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Bounds and Constructions of Codes with All-Symbol Locality and Availability [article]

Stanislav Kruglik, Alexey Frolov
2017 arXiv   pre-print
We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability.  ...  To reduce the gap in between upper and lower bounds we do not restrict the alphabet size and propose explicit constructions of codes with locality and availability via rank-metric codes.  ...  The first construction relies on expander graphs and is better in low rate region, the second construction utilizes codes with arbitrarily all-symbol locality and availability, high rate and small minimum  ... 
arXiv:1702.01314v1 fatcat:gsccxznyuzgqjkz72qxwdvwa5u

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

Kang-Seok Lee, Hosung Park, Jong-Seon No
2018 Entropy  
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  ...  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  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e20090636 pmid:33265725 fatcat:odiha3doanckng4jc7tv2p33xu

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

Yanbo Lu, Xinji Liu, Shutao Xia
2018 Information  
For an [ n , k , d ] linear code, if a code symbol can be repaired by t disjoint groups of other code symbols, where each group contains at most r code symbols, it is said to have availability- ( r , t  ...  Locally repairable codes (LRCs) are a new family of erasure codes used in distributed storage systems which have attracted a great deal of interest in recent years.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/info9110265 fatcat:f4mxjtpu3vbqhcnsnr45cxkzp4

Binary Linear Locally Repairable Codes [article]

Pengfei Huang, Eitan Yaakobi, Hironori Uchikawa, Paul H. Siegel
2015 arXiv   pre-print
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.  ...  Compared to other previous constructions of binary LRCs with fixed locality or minimum distance, our construction is much more flexible in terms of code parameters, and gives various families of high-rate  ...  Thus, this code has all-symbol locality r = 2 m and availability t = 2 m + 1.  ... 
arXiv:1511.06960v1 fatcat:j7t7sjku7vhlhcbpjatr4xnlxe

Locality and Availability in Distributed Storage [article]

Ankit Singh Rawat, Dimitris S. Papailiopoulos, Alexandros G. Dimakis,, Sriram Vishwanath
2014 arXiv   pre-print
This paper also presents a bound demonstrating a trade-off between minimum distance, availability and locality.  ...  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.  ...  If an (n, k, r, t)-LRC allows for locality of r for all n coded symbols, i.e., all-symbol locality, then it is referred to as an (n, k, r, t)-LRC with all-symbol locality.  ... 
arXiv:1402.2011v1 fatcat:rjhorgzkhzfzpb3fwi3gfzd464

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

Overview of Binary Locally Repairable Codes for Distributed Storage Systems

Young-Sik Kim, Chanki Kim, Jong-Seon No
2019 Electronics  
The construction of codes over a small alphabet size of symbols is of particular interest for efficient hardware implementation.  ...  This paper summarizes the details of recently proposed binary locally repairable codes (BLRCs) and their features.  ...  One possible solution is LRC with multiple disjoint recovery sets. There are two types of availabilities, namely information-symbol availability and all-symbol availability.  ... 
doi:10.3390/electronics8060596 fatcat:zletmcs3g5g7rldozu3jjboly4

Erasure Coding for Distributed Storage: An Overview [article]

S. B. Balaji, M. Nikhil Krishnan, Myna Vajha, Vinayak Ramkumar, Birenjith Sasidharan, P. Vijay Kumar
2018 arXiv   pre-print
Coding theory has evolved to handle these challenges by introducing two new classes of erasure codes, namely regenerating codes and locally recoverable codes as well as by coming up with novel ways to  ...  In a distributed storage system, code symbols are dispersed across space in nodes or storage units as opposed to time.  ...  LRG codes with MSR or MBR all-symbol locality, and information-symbol locality that meet the minimum-distance bound, are provided for various parameters.  ... 
arXiv:1806.04437v1 fatcat:6ivmg6n44jhtjal26btpwjbkpy

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.  ...  In this paper, a link between polymatroid theory and locally repairable codes (LRCs) is established.  ...  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

Locally repairable codes from combinatorial designs

Yu Zhang, Haibin Kan
2020 Science China Information Sciences  
We introduce several constructions of LRCs with strict availability and some constructions of distance-optimal LRCs with information-symbol locality.  ...  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  ...  The responsibility for scientific accuracy and content remains entirely with the authors.  ... 
doi:10.1007/s11432-019-2649-5 fatcat:loeql6eosrdt3hi7nmu4bljqiy

Batch and PIR Codes and Their Connections to Locally Repairable Codes [article]

Vitaly Skachek
2017 arXiv   pre-print
Bounds on the parameters of the codes, as well as basic constructions, are presented. Connections between different code families are discussed.  ...  In this survey, two related families of codes are discussed: batch codes and codes for private information retrieval.  ...  Acknowledgements The material in this survey has benefited a lot from discussions of the author with his students and colleagues, including Venkatesan Guruswami, Camilla Hollanti, Helger Lipmaa, Sushanta  ... 
arXiv:1611.09914v4 fatcat:qmj3i24exjcnjmuykep2h3aowq

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

Yichong Xia, Bin Chen
2019 IEEE Access  
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.  ...  A locally repairable code (LRC) is a [n, k, d] linear code with length n, dimension k, minimum distance d and locality r, which means that every code symbol can be repaired by at most r other symbols.  ...  Lemma 3 ( [14] , Proposition 2): For a linear code C with all symbol locality attaining the bound (2), if r | k, then r+δ−1 | n and the supports of the local parity-check matrices H s L (1 ≤ s ≤ n r+δ−  ... 
doi:10.1109/access.2019.2934769 fatcat:b223oyhy5feo5ast7cwuge7qmq

Irregular Recovery and Unequal Locality for Locally Recoverable Codes with Availability [article]

Sourbh Bhadane, Andrew Thangaraj
2017 arXiv   pre-print
For the case of regular and fixed recovery profile, we show that a specific Tamo-Barg polynomial-evaluation construction is optimal for all-symbol locality, and we provide parity-check matrix constructions  ...  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.  ...  All-symbol locality We now derive a minimum distance upper bound for codes with (r, t) all-symbol locality.  ... 
arXiv:1705.05005v1 fatcat:yq2mqk6apvfgddjaas7uwgn4wa

Locality and Availability in Distributed Storage

Ankit Singh Rawat, Dimitris S. Papailiopoulos, Alexandros G. Dimakis, Sriram Vishwanath
2016 IEEE Transactions on Information Theory  
(systematic) Gabidulin code [N + t, k] F M q -LRC (N + (t 1) k r , r, t 1) Construction of (n, k, r, t)-LRCs with All-symbol Locality x 2 F M q F q F q F q F q Local parities for all-symbol locality (over  ...  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  
(systematic) Gabidulin code [N + t, k] F M q -LRC (N + (t 1) k r , r, t 1) Construction of (n, k, r, t)-LRCs with All-symbol Locality x 2 F M q F q F q F q F q Local parities for all-symbol locality (over  ...  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
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