### Abstract

We consider exact repair of failed nodes in maximum distance separable (MDS) code based distributed storage systems. It is well known that an (n, k) MDS code can tolerate failure (erasure) of up to n - k storage disks, when the code is used to store k information elements over n distributed storage disks. The focus of this paper is optimal recovery, in terms of repair bandwidth - the amount of data to be downloaded to repair a failed node - for a single failed node. When a single node fails, it has been previously shown by Dimakis et. al. that the amount of repair bandwidth is at least L(n-1)/(n-k) units, when each storage disk stores L units of data. The achievability of this lower bound of L(n-1)/(n-k) units, for arbitrary values of (n, k); has been shown previously using asymptotic code constructions based on asymptotic interference alignment. However, the existence of finite codes satisfying this lower bound has been shown only for specific regimes of (n, k) and their existence for arbitrary values of (n, k) remained open. In this paper, we provide the first known construction of a finite code for arbitrary (n, k), which can repair a single failed systematic node by downloading exactly L(n-1)/(n-k) units of data. The code that we construct is based on permutation matrices and hence termed the Permutation Code.

Original language | English (US) |
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Title of host publication | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 |

Pages | 1225-1229 |

Number of pages | 5 |

DOIs | |

State | Published - Oct 26 2011 |

Event | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation Duration: Jul 31 2011 → Aug 5 2011 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8104 |

### Other

Other | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 |
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Country | Russian Federation |

City | St. Petersburg |

Period | 7/31/11 → 8/5/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

### Cite this

*2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011*(pp. 1225-1229). [6033730] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2011.6033730

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*2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011.*, 6033730, IEEE International Symposium on Information Theory - Proceedings, pp. 1225-1229, 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011, St. Petersburg, Russian Federation, 7/31/11. https://doi.org/10.1109/ISIT.2011.6033730

**Permutation code : Optimal exact-repair of a single failed node in MDS code based distributed storage systems.** / Cadambe, Viveck R.; Huang, Cheng; Li, Jin.

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

TY - GEN

T1 - Permutation code

T2 - Optimal exact-repair of a single failed node in MDS code based distributed storage systems

AU - Cadambe, Viveck R.

AU - Huang, Cheng

AU - Li, Jin

PY - 2011/10/26

Y1 - 2011/10/26

N2 - We consider exact repair of failed nodes in maximum distance separable (MDS) code based distributed storage systems. It is well known that an (n, k) MDS code can tolerate failure (erasure) of up to n - k storage disks, when the code is used to store k information elements over n distributed storage disks. The focus of this paper is optimal recovery, in terms of repair bandwidth - the amount of data to be downloaded to repair a failed node - for a single failed node. When a single node fails, it has been previously shown by Dimakis et. al. that the amount of repair bandwidth is at least L(n-1)/(n-k) units, when each storage disk stores L units of data. The achievability of this lower bound of L(n-1)/(n-k) units, for arbitrary values of (n, k); has been shown previously using asymptotic code constructions based on asymptotic interference alignment. However, the existence of finite codes satisfying this lower bound has been shown only for specific regimes of (n, k) and their existence for arbitrary values of (n, k) remained open. In this paper, we provide the first known construction of a finite code for arbitrary (n, k), which can repair a single failed systematic node by downloading exactly L(n-1)/(n-k) units of data. The code that we construct is based on permutation matrices and hence termed the Permutation Code.

AB - We consider exact repair of failed nodes in maximum distance separable (MDS) code based distributed storage systems. It is well known that an (n, k) MDS code can tolerate failure (erasure) of up to n - k storage disks, when the code is used to store k information elements over n distributed storage disks. The focus of this paper is optimal recovery, in terms of repair bandwidth - the amount of data to be downloaded to repair a failed node - for a single failed node. When a single node fails, it has been previously shown by Dimakis et. al. that the amount of repair bandwidth is at least L(n-1)/(n-k) units, when each storage disk stores L units of data. The achievability of this lower bound of L(n-1)/(n-k) units, for arbitrary values of (n, k); has been shown previously using asymptotic code constructions based on asymptotic interference alignment. However, the existence of finite codes satisfying this lower bound has been shown only for specific regimes of (n, k) and their existence for arbitrary values of (n, k) remained open. In this paper, we provide the first known construction of a finite code for arbitrary (n, k), which can repair a single failed systematic node by downloading exactly L(n-1)/(n-k) units of data. The code that we construct is based on permutation matrices and hence termed the Permutation Code.

UR - http://www.scopus.com/inward/record.url?scp=80054801912&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054801912&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2011.6033730

DO - 10.1109/ISIT.2011.6033730

M3 - Conference contribution

AN - SCOPUS:80054801912

SN - 9781457705953

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1225

EP - 1229

BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

ER -