	2017 IEEE Information Theory Workshop, ITW 2017 - Kaohsiung, Taiwan, Province of China Duration: 6 Nov 2017 → 10 Nov 2017

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2018-January
ISSN (Print)	2157-8095

Conference

Conference	2017 IEEE Information Theory Workshop, ITW 2017
Country/Territory	Taiwan, Province of China
City	Kaohsiung
Period	6/11/17 → 10/11/17

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ITW.2017.8277983

Cite this

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title = "Codes for erasures over directed graphs",

abstract = "In this work we continue the study of a new class of codes, called codes over graphs. Here we consider storage systems where the information is stored on the edges of a complete directed graph with n nodes. The failure model we consider is of node failures which are erasures of all edges, both incoming and outgoing, connected to the failed node. It is said that a code over graphs is a ρ-node-erasure-correcting code if it can correct the failure of any ρ nodes in the graphs of the code. While the construction of such optimal codes is an easy task if the field size is O(n2), our main goal in the paper is the construction of codes over smaller fields. In particular, our main result is the construction of optimal binary codes over graphs which correct two node failures with a prime number of nodes.",

author = "Lev Yohananov and Eitan Yaakobi",

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year = "2017",

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doi = "10.1109/ITW.2017.8277983",

language = "English",

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Yohananov, L & Yaakobi, E 2017, Codes for erasures over directed graphs. in 2017 IEEE Information Theory Workshop, ITW 2017. IEEE International Symposium on Information Theory - Proceedings, vol. 2018-January, Institute of Electrical and Electronics Engineers, pp. 116-120, 2017 IEEE Information Theory Workshop, ITW 2017, Kaohsiung, Taiwan, Province of China, 6/11/17. https://doi.org/10.1109/ITW.2017.8277983

Codes for erasures over directed graphs. / Yohananov, Lev; Yaakobi, Eitan.
2017 IEEE Information Theory Workshop, ITW 2017. Institute of Electrical and Electronics Engineers, 2017. p. 116-120 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Codes for erasures over directed graphs

AU - Yohananov, Lev

AU - Yaakobi, Eitan

PY - 2017/7/2

Y1 - 2017/7/2

N2 - In this work we continue the study of a new class of codes, called codes over graphs. Here we consider storage systems where the information is stored on the edges of a complete directed graph with n nodes. The failure model we consider is of node failures which are erasures of all edges, both incoming and outgoing, connected to the failed node. It is said that a code over graphs is a ρ-node-erasure-correcting code if it can correct the failure of any ρ nodes in the graphs of the code. While the construction of such optimal codes is an easy task if the field size is O(n2), our main goal in the paper is the construction of codes over smaller fields. In particular, our main result is the construction of optimal binary codes over graphs which correct two node failures with a prime number of nodes.

AB - In this work we continue the study of a new class of codes, called codes over graphs. Here we consider storage systems where the information is stored on the edges of a complete directed graph with n nodes. The failure model we consider is of node failures which are erasures of all edges, both incoming and outgoing, connected to the failed node. It is said that a code over graphs is a ρ-node-erasure-correcting code if it can correct the failure of any ρ nodes in the graphs of the code. While the construction of such optimal codes is an easy task if the field size is O(n2), our main goal in the paper is the construction of codes over smaller fields. In particular, our main result is the construction of optimal binary codes over graphs which correct two node failures with a prime number of nodes.

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BT - 2017 IEEE Information Theory Workshop, ITW 2017

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T2 - 2017 IEEE Information Theory Workshop, ITW 2017

Y2 - 6 November 2017 through 10 November 2017

ER -

Codes for erasures over directed graphs

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