# Irregular Recovery and Unequal Locality for Locally Recoverable Codes with Availability

@article{Bhadane2017IrregularRA, title={Irregular Recovery and Unequal Locality for Locally Recoverable Codes with Availability}, author={Sourbh Bhadane and Andrew Thangaraj}, journal={ArXiv}, year={2017}, volume={abs/1705.05005} }

A code is said to be a Locally Recoverable Code (LRC) with availability if every coordinate can be recovered from multiple disjoint sets of other coordinates called recovering sets. The vector of sizes of recovering sets of a coordinate is called its recovery profile. In this work, we consider LRCs with availability under two different settings: (1) irregular recovery: non-constant recovery profile that remains fixed for all coordinates, (2) unequal locality: regular recovery profile that can…

## Tables and Topics from this paper

## 3 Citations

RS-like locally recoverable codes with intersecting recovering sets

- Computer Science, MathematicsFinite Fields Their Appl.
- 2020

This paper has presented a sufficient condition for a cyclic code over a finite field to be an LRC code with intersecting recovering sets and obtained a bound on the rate of the codes from the present construction.

On Optimal Locally Repairable Codes With Super-Linear Length

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2020

In this paper, locally repairable codes which have optimal minimum Hamming distance with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such…

On Optimal Locally Repairable Codes with Super-Linear Length

- Computer Science, Mathematics2019 IEEE International Symposium on Information Theory (ISIT)
- 2019

Optimal locally repairable codes with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve…

## References

SHOWING 1-10 OF 13 REFERENCES

Bounds on the Parameters of Locally Recoverable Codes

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2016

New finite-length and asymptotic bounds on the parameters of LRC codes are derived and an asymPTotic Gilbert-Varshamov type bound is derived for LRC code types and the maximum attainable relative distance is found.

Linear locally repairable codes with availability

- Mathematics, Computer Science2015 IEEE International Symposium on Information Theory (ISIT)
- 2015

In this work, we present a new upper bound on the minimum distance d of linear locally repairable codes (LRCs) with information locality and availability. The bound takes into account the code length…

A family of optimal locally recoverable codes

- Mathematics, Computer Science2014 IEEE International Symposium on Information Theory
- 2014

A family of LRC codes that attain the maximum possible value of the distance for a given locality parameter and code cardinality are presented.

Achieving arbitrary locality and availability in binary codes

- Computer Science, Mathematics2015 IEEE International Symposium on Information Theory (ISIT)
- 2015

A binary linear code of length equation is constructed which has locality r and availability t for all coordinates, the only known construction that can achieve arbitrary locality and availability.

Repair locality from a combinatorial perspective

- Computer Science, Mathematics2014 IEEE International Symposium on Information Theory
- 2014

The concept of regenerating set is introduced to characterize the local repair groups and a tighter distance bound is derived for the square code which is a class of linear codes with locality r(2) and high information rate, and an explicit code construction attaining the optimal distance bound.

Codes with unequal locality

- Computer Science, Mathematics2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

This paper introduces the concept of locality requirement of a code, which can be viewed as a recoverability requirement on symbols, and presents a greedy algorithm to construct codes that have maximum minimum distance among all codes that satisfy the locality requirement.

Repair Locality With Multiple Erasure Tolerance

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2014

The (r, δ)c-locality is proposed, providing δ-1 nonoverlapping local repair groups of size no more than r for a coordinate so that the repair locality r can tolerate δ -1 erasures in total and an upper bound on the minimum distance is derived.

Bounds and constructions of codes with multiple localities

- Mathematics, Computer Science2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

Two bounds are extended, the Singleton and the alphabet-dependent upper bound on the dimension of Cadambe-Mazumdar for LRCs, to the case of ML-LRCs with more than two localities and Singleton-optimal ML- lRCs codes are constructed.

Locality and Availability in Distributed Storage

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2016

It is shown that it is possible to construct codes that can support a scaling number of parallel reads while keeping the rate to be an arbitrarily high constant, and that this is possible with the minimum Hamming distance arbitrarily close to the Singleton bound.

Optimal locally repairable codes and connections to matroid theory

- Computer Science, Mathematics2013 IEEE International Symposium on Information Theory
- 2013

This work presents an explicit and simple to implement construction of optimal LRCs, for code parameters previously established by existence results, and derives a new result on the matroid represented by the code's generator matrix.