A Bound on Rate of Codes with Locality with Sequential Recovery from Multiple Erasures

In this paper, we derive an upper bound on rate of a code with locality with sequential recovery from multiple erasures for any $r \geq 3$ and any $t>0$ . We also give a construction of codes achieving our rate bound for any $r$ and $t \in 2\mathbb{Z_{+}}$.

[1]  Chau Yuen,et al.  Binary Locally Repairable Codes - Sequential Repair for Multiple Erasures , 2016, 2016 IEEE Global Communications Conference (GLOBECOM).

[2]  Frédérique Oggier,et al.  Self-repairing homomorphic codes for distributed storage systems , 2010, 2011 Proceedings IEEE INFOCOM.

[3]  Zhifang Zhang,et al.  Repair locality from a combinatorial perspective , 2014, 2014 IEEE International Symposium on Information Theory.

[4]  Dimitris S. Papailiopoulos,et al.  Locally Repairable Codes , 2012, IEEE Transactions on Information Theory.

[5]  Minghua Chen,et al.  Pyramid Codes: Flexible Schemes to Trade Space for Access Efficiency in Reliable Data Storage Systems , 2007, Sixth IEEE International Symposium on Network Computing and Applications (NCA 2007).

[6]  Itzhak Tamo,et al.  A Family of Optimal Locally Recoverable Codes , 2013, IEEE Transactions on Information Theory.

[7]  Zoltán Füredi,et al.  Graphs of Prescribed Girth and Bi-Degree , 1995, J. Comb. Theory, Ser. B.

[8]  Wentu Song,et al.  On Sequential Locally Repairable Codes , 2018, IEEE Transactions on Information Theory.

[9]  Paul H. Siegel,et al.  Binary Linear Locally Repairable Codes , 2015, IEEE Transactions on Information Theory.

[10]  Balaji Srinivasan Babu,et al.  Binary Codes with Locality for Four Erasures , 2016, ArXiv.

[11]  Fang-Wei Fu,et al.  On the Locality and Availability of Linear Codes Based on Finite Geometry , 2015, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[12]  P. Vijay Kumar,et al.  Codes with local regeneration , 2012, 2013 IEEE International Symposium on Information Theory.

[13]  Chau Yuen,et al.  Locally Repairable Codes with Functional Repair and Multiple Erasure Tolerance , 2015, ArXiv.

[14]  Chau Yuen,et al.  Optimal Locally Repairable Linear Codes , 2014, IEEE Journal on Selected Areas in Communications.

[15]  Frédérique E. Oggier,et al.  Locally repairable codes with multiple repair alternatives , 2013, 2013 IEEE International Symposium on Information Theory.

[16]  Hong-Yeop Song,et al.  Binary locally repairable codes from complete multipartite graphs , 2015, 2015 International Conference on Information and Communication Technology Convergence (ICTC).

[17]  Zhifang Zhang,et al.  Repair Locality With Multiple Erasure Tolerance , 2014, IEEE Transactions on Information Theory.

[18]  Itzhak Tamo,et al.  Bounds on the Parameters of Locally Recoverable Codes , 2015, IEEE Transactions on Information Theory.

[19]  Xin Wang,et al.  Some Improvements on Locally Repairable Codes , 2015, ArXiv.

[20]  Sriram Vishwanath,et al.  Cooperative local repair in distributed storage , 2014, EURASIP Journal on Advances in Signal Processing.

[21]  Cheng Huang,et al.  On the Locality of Codeword Symbols , 2011, IEEE Transactions on Information Theory.

[22]  P. Vijay Kumar,et al.  Codes with locality for two erasures , 2014, 2014 IEEE International Symposium on Information Theory.

[23]  Dimitris S. Papailiopoulos,et al.  Locality and Availability in Distributed Storage , 2016, IEEE Trans. Inf. Theory.

[24]  Hong-Yeop Song,et al.  Binary Locally Repairable Codes from Complete Multipartite Graphs , 2015 .

[25]  Balaji Srinivasan Babu,et al.  Binary codes with locality for multiple erasures having short block length , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[26]  P. Vijay Kumar,et al.  Codes with local regeneration , 2013, ISIT.