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On One Generalization of LRC Codes with Availability [article]

Stanislav Kruglik, Marina Dudina, Valeriya Potapova, Alexey Frolov
2017 arXiv   pre-print
We investigate one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates.  ...  In this paper we derive an upper bound for the rate of such codes and give explicit constructions of codes with such a property. These constructions utilize LRC codes developed by Wang et al.  ...  Barg for introducing this problem to him and for numerous fruitful discussions during his stay in University of Maryland.  ... 
arXiv:1705.11095v1 fatcat:gxy374datbchnblz4lnclbro5m

On the Single-Parity Locally Repairable Codes with Multiple Repairable Groups

Yanbo Lu, Xinji Liu, Shutao Xia
2018 Information  
Based on the standard form of generator matrices, we present a novel characterization of single-parity LRCs with availability t ≥ 1 .  ...  In this paper, we focus on the study of single-parity LRCs with availability- ( r , t ) for information symbols.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/info9110265 fatcat:f4mxjtpu3vbqhcnsnr45cxkzp4

Complete Characterizations of Optimal Locally Repairable Codes with Locality 1 and k – 1

Yichong Xia, Bin Chen
2019 IEEE Access  
Thus we can completely characterize the three types of optimal LRCs with r = 1 based on some known constructions of MDS codes.  ...  This paper considers the optimal constructions of LRCs with locality r = 1 and r = k − 1, which involves three types: r-local LRCs, (r, δ)-LRCs and LRCs with t-availability.  ...  From the point of view of parallel repairing, Wang and Zhang [5] introduce the notion of LRC with t-availability, i.e., a linear code C with locality r is said to have t-availability if for every i ∈  ... 
doi:10.1109/access.2019.2934769 fatcat:b223oyhy5feo5ast7cwuge7qmq

Locally repairable codes from combinatorial designs

Yu Zhang, Haibin Kan
2020 Science China Information Sciences  
In particular, LRCs with availability are highly desirable for distributed storage systems, since this kind of codes provide the mechanism of local repair for code symbols and parallel reading of hot data  ...  We introduce several constructions of LRCs with strict availability and some constructions of distance-optimal LRCs with information-symbol locality.  ...  The responsibility for scientific accuracy and content remains entirely with the authors.  ... 
doi:10.1007/s11432-019-2649-5 fatcat:loeql6eosrdt3hi7nmu4bljqiy

New Binary Locally Repairable Codes with Locality 2 and Uneven Availabilities for Hot Data

Kang-Seok Lee, Hosung Park, Jong-Seon No
2018 Entropy  
The proposed BLRCs with k = 4 achieve the optimality on the information length for their given code length, minimum Hamming distance, locality, and availability in terms of the well-known theoretical upper  ...  In this paper, a new family of binary LRCs (BLRCs) with locality 2 and uneven availabilities for hot data is proposed, which has a high information symbol availability and low parity symbol availabilities  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e20090636 pmid:33265725 fatcat:odiha3doanckng4jc7tv2p33xu

Generalized construction of cyclic (r, t)-locally repairable codes using trace function

Quang Thanh Pham, Hideki Yagi
2017 IEICE Communications Express  
Wang, Zhang, and Lin recently have proposed a construction method of cyclic (r, t)-LRCs that can have high availability with a guaranteed lower bound on the minimum distance.  ...  This letter presents a generalized construction of cyclic (r, t)-LRCs based on the trace function whose high-degree terms are truncated.  ...  It can achieve high availability with a guaranteed lower bound on the minimum distance shown in Theorem 2.  ... 
doi:10.1587/comex.2017xbl0055 fatcat:eu5t5urngrfzxdbeu7gbbiht2e

Locality and Availability in Distributed Storage

Ankit Singh Rawat, Dimitris S. Papailiopoulos, Alexandros G. Dimakis, Sriram Vishwanath
2016 IEEE Transactions on Information Theory  
(n, k, r, t)-LRCs: • Serve any general request pattern for t data items. • Our codes also give batch codes for some set of parameters.  ...  symbol has locality r and availability t. • (n, k, r, t =1)-LRCs = codes with r information locality.  ... 
doi:10.1109/tit.2016.2524510 fatcat:vhcut4sk6zdc3h5t7wvdlkeko4

Locality and availability in distributed storage

Ankit Singh Rawat, Dimitris S. Papailiopoulos, Alexandros G. Dimakis, Sriram Vishwanath
2014 2014 IEEE International Symposium on Information Theory  
(n, k, r, t)-LRCs: • Serve any general request pattern for t data items. • Our codes also give batch codes for some set of parameters.  ...  symbol has locality r and availability t. • (n, k, r, t =1)-LRCs = codes with r information locality.  ... 
doi:10.1109/isit.2014.6874919 dblp:conf/isit/RawatPDV14 fatcat:3wtrnom54vd5xl7sduhjqvkxoa

Binary cyclic codes that are locally repairable

Sreechakra Goparaju, Robert Calderbank
2014 2014 IEEE International Symposium on Information Theory  
In doing so, we discover new upper bounds on the code dimension, and prove the optimality of enabling local repair by provisioning disjoint groups of disks.  ...  Simultaneously, the code must sustain a high rate, operate on a small finite field to be practically significant and be tolerant to a large number of erasures.  ...  Then C is a 3-available-2-local LRC with dimension k = 3n/7, and distance d = 4.  ... 
doi:10.1109/isit.2014.6874918 dblp:conf/isit/GoparajuC14 fatcat:ijxy3ghsmbcahh4bo22zzasfeu

Binary Linear Locally Repairable Codes [article]

Pengfei Huang, Eitan Yaakobi, Hironori Uchikawa, Paul H. Siegel
2015 arXiv   pre-print
We also show the construction of a long LRC with availability from a short one-step majority-logic decodable code.  ...  In this work, we present an upper bound on the minimum distance d of linear LRCs with availability, based on the work of Cadambe and Mazumdar.  ...  Finally, we studied the locality and availability properties of one-step majority-logic decodable codes, and demonstrated a construction of a long binary LRC with availability from a short one-step majority-logic  ... 
arXiv:1511.06960v1 fatcat:j7t7sjku7vhlhcbpjatr4xnlxe

Two classes of (r, t)-locally repairable codes

Anyu Wang, Zhifang Zhang, Dongdai Lin
2016 2016 IEEE International Symposium on Information Theory (ISIT)  
This code can achieve high availability and large minimum distance. The second one is based on the incidence matrix of linear subspaces in F m q .  ...  A locally repairable code with locality r and availability t, which is termed an (r, t)-LRC, is a code satisfying the property that the value at each coordinate can be recovered from t disjoint repair  ...  Instead of considering only information coordinates, here we focus on the linear code that has locality r and availability t for all its coordinates, termed (r, t)-LRC for short.  ... 
doi:10.1109/isit.2016.7541338 dblp:conf/isit/WangZL16 fatcat:l6frfe3qofevhbbrgz6b3s5fey

Applications of Polymatroid Theory to Distributed Storage Systems [article]

Thomas Westerbäck, Ragnar Freij-Hollanti, Camilla Hollanti
2015 arXiv   pre-print
Three classes of LRCs are considered, both with and without availability, and for both information-symbol and all-symbol locality.  ...  The parameters and classes of LRCs are generalized to polymatroids, and a general- ized Singelton bound on the parameters for these three classes of polymatroids and LRCs is given.  ...  ACKNOWLEDGMENTS This work was partially supported by the Academy of Finland grants #276031, #282938, and #283262, and by a grant from Magnus Ehrnrooth Foundation, Finland.  ... 
arXiv:1510.02499v1 fatcat:qkkkameedvc3vka4ddjwfrawqi

Some Improvements on Locally Repairable Codes [article]

Jun Zhang and Xin Wang and Gennian Ge
2015 arXiv   pre-print
By using the deep results from graph theory, we construct a family of LRCs with any locality r and availability 2 with code rate r-1/r+1 and optimal minimum distance O( n) where n is the length of the  ...  Secondly, we consider the constructions of LRCs with any locality and availability which have high code rate and minimum distance as large as possible. We give a graphical model for LRCs.  ...  Section 5 gives a construction of a family of LRCs with any locality r and availability 2 having code rate r−1 r+1 and minimum distance O(log n) where n is the length of the code.  ... 
arXiv:1506.04822v1 fatcat:atvy4pxribd6bg3lizv7vaa5ju

Locality and Availability in Distributed Storage [article]

Ankit Singh Rawat, Dimitris S. Papailiopoulos, Alexandros G. Dimakis,, Sriram Vishwanath
2014 arXiv   pre-print
This paper studies the problem of code symbol availability: a code symbol is said to have (r, t)-availability if it can be reconstructed from t disjoint groups of other symbols, each of size at most r.  ...  Our codes match the aforementioned bound and their construction relies on combinatorial objects called resolvable designs.  ...  In a parallel work, Wang et al. present a more general upper bound on minimum distance of linear codes with (r, t)-availability [28] .  ... 
arXiv:1402.2011v1 fatcat:rjhorgzkhzfzpb3fwi3gfzd464

Overview of Binary Locally Repairable Codes for Distributed Storage Systems

Young-Sik Kim, Chanki Kim, Jong-Seon No
2019 Electronics  
We also describe code generation methods based on modifications for linear codes such as extending, shorting, expurgating, and augmenting.  ...  We explain the various construction approaches of BLRCs such as cyclic code based, bipartite graph based, anticode based, partial spread based, and generalized Hamming code based techniques.  ...  If an (n, k, r, d) LRC supports availability t for local repair on each of k information symbols, it is referred to as an (n, k, r, t, d) LRC with information symbol availability.  ... 
doi:10.3390/electronics8060596 fatcat:zletmcs3g5g7rldozu3jjboly4
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