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Secrecy and Accessibility in Distributed Storage [article]

Lukas Holzbaur, Stanislav Kruglik, Alexey Frolov, Antonia Wachter-Zeh
2020 arXiv   pre-print
A distributed storage system (DSS) needs to be efficiently accessible and repairable. Recently, considerable effort has been made towards the latter, while the former is usually not considered, since a trivial solution exists in the form of systematic encoding. However, this is not a viable option when considering storage that has to be secure against eavesdroppers. This work investigates the problem of efficient access to data stored on an DSS under such security constraints. Further, we
more » ... ish methods to balance the access load, i.e., ensure that each node is accessed equally often. We establish the capacity for the alphabet independent case and give an explicit code construction. For the alphabet-dependent case we give existence results based on a random coding argument.
arXiv:2001.05337v1 fatcat:fb4en3y7jfbvlo5k25d4jffhcu

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. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the shortening method and improves existing shortening bounds. 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
more » ... truction relies on expander graphs and is better in low rate region, the second construction utilizes LRC codes developed by Wang et al. as inner codes and better in high rate region.
arXiv:1702.01314v1 fatcat:gsccxznyuzgqjkz72qxwdvwa5u

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. This feature allows us to increase the achievable code rate and still meet load balancing requirements. 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.
arXiv:1705.11095v1 fatcat:gxy374datbchnblz4lnclbro5m

A method for constructing parity-check matrices of non-binary quasi-cyclic LDPC codes [article]

Stanislav Kruglik, Valeriya Potapova, Alexey Frolov
2017 arXiv   pre-print
Acknowledgments The research of Stanislav Kruglik was supported by the Russian Foundation for Basic Research (project 16-01-00716).  ... 
arXiv:1705.10717v1 fatcat:lxm2ik72rjfjzcpsbsskcatm7a

Information-theoretic problems of DNA-based storage systems

Stanislav Kruglik, Gregory Kucherov, Kamilla Nazirkhanova, Mikhail Filitov
2021 Information and Control Systems  
Currently, we witness an explosive growth in the amount of information produced by humanity. This raises new fundamental problems of its efficient storage and processing. Commonly used magnetic, optical, and semiconductor information storage devices have several drawbacks related to small information density and limited durability. One of the promising novel approaches to solving these problems is DNA-based data storage. Purpose: An overview of modern DNA-based storage systems and related
more » ... ation-theoretic problems. Results: The current state of the art of DNA-based storage systems is reviewed. Types of errors occurring in them as well as corresponding error-correcting codes are analized. The disadvantages of these codes are shown, and possible pathways for improvement are mentioned. Proposed information-theoretic models of DNA-based storage systems are analyzed, and their limitation highlighted. In conclusion, main obstacles to practical implementation of DNA-based storage systems are formulated, which can be potentially overcome using information-theoretic methods considered in this overview.
doi:10.31799/1684-8853-2021-3-39-52 fatcat:o5tw4tm5azawlgol5ox2gc3xiu

Explicit Low-Bandwidth Evaluation Schemes for Weighted Sums of Reed-Solomon-Coded Symbols [article]

Han Mao Kiah, Wilton Kim, Stanislav Kruglik, San Ling, Huaxiong Wang
2022 arXiv   pre-print
Motivated by applications in distributed storage, distributed computing, and homomorphic secret sharing, we study communication-efficient schemes for computing linear combinations of coded symbols. Specifically, we design low-bandwidth schemes that evaluate the weighted sum of ℓ coded symbols in a codeword c∈𝔽^n, when we are given access to d of the remaining components in c. Formally, suppose that 𝔽 is a field extension of 𝔹 of degree t. Let c be a codeword in a Reed-Solomon code of dimension
more » ... and our task is to compute the weighted sum of ℓ coded symbols. In this paper, for some s<t, we provide an explicit scheme that performs this task by downloading d(t-s) sub-symbols in 𝔹 from d available nodes, whenever d≥ℓ|𝔹|^s-ℓ+k. In many cases, our scheme outperforms previous schemes in the literature. Furthermore, we provide a characterization of evaluation schemes for general linear codes. Then in the special case of Reed-Solomon codes, we use this characterization to derive a lower bound for the evaluation bandwidth.
arXiv:2209.03251v1 fatcat:yk5rhiyw2rfhbef2pcbt4os2ay