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Erasure codes with simplex locality [article]

Margreta Kuijper, Diego Napp
2014 arXiv   pre-print
We then examine the locality properties of a family of non-binary codes with simplex structure. We investigate their optimality and design several easy repair decoding methods.  ...  We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder.  ...  These non-binary codes are constructed using the generator matrix of binary simplex codes and hence inherit excellent locality properties even in the presence of large erasure patterns.  ... 
arXiv:1403.2779v1 fatcat:tsnz3p43gbatnnzkxarenwelw4

Erasure codes with simplex locality

Margreta Kuijper, Diego Napp
unpublished
We then examine the locality properties of a family of nonbinary codes with simplex structure. We investigate their optimality and design several easy repair decoding methods.  ...  We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder.  ...  These non-binary codes are constructed using the generator matrix of binary simplex codes and hence inherit excellent locality properties even in the presence of large erasure patterns.  ... 
fatcat:wtrcyiq6brcrha4uctdjfombuy

Packet-layer forward error correction coding for fading mitigation

Hennes Henniger
2006 Free-Space Laser Communications VI  
Therefore packet-layer coding is a favorable way to implement a code with codewords longer than typical fading events.  ...  A code validation platform based on Ethernet transmission technology and packet-layer coding using UDP packets was built up to prove the performance of packet-layer coding.  ...  The family of LDPC codes available in MCLv3 [4] was evaluated in terms of code efficiency by means of simulations. A file with 13.7 Mbyte was transmitted over a channel with 40 % packet erasure.  ... 
doi:10.1117/12.680402 fatcat:ea4yy7ezybhq7b7tsslufhze5y

Hamming and simplex codes for the sum-rank metric [article]

Umberto Martínez-Peñas
2021 arXiv   pre-print
Duals of sum-rank Hamming codes, called sum-rank simplex codes, are then introduced.  ...  As applications, sum-rank Hamming codes are proposed for error correction in multishot matrix-multiplicative channels and to construct locally repairable codes over small fields, including binary.  ...  Finally, C glob may correct one erasure locally by a simple XOR of the remaining nodes in that local group, and it may correct any erasure pattern with one erasure per local group plus any other 2 extra  ... 
arXiv:1908.03239v2 fatcat:5vopp3cknrgnln74mrb7ayooaa

Cooperative local repair in distributed storage

Ankit Singh Rawat, Arya Mazumdar, Sriram Vishwanath
2015 EURASIP Journal on Advances in Signal Processing  
Some other results regarding cooperative local repair are also presented, including an analysis for the well-known Hadamard/Simplex codes.  ...  Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems.  ...  Punctured Hadamard codes are also referred to as Simplex codes, which are the dual codes of Hamming codes.  ... 
doi:10.1186/s13634-015-0292-0 fatcat:o7yalwps25gqtbz6s6uqcg2t6e

Optimal linear and cyclic locally repairable codes over small fields

Alexander Zeh, Eitan Yaakobi
2015 2015 IEEE Information Theory Workshop (ITW)  
Four new constructions of optimal linear codes over small fields with locality properties are developed. The first two approaches give binary cyclic codes with locality two.  ...  Non-cyclic optimal binary linear codes with locality greater than two are obtained by the fourth construction.  ...  Construction 13 ( 13 Binary Code with Simplex Locality). Let n = 2 m − 1 and be divisible by 2 a − 1 and therefore a|m.  ... 
doi:10.1109/itw.2015.7133123 dblp:conf/itw/ZehY15 fatcat:r2un6f46n5bgngyvyi6prmjfam

On cooperative local repair in distributed storage

Ankit Singh Rawat, Arya Mazumdar, Sriram Vishwanath
2014 2014 48th Annual Conference on Information Sciences and Systems (CISS)  
Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems.  ...  We call this cooperative local repair. We present bounds on the dimension of such codes as well as give explicit constructions of families of codes.  ...  Punctured Hadamard codes are also referred to as Simplex codes, which are the dual codes of Hamming codes.  ... 
doi:10.1109/ciss.2014.6814152 dblp:conf/ciss/RawatMV14 fatcat:kilywgihvbfnfkls37jt3dibvu

Binary codes with locality for multiple erasures having short block length

S. B. Balaji, K. P. Prasanth, P. Vijay Kumar
2016 2016 IEEE International Symposium on Information Theory (ISIT)  
The focus of this paper is on linear, binary codes with locality having locality parameter r, that are capable of recovering from t≥ 2 erasures and that moreover, have short block length.  ...  Most of the constructions provided are of binary codes.  ...  in Section V-D for k = 16, [7, 3] Simplex code, [7, 3] Simplex code, [7, 3] Simplex code) The rate of the resulting code C will be : 0.026239067 with locality r = 2 and t = 2 9 − 1 and block length  ... 
doi:10.1109/isit.2016.7541380 dblp:conf/isit/BalajiPK16 fatcat:syr752ke2vbtxebtl2gthgfelm

Service Rate Region: A New Aspect of Coded Distributed System Design [article]

Mehmet Aktas, Gauri Joshi, Swanand Kadhe, Fatemeh Kazemi, Emina Soljanin
2021 arXiv   pre-print
As contributions along the first thread, we characterize the rate regions of maximum-distance-separable, locally repairable, and Simplex codes.  ...  underlying erasure code for a given service rate region.  ...  Simplex codes can also be considered as LRCs with (3, 2) locality [45] , [46] . Therefore, one can use the waterfilling algorithm to allocate requests in a Simplex coded system as well.  ... 
arXiv:2009.01598v2 fatcat:6kpn43dkmfcpdhmcj2qovkzzf4

Binary Linear Locally Repairable Codes [article]

Pengfei Huang, Eitan Yaakobi, Hironori Uchikawa, Paul H. Siegel
2015 arXiv   pre-print
Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures.  ...  We investigate the locality and availability properties of several classes of one-step majority-logic decodable codes, including cyclic simplex codes, cyclic difference-set codes, and 4-cycle free regular  ...  Finally, it is called r-optimal if there does not exist an [n, k, d] q code with all-symbol locality r − 1.Example 1. Consider the binary simplex code C with parameters [2 m − 1, m, 2 m−1 ].  ... 
arXiv:1511.06960v1 fatcat:j7t7sjku7vhlhcbpjatr4xnlxe

Optimal Binary Locally Repairable Codes via Anticodes [article]

Natalia Silberstein, Alexander Zeh
2015 arXiv   pre-print
This paper presents a construction for several families of optimal binary locally repairable codes (LRCs) with small locality (2 and 3). This construction is based on various anticodes.  ...  Moreover, most of these codes are optimal with respect to the Griesmer bound.  ...  INTRODUCTION Locally repairable codes (LRCs) are a family of erasure codes which allow local correction of erasures, where any code symbol can be recovered by using a small (fixed) number of other code  ... 
arXiv:1501.07114v1 fatcat:izkmwqxkjzdxjh2wodaplnlscy

Design of Convergence-Optimized Non-Binary LDPC Codes over Binary Erasure Channel

Yang Yu, Wen Chen, Lili Wei
2012 IEEE Wireless Communications Letters  
derived to design non-binary LDPC codes with convergence-optimized degree distributions.  ...  In this letter, we present a hybrid iterative decoder for non-binary low density parity check (LDPC) codes over binary erasure channel (BEC), based on which the recursion of the erasure probability is  ...  The optimized code C(0.5, 20) solves this problem by adding a simplex Manuscript received April 20, 2012.  ... 
doi:10.1109/wcl.2012.050112.120297 fatcat:bhyozznvhvf45daf3ls6fre7fi

Design of Convergence-Optimized Non-binary LDPC Codes over Binary Erasure Channel [article]

Yang Yu, Wen Chen, Lili Wei
2020 arXiv   pre-print
derived to design non-binary LDPC codes with convergence-optimized degree distributions.  ...  In this letter, we present a hybrid iterative decoder for non-binary low density parity check (LDPC) codes over binary erasure channel (BEC), based on which the recursion of the erasure probability is  ...  In order to show that the proposed hybrid iterative decoder can provide an enhanced erasure recovery performance, we compare our 4-ary code with the binary code D 2 (N p) characterized by λ(x) = 0.303x  ... 
arXiv:2003.01340v1 fatcat:gdzrtyu2dfgj7fr542e4vjy7uy

Delay Minimization in Real-time Communications with Joint Buffering and Coding [article]

Jesper H. Sørensen and Petar Popovski and Jan Østergaard
2016 arXiv   pre-print
The erasure code is modeled according to the recent information-theoretic results on finite block length codes.  ...  Therefore, in this case the delay budget should be spent mainly on the erasure code.  ...  Finally, simulation results are shown for a system with buffer delay t∆ ts = 8 and erasure codes with R = 1 2 and k = {5, 10, 15}, such that n = {10, 20, 30}.  ... 
arXiv:1610.04364v1 fatcat:h7msrs5lczgvbkcokabolqzf2q

An upper bound on the size of locally recoverable codes

Viveck Cadambe, Arya Mazumdar
2013 2013 International Symposium on Network Coding (NetCod)  
It turns out that the binary Simplex codes satisfy our bound with equality; hence the Simplex codes are the first example of a optimal binary locally repairable code family.  ...  The notion of local recoverability is important in the area of distributed storage where a most frequent error-event is a single storage node failure (erasure).  ...  It is well known that an erasure code with length n, dimension k and minimum distance d, or an (n, k, d) code, can recover from any set of d − 1 erasures.  ... 
doi:10.1109/netcod.2013.6570829 dblp:conf/netcod/CadambeM13 fatcat:fbktkgp5y5cyzoivrhhtgudzbm
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