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Cyclic Codes with Locality and Availability [article]

Lukas Holzbaur, Ragnar Freij-Hollanti, Antonia Wachter-Zeh
2019 arXiv   pre-print
In this work codes with availability are constructed based on the cyclic locally repairable code (LRC) construction by Tamo et al. and their extension to (r,ρ)-locality by Chen et al.  ...  We give a bound on the dimension of LRCs with availability and orthogonal repair sets and show that the given construction is optimal for a range of parameters.  ...  In the following we will consider cyclic Tamo-Barg codes with (r, ρ)locality and availability.  ... 
arXiv:1812.06897v3 fatcat:j7ukyvajwjehvbs23zwpcb6viy

Optimal linear and cyclic locally repairable codes over small fields

Alexander Zeh, Eitan Yaakobi
2015 2015 IEEE Information Theory Workshop (ITW)  
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length.  ...  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.  ...  The constructed [n = 2 m − 1, k = 3n/7 − m, d ≥ 12] 2 cyclic code C is a 2-local code and has availability t = 3 as defined in Def. 4. Example 11 (2-Local Binary Code with Availability Three).  ... 
doi:10.1109/itw.2015.7133123 dblp:conf/itw/ZehY15 fatcat:r2un6f46n5bgngyvyi6prmjfam

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

Quang Thanh Pham, Hideki Yagi
2017 IEICE Communications Express  
r and t are called locality and availability, respectively.  ...  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.  ...  Huang, Yaakobi, Uchikawa, and Siegel [4] showed that a class of cyclic LRCs offers an efficient way to evaluate locality r and availability t.  ... 
doi:10.1587/comex.2017xbl0055 fatcat:eu5t5urngrfzxdbeu7gbbiht2e

Binary cyclic codes that are locally repairable

Sreechakra Goparaju, Robert Calderbank
2014 2014 IEEE International Symposium on Information Theory  
Specifically, we construct cyclic codes that are locally repairable for locality 2 and distances 2, 6 and 10.  ...  To this end, we construct new families of binary linear codes that have an optimal dimension (rate) for a given minimum distance and locality.  ...  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 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  ...  First, we focus on analyzing the locality of some classical codes, i.e., cyclic codes and Reed-Muller codes, and their modified versions, which are obtained by applying the operations of extend, shorten  ...  Several recent works have considered codes with both locality and availability properties.  ... 
arXiv:1511.06960v1 fatcat:j7t7sjku7vhlhcbpjatr4xnlxe

Codes with locality from cyclic extensions of Deligne-Lusztig curves [article]

Gretchen L. Matthews, Fernando L. Piñero
2020 arXiv   pre-print
The second yields codes with availability by appealing to the use of fiber products as described by Haymaker, Malmskog, and Matthews, while the third accomplishes availability by taking products of codes  ...  We see that cyclic extensions of the Deligne-Lusztig curves provide codes with smaller locality than those typically found in the literature.  ...  In Section 2, we obtain codes with locality from the cyclic extensionS q of the Suzuki curve S q and the cyclic extensionR q of the Ree curve R q .  ... 
arXiv:2006.06397v1 fatcat:c7oisc5ymrfttd7s4giia3sjmq

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

Anyu Wang, Zhifang Zhang, Dongdai Lin
2016 2016 IEEE International Symposium on Information Theory (ISIT)  
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  ...  The first one is a cyclic code of which the parity check polynomial is closely related to the trace function over finite fields. This code can achieve high availability and large minimum distance.  ...  The first one is an [n = q m − 1, k = q m−1 − 1] p p-ary cyclic code with locality r = m − 1 and availability t = em, where q = p e is a prime power.  ... 
doi:10.1109/isit.2016.7541338 dblp:conf/isit/WangZL16 fatcat:l6frfe3qofevhbbrgz6b3s5fey

Overview of Binary Locally Repairable Codes for Distributed Storage Systems

Young-Sik Kim, Chanki Kim, Jong-Seon No
2019 Electronics  
This paper summarizes the details of recently proposed binary locally repairable codes (BLRCs) and their features.  ...  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.  ...  alphabets [33] ; -codes with short local MDS [24, 30] ; and codes with local regeneration [30, 32] .  ... 
doi:10.3390/electronics8060596 fatcat:zletmcs3g5g7rldozu3jjboly4

Cyclic and convolutional codes with locality [article]

Zitan Chen, Alexander Barg
2020 arXiv   pre-print
Among other results, we extend the general approach to cyclic codes with locality to multidimensional cyclic codes, yielding new families of LRC codes with availability, and construct a family of q-ary  ...  In this paper we focus on cyclic constructions of LRC codes and derive conditions on the zeros of the code that support the property of hierarchical locality.  ...  . . . . . . . . . . . . . . . . . . . . . 14 IV Bi-cyclic codes with availability 17 I.  ... 
arXiv:2004.06770v1 fatcat:uzu2jxeo5zc7lj2dy5zimqokua

Matroid Theory and Storage Codes: Bounds and Constructions [article]

Ragnar Freij-Hollanti, Camilla Hollanti, Thomas Westerbäck
2017 arXiv   pre-print
The chapter embeds all the essential features of LRCs, namely locality, availability, and hierarchy alongside with related generalised Singleton bounds.  ...  Recent research on distributed storage systems (DSSs) has revealed interesting connections between matroid theory and locally repairable codes (LRCs).  ...  Linear Locally Repairable Codes with Availability The very broad class of linear LRCs will be defined next.  ... 
arXiv:1704.04007v2 fatcat:vzvtotomevgxhhbxo5otfaosbq

A Study on the Impact of Locality in the Decoding of Binary Cyclic Codes [article]

M. Nikhil Krishnan, Bhagyashree Puranik, P. Vijay Kumar, Itzhak Tamo, Alexander Barg
2017 arXiv   pre-print
Given a binary cyclic code having locality or availability, we suitably modify the OSD to obtain gains in terms of the Signal-To-Noise ratio, for a given reliability and essentially the same level of decoder  ...  In this paper, we study the impact of locality on the decoding of binary cyclic codes under two approaches, namely ordered statistics decoding (OSD) and trellis decoding.  ...  LOCALITY AND CYCLIC CODES A.  ... 
arXiv:1702.03786v1 fatcat:a25tlhe5hvde5desjvplhidvwq

Minimum Bandwidth Regenerating Codes Based on Cyclic VFR Codes

2019 KSII Transactions on Internet and Information Systems  
Compared with RS codes and simple regenerating codes, the proposed MBR codes based on cyclic VFR codes have lower repair locality, repair complexity and bandwidth overhead, as well as higher repair efficiency  ...  Performance analysis and simulation results show that, the repair locality of a single node failure is always 2 when MBR codes based on cyclic VFR codes are adopted in distributed storage systems, which  ...  With the increasing of k , the repair locality of RS codes increases linearly, and the repair localities of SRC and MBR codes based on cyclic VFR codes are 8 and 2 respectively.  ... 
doi:10.3837/tiis.2019.07.014 fatcat:br322ejsl5gubi4xldlwynw4o4

Six new binary quasi-cyclic codes

Zhi Chen
1994 IEEE Transactions on Information Theory  
A local exhaustive search is used to find these codes and many other quasi-cyclic codes which attain the lower bounds. Index Terms-Quasi-cyclic codes, best known binary codes, coding and codes.  ...  Abstract-Six new quasi-cyclic codes are presented, which improve the lower bounds on the minimum distance for a binary code.  ...  With this local exhaustive search, many good QC codes have been obtained.  ... 
doi:10.1109/18.333888 fatcat:hbdu25n25vfhljhdt3jv6gqwgi

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

Wireless Communication Network Security System Based on Big Data Information Transmission Technology

Yichao Zhao, Wenjun Ouyang, Kalidoss Rajakani
2022 Wireless Communications and Mobile Computing  
The study found that the total interference intensity in the cyclic delay diversity system is lower than that of the frequency division duplex and time division duplex.  ...  At the same time, this paper introduces a cyclic delay full diversity sensing information coding transmission scheme for the security risks of wireless communication networks.  ...  So, what kind of clever code we choose and how to use the brilliant code become the key to the cyclic delay diversity system. Smart Code.  ... 
doi:10.1155/2022/1066331 fatcat:qr7z4ucs3rbb3btw72rctphvpy
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