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An $(r, \delta)$ -locally repairable code ($(r, \delta)$ -LRC for short) was introduced by Prakash et al. for tolerating multiple failed nodes in distributed storage systems, which was a generalization of the concept of $r$ -LRCs produced by Gopalan et al.. An $(r, \delta)$ -LRC is said to be optimal if it achieves the Singleton-like bound. Recently, Chen et al. generalized the construction of cyclic $r$ -LRCs proposed by Tamo et al. , and constructed several classes of optimal $(r, \delta)$ -LRCs of length $n$ for $n\, |\, (q-1)$ or $n\,|\, (q+1)$ , respectively in terms of a union of the set of zeros controlling the minimum distance and the set of zeros ensuring the locality. Following the work of , , this paper first characterizes $(r, \delta)$ -locality of a cyclic code via its zeros. Then we construct several classes of optimal cyclic $(r, \delta)$ -LRCs of length $n$ for $n\, |\, (q-1)$ or $n\,|\, (q+1)$ , respectively from the product of two sets of zeros. Our constructions include all optimal cyclic $(r,\delta)$ -LRCs proposed in , , and our method seems more convenient to obtain optimal cyclic $(r, \delta)$ -LRCs with flexible parameters. Moreover, many optimal cyclic $(r,\delta)$ -LRCs of length $n$ for $n\, |\, (q-1)$ or $n\,|\, (q+1)$ , respectively with $(r+\delta -1)\nmid n$ can be obtained from our method. [ABSTRACT FROM AUTHOR]

Integration of electric vehicles (EVs) into the smart grid has attracted considerable interest from researchers, governments, and private companies alike. Such integration may bring problems if not conducted well, but EVs can be also used by utilities and other industry stakeholders to enable the smart grid. This paper presents a systematic literature review of the topic and offer a research framework to guide future research and enrich the body of knowledge. The systematic literature review presented in this paper does not contain all the material available on this subject. It does, however, include most of the key publications readily available in a power-utility or technical-reference library together with some of the earlier papers in the field (the anchor papers). For this review, we selected appropriate digital sources (digital libraries and indexing systems; IEEE Xplore and Web of Science), determined the search terms, and conducted a broad automated search. This article also details the components of the research theme—EV integration into the smart grid—as well as its accompanying use cases. The analysis of the relevant papers indicated four types of key research concerns: power-grid, power-system, and smart-grid reliability and the impacts of changes on them. These results can help guide future research to further smart-grid development. Future research can also expand the reach of this research to address its limitations in scope and depth. [ABSTRACT FROM AUTHOR]

The knowledge graph with relational abundant information has been widely used as the basic data support for the retrieval platforms. Image and text descriptions added to the knowledge graph enrich the node information, which accounts for the advantage of the multi-modal knowledge graph. In the field of cross-modal retrieval platforms, multi-modal knowledge graphs can help to improve retrieval accuracy and efficiency because of the abundant relational information provided by knowledge graphs. The representation learning method is significant to the application of multi-modal knowledge graphs. This paper proposes a distributed collaborative vector retrieval platform (DCRL-KG) using the multimodal knowledge graph VisualSem as the foundation to achieve efficient and high-precision multimodal data retrieval. Firstly, use distributed technology to classify and store the data in the knowledge graph to improve retrieval efficiency. Secondly, this paper uses BabelNet to expand the knowledge graph through multiple filtering processes and increase the diversification of information. Finally, this paper builds a variety of retrieval models to achieve the fusion of retrieval results through linear combination methods to achieve high-precision language retrieval and image retrieval. The paper uses sentence retrieval and image retrieval experiments to prove that the platform can optimize the storage structure of the multimodal knowledge graph and have good performance in multi-modal space. [ABSTRACT FROM AUTHOR]

Recently, research on a distributed storage system that efficiently manages a large amount of data has been actively conducted following data production and demand increase. Physical expansion limits exist for traditional standalone storage systems, such as I/O and file system capacity. However, the existing distributed storage system does not consider where data is consumed and is more focused on data dissemination and optimizing the lookup cost of data location. And this leads to system performance degradation due to low locality occurring in a Wide Area Network (WAN) environment with high network latency. This problem hinders deploying distributed storage systems to multiple data centers over WAN. It lowers the scalability of distributed storage systems to accommodate data storage needs. This paper proposes a method for distributing data in a WAN environment considering network latency and data locality to solve this problem and increase overall system performance. The proposed distributed storage method monitors data utilization and locality to classify data temperature as hot, warm, and cold. With assigned data temperature, the proposed algorithm adaptively selects the appropriate data center and places data accordingly to overcome the excess latency from the WAN environment, leading to overall system performance degradation. This paper also conducts simulations to evaluate the proposed and existing distributed storage methods. The result shows that our proposed method reduced latency by 38% compared to the existing method. Therefore, the proposed method in this paper can be used in large-scale distributed storage systems over a WAN environment to improve latency and performance compared to existing methods, such as consistent hashing. [ABSTRACT FROM AUTHOR]

Nowadays exponential growth of the total amount of data stored by humanity leads to the expansion of distributed storage systems. Such systems have a huge amount of geographically distributed servers that give good scalability. The main challenges with such systems are the temporary unavailability of servers due to features of hardware inside them as well as confidentiality issues. In this paper we consider the information-theoretic approach to solve these issues and give possible further research direction in this area. [ABSTRACT FROM AUTHOR]

Distributed storage systems play a pivotal role in modern data-intensive applications, with Hadoop distributed file system (HDFS) being a prominent example. However, optimizing the efficiency of such systems remains a complex challenge. This research paper presents a novel approach to enhance the efficiency of distributed storage by leveraging multi-agent systems (MAS). Our research is centered on enhancing the efficiency of the HDFS by incorporating intelligent agents that can dynamically assign storage tasks to nodes based on their performance characteristics. Utilizing a decentralized decision-making framework, the suggested approach based on MAS considers the real-time performance of nodes and allocates storage tasks adaptively. This strategy aims to alleviate performance bottlenecks and minimize data transfer latency. Through extensive experimental evaluation, we demonstrate the effectiveness of our approach in improving HDFS performance in terms of data storage, retrieval, and overall system efficiency. The results reveal significant reductions in job execution times and enhanced resource utilization, there by offering a promising avenue for enhancing the efficiency of distributed storage systems. [ABSTRACT FROM AUTHOR]

In distributed storage systems, the utilization of locally repairable codes offers the potential to reduce the complexity and bandwidth required for repairs. This paper focuses on a scenario where each information symbol is associated with several distinct repair sets, each of which includes a single parity check symbol. By leveraging various combinatorial designs, such as resolvable balanced incomplete block designs and resolvable group divisible designs, we establish regular packings and resolvable packings for all alphabet sizes greater than a specified constant. These packings enable the construction of optimal locally repairable codes with multiple repair sets. Specifically, in the case where r = 4 , we successfully construct optimal locally repairable codes with multiple repair sets, provided that the code dimension k is greater than or equal to 277. [ABSTRACT FROM AUTHOR]

The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate freely without taxing the system bandwidth, and that the only information transmission that counts is the one between the racks. This assumption implies that the nodes within each of the racks can collaborate before providing information to the failed node. The main emphasis of the paper is on code construction for this storage model. We present an explicit family of maximum distance separable (MDS) array codes that support recovery of a single failed node from any number of helper racks using the minimum possible amount of inter-rack communication(such codes are said to provide optimal repair). The codes are constructed over finite fields of size comparable to the code length. We also derive a bound on the number of symbols accessed at helper nodes for the purposes of repair, and construct a code family that approaches this bound, while still maintaining the optimal repair property. Finally, we present a construction of scalar Reed-Solomon codes that support optimal repair for the rack-oriented storage model. [ABSTRACT FROM AUTHOR]

Reed-Solomon (RS) codes are widely used in distributed storage systems. In this paper, we study the repair bandwidth and sub-packetization size of RS codes. The repair bandwidth is defined as the amount of transmitted information from surviving nodes to a failed node. The RS code can be viewed as a polynomial over a finite field $GF(q^\ell)$ evaluated at a set of points, where $\ell $ is called the sub-packetization size. Smaller bandwidth reduces the network traffic in distributed storage, and smaller $\ell $ facilitates the implementation of RS codes with lower complexity. Recently, Guruswami and Wootters proposed a repair method for RS codes when the evaluation points are the entire finite field. While the sub-packetization size can be arbitrarily small, the repair bandwidth is higher than the minimum storage regenerating (MSR) bound. Tamo, Ye, and Barg achieved the MSR bound but the sub-packetization size grows faster than the exponential function of the number of the evaluation points. In this paper, we present code constructions and repair schemes that extend these results to accommodate different sizes of the evaluation points. In other words, we design schemes that provide points in between. These schemes provide a flexible tradeoff between the sub-packetization size and the repair bandwidth. In addition, we generalize our schemes to manage multiple failures. [ABSTRACT FROM AUTHOR]

The demand for global video has been burgeoning across industries. With the expansion and improvement of video-streaming services, cloud-based video is evolving into a necessary feature of any successful business for reaching internal and external audiences. This paper considers video streaming over distributed systems where the video segments are encoded using an erasure code for better reliability, thus being the first work to our best knowledge that considers video streaming over erasure-coded distributed cloud systems. The download time of each coded chunk of each video segment is characterized, and the ordered statistics over the choice of the erasure-coded chunks is used to obtain the playback time of different video segments. Using the playback times, bounds on the moment generating function on the stall duration are used to bound the mean stall duration. Moment generating function-based bounds on the ordered statistics are also used to bound the stall duration tail probability, which determines the probability that the stall time is greater than a pre-defined number. These two metrics, mean stall duration and the stall duration tail probability, are important quality of experience (QoE) measures for the end users. Based on these metrics, we formulate an optimization problem to jointly minimize the convex combination of both the QoE metrics averaged over all requests over the placement and access of the video content. The non-convex problem is solved using an efficient iterative algorithm. Numerical results show a significant improvement in QoE metrics for cloud-based video compared to the considered baselines. [ABSTRACT FROM AUTHOR]

Wireless body area networks (WBANs) are an upcoming technology for achieving effective healthcare. The security and privacy of patient-related data are two essential aspects of WBAN system security. Storing data on a single server is simple but may lead to a single point of failure (whether a typical failure or a failure due to security attacks). In this paper, enhanced security and privacy of patient information and E-health systems based on distributed storage systems (DSSs) are developed using public-key cryptography to store patient information. The storage of data and the security requirements (such as confidentiality, reliability, authentication, and dynamic integrity) are simultaneously distributed among individual nodes throughout the network. The patient data are encrypted using the redundant residue number system (RRNS) technique, which depends on a library of moduli in the encrypting process to generate residues. Three algorithms were implemented to decode the RRNS: the Chinese Remainder Theorem (CRT), Base Extension (BEX) with mixed radix conversion, and the new Chinese Remainder Theorem I (CRT I). The results of a system prototype implementation showed that whenever the value of the moduli was a big prime number, the coding efficiency became large, and the time to send a message decreased by 2 s. The performance of the algorithms was expressed in terms of execution time and cyclomatic complexity (CC). The results showed that the CRT I was 1 s faster than the other decoding algorithms and took around 2.5 s to decode the RRNS. The CRT had a low CC of 15, whereas the MRC and CRT I had a CC of 45 and 40, respectively. The main operation phases of the proposed system are described. [ABSTRACT FROM AUTHOR]

Distributed storage can store data in multiple devices or servers to improve data security. However, in today’s explosive growth of network data, traditional distributed storage scheme is faced with some severe challenges such as insufficient performance, data tampering, and data lose. A distributed storage scheme based on blockchain has been proposed to improve security and efficiency of traditional distributed storage. Under this scheme, the following improvements have been made in this paper. This paper first analyzes the problems faced by distributed storage. Then proposed to build a new distributed storage blockchain scheme with sharding blockchain. The proposed scheme realizes the partitioning of the network and nodes by means of blockchain sharding technology, which can improve the efficiency of data verification between nodes. In addition, this paper uses polynomial commitment to construct a new verifiable secret share scheme called PolyVSS. This new scheme is one of the foundations for building our improved distributed storage blockchain scheme. Compared with the previous scheme, our new scheme does not require a trusted third party and has some new features such as homomorphic and batch opening. The security of VSS can be further improved. Experimental comparisons show that the proposed scheme significantly reduces storage and communication costs. [ABSTRACT FROM AUTHOR]

The repair problem in distributed storage addresses recovery of the data encoded using an erasure code, for instance, a Reed–Solomon (RS) code. We consider the problem of repairing a single node or multiple nodes in RS-coded storage systems using the smallest possible amount of inter-nodal communication. According to the cut-set bound, communication cost of repairing $h\geqslant 1$ failed nodes for an $(n,k=n-r)$ maximum distance separable (MDS) code using $d$ helper nodes is at least $dhl/(d+h-k)$ , where $l$ is the size of the node. Guruswami and Wootters (2016) initiated the study of efficient repair of RS codes, showing that they can be repaired using a smaller bandwidth than under the trivial approach. At the same time, their work as well as follow-up papers stopped short of constructing RS codes (or any scalar MDS codes) that meet the cut-set bound with equality. In this paper, we construct the families of RS codes that achieve the cut-set bound for repair of one or several nodes. In the single-node case, we present the RS codes of length $n$ over the field ${\mathbb F}_{q^{l}}, l=\exp ((1+o(1))n\log n)$ that meet the cut-set bound. We also prove an almost matching lower bound on $l$ , showing that super-exponential scaling is both necessary and sufficient for scalar MDS codes to achieve the cut-set bound using linear repair schemes. For the case of multiple nodes, we construct a family of RS codes that achieve the cut-set bound universally for the repair of any $h=1,2, {\dots },r$ failed nodes from any subset of $d$ helper nodes, $k\leqslant d\leqslant n-h$. For a fixed number of parities $r$ , the node size of the constructed codes is close to the smallest possible node size for codes with such properties. [ABSTRACT FROM AUTHOR]

In the classical model for (information theoretically secure) Private Information Retrieval (PIR) due to Chor, Goldreich, Kushilevitz and Sudan, a user wishes to retrieve one bit of a database that is stored on a set of ${n}$ servers, in such a way that no individual server gains information about which bit the user is interested in. The aim is to design schemes that minimise the total communication between the user and the servers. More recently, there have been moves to consider more realistic models where the total storage of the set of servers, or the per server storage, should be minimised (possibly using techniques from distributed storage), and where the database is divided into ${R}$ -bit records with ${R}>1$ , and the user wishes to retrieve one record rather than one bit. When ${R}$ is large, downloads from the servers to the user dominate the communication complexity and so the aim is to minimise the total number of downloaded bits. Work of Shah, Rashmi and Ramchandran shows that at least ${R}+1$ bits must be downloaded from servers in the worst case, and provides PIR schemes meeting this bound. Sun and Jafar have considered the download cost of a scheme, defined as the ratio of the message length ${R}$ and the total number of bits downloaded. They determine the best asymptotic download cost of a PIR scheme (as ${R}\rightarrow \infty $) when a database of ${k}$ messages is stored by ${n}$ servers. This paper provides various bounds on the download complexity of a PIR scheme, generalising those of Shah et al. to the case when the number ${n}$ of servers is bounded, and providing links with classical techniques due to Chor et al. The paper also provides a range of constructions for PIR schemes that are either simpler or perform better than previously known schemes. These constructions include explicit schemes that achieve the best asymptotic download complexity of Sun and Jafar with significantly lower upload complexity, and general techniques for constructing a scheme with good worst case download complexity from a scheme with good download complexity on average. [ABSTRACT FROM AUTHOR]

Repair operations in erasure-coded distributed storage systems involve a lot of data movement. This can potentially expose data to malicious acts of passive eavesdroppers or active adversaries, putting security of the system at risk. This paper presents coding schemes and repair algorithms that ensure security of the data in the presence of passive eavesdroppers and active adversaries while maintaining high availability, reliability, and resource efficiency in the system. The proposed codes are optimal in that they meet previously proposed lower bounds on storage and network-bandwidth requirements for a wide range of system parameters. The results thus establish the secure storage capacity of such systems. The proposed codes are based on an optimal class of codes called product-matrix codes. The constructions presented for security from active adversaries provide an additional appealing feature of “on-demand security,” where the desired level of security can be chosen separately for each instance of repair, and the proposed algorithms remain optimal simultaneously for all possible security levels. This paper also provides necessary and sufficient conditions governing the transformation of any (non-secure) code into one providing on-demand security. [ABSTRACT FROM PUBLISHER]

This paper provides an overview on how content can be managed with a blockchain or other distributed ledger technology (DLT), and what challenges need to be addressed in managing this content as part of transactions. Transactions on a blockchain may require supporting documents, for example, photos, reference documents, or actual contracts. As DLTs becoming an increasingly popular method to complete transactions and share information, several issues are arising that need to be addressed, such as: Where should this electronic content in documents be stored? Will the storage system have the features and functionality to properly manage this content through the "information lifecycle", including the retention and disposition of business records based on legal and regulatory requirements? The paper presents an overview of the emerging technology involved with distributed storage systems. It presents five solutions currently available, including their designs, how they secure and store files, and whether or not these files can be deleted in order to meet record disposition requirements and regulations. The discussion points out the need for alignment between multiple stakeholders and consortium members in a distributed ledger-based community with shared ecosystem scaling objectives. The challenges of scaling include the need to protect personal and sensitive information, especially when this information should normally be disposed after a record's retention period has ended. [ABSTRACT FROM AUTHOR]

A new family of scalable codes with locality and availability for information repair in data storage systems for e-health applications was presented recently. The construction was based on a graph of the [7, 3-4] Simplex code. In this paper it is shown that the construction can be generalized via tessellation in a Euclidian plane. The codes obtained have new interesting recoverability properties. They can in some cases repair damage to many storage nodes in multiple connected graphs via sequential decoding, which is similar to healing wounds in biological systems. The advantages of the original codes, namely the availability, functionality, efficiency and high data accessibility, will be preserved also in these new codes. The computational complexity and communication costs of their incrementation will remain constant and modest. These codes could be adapted to disaster recovery because it is straightforward to place the nodes so that the graph is easily mapped on a real structure in space. [ABSTRACT FROM AUTHOR]

Coding-based distributed storage systems (DSS) are employed in many diverse heterogeneous settings, e.g., cloud storage data centers, peer-to-peer systems, wireless sensor networks, fog/edge computing system, to provide better throughput, latency, reliability, scalability, load adaptation, geographical migration and fault tolerance with respect to traditional monolithic enterprise storage systems. Despite the undoubted advantages offered by coding, reliability and security are jeopardized by a pollution attack that can easily disrupt the entire system and degrade performance. In this paper we take an abstract view of a DSS and we investigate by means of mathematical modeling what are the availability, robustness, and timeliness of heterogeneous, coding-based DSS when storage nodes (SN) are unreliable and can be malicious. To this end, we focus on a class of allocations of coded fragments to SNs that we call feasible allocations; the model takes into account both reliability and reactivity of SNs. We define robust availability and timeliness of feasible allocations that we use to characterize the overall performance and robustness of the DSS in a reference scenario. Our analysis reveals that code redundancy is a double-edged sword in a DSS where malicious SNs come into play and that there exists an optimal value of code redundancy regardless all system parameters that maximizes the number of malicious SNs that can be tolerated to achieve maximum DSS performance. We also found that larger codes are preferred over short ones as they yield superior DSS performance in the presence of malicious SNs. Furthermore, when multiple feasible allocations yield the highest DSS performance timeliness can be used as a guide for the choice. Finally, heterogeneity plays a role in determining the timeliness of the maximally spread allocations in the case of targeted attacks. [ABSTRACT FROM AUTHOR]

A block code is called a locally recoverable code (LRC for short) with $(r,\delta)$ -locality, if subject to any $\delta -1$ erasure failures, every symbol in the encoding can still be recovered by accessing at most $r$ other symbols. Recently, it was discovered by several authors that a $q$ -ary optimal $(r,\delta)$ -LRC, i.e., an LRC achieving the generalized Singleton-type bound, can have length much bigger than $q+1$. This is quite different from the classical $q$ -ary MDS codes where it is conjectured that the code length is upper bounded by $q+1$ (or $q+2$ for some special cases). In this paper, we further investigate constructions of optimal $(r,\delta)$ -LRCs along the line of using parity-check matrices. Inspired by classical Reed-Solomon codes and the work in Jin (2019), we equip parity-check matrices with the Vandermonde structure. It turns out that a parity-check matrix with the Vandermonde structure that produces an optimal LRC must obey certain disjoint property for subsets of $\mathbb {F}_{q}$. We manage to show the existence of these disjoint subsets. Thus, this yields an optimal $(r,\delta)$ -LRC with code length $\Omega \left({q^{\frac {\delta }{2}\left({1+\frac {1}{\lfloor \frac {d-1}{\delta }\rfloor -1}}\right)}}\right)\vphantom {\bigg)_{j}}$ , where $d$ is the minimum distance. In particular, to our surprise, for $\delta =2$ this disjoint condition is equivalent to a well-studied problem in extremal graph theory. With the help of extremal graph theory, we succeed to improve all of the best known results in Guruswami et al. (2018) for $d\geq 7$. In addition, for $d=6$ , we are able to remove the constraint required in Jin (2019) that $q$ is even. [ABSTRACT FROM AUTHOR]

Distributed renewable energy has emerged as a promising resource because of its environmental friendliness and economic considerations. However, most renewable energy sources are unreliable and may require considerable effort to be efficiently utilized in a computing center for providing services. In this paper, we exploit distributed renewable energy (e.g., solar energy) and peer-to-peer (P2P) technologies to aggregate distributed computing resources to provide an infrastructure called solar-based energy-efficient distributed server (SEEDS) farm for distributed computing and distributed storage. Energy-efficient devices (e.g., embedded devices) powered by solar energy form a P2P computing system to provide their computing resources to end-users. Specifically, this paper uses a Web-based service as a case study. A group of solar-powered embedded devices acts as a front-end cooperative caching system for Web servers. Web objects may be accessed through the distributed caching system without going through servers, and thus we can reduce brown energy consumption of the servers. This paper also develops an analytical model to evaluate the total energy consumption of Web-based services with and without SEEDS. Theoretical and simulation results show that the SEEDS system can support services and achieve significant improvements in energy efficiency by aggregating distributed energy resources. [ABSTRACT FROM AUTHOR]

As the distributed ledger technology underlying cryptocurrencies such as Bitcoin and Ethereum, blockchain has empowered various industries, such as supply chain management, healthcare, government services, e-voting, etc. However, the ever-growing ledger on each node has been the main bottleneck for blockchain scalability as the network scale expands, which worsens in blockchain-enabled IoT scenarios with resource-limited devices. With the support of the Reed–Solomon (RS) code, the Cuckoo-Store (CS), a ledger storage optimization engine, is proposed in this paper to dramatically decrease the storage burden on each node by encoding the ledger as data segments with redundancy and distributing them to multiple nodes. These distributed data segments can be collected and decoded using RS code to recover the original ledger. Furthermore, the Cuckoo filter (CF) is used to guarantee the integrity of the encoded segments, which helps detect the forged segments and facilitates the process of ledger recovery. Theoretical analysis and simulation results show that the CS engine can decrease the storage in each node by more than 94%, and the original ledger can be recovered efficiently with acceptable communication overheads. [ABSTRACT FROM AUTHOR]

In a traditional distributed storage system, a source can be restored perfectly when a certain subset of servers is contacted. The coding is independent of the contents of the source. This paper considers instead a lossy source coding version of this problem where the more servers that are contacted, the higher the quality of the restored source. An example could be video stored on distributed storage. In information theory, this is called the multiple description problem, where the distortion depends on the number of descriptions received. The problem considered in this paper is how to restore the system operation when one of the servers fail and a new server replaces it, that is, repair. The requirement is that the distortions in the restored system should be no more than in the original system. The question is how many extra bits are needed for repair. We find an achievable rate and show that this is optimal in certain cases. One conclusion is that it is necessary to design the multiple description codes with repair in mind; just using an existing multiple description code results in unnecessary high repair rates. [ABSTRACT FROM AUTHOR]

Locally recoverable codes are very important due to their applications in distributed storage systems. In this paper, by using cyclic codes, we construct two classes of optimal q-ary cyclic $(\text {r}, \delta _{1})$ locally recoverable codes with parameters $[2(\text {q}+1), 2(\text {q}+1)-2\delta _{1}, \delta _{1}+2]_{\text {q}}$ , where $q$ is an odd prime power and $\text {r}+\delta _{1}-1=\text {q}+1$ , and $(\text {r}, \delta _{2})$ locally recoverable codes with parameters $[2(\text {q}+1), 2(\text {q}+1)-4\delta _{2}+2, \delta _{2}+2]_{q}$ , where $\text {q}\geq 7$ is an odd prime power, $\text {q}\equiv 3~ (mod~ 4)$ and $r+\delta _{2}-1=\frac {\text {q}+1}{2}$. Compared with the known cyclic and constacyclic $(\text {r}, \delta)$ locally recoverable codes, our construction yields new optimal cyclic $(\text {r}, \delta)$ locally recoverable codes. [ABSTRACT FROM AUTHOR]

This paper focuses on the self-scheduling problem of an aggregator of plug-in electric vehicles (PEVs) purchasing energy in the day-ahead market, and offering balancing services for a wind power producer, i.e., committing to compensate the forecast errors of wind power plants. The aggregated charging and discharging flexibility of the PEV fleet is represented by a probabilistic virtual battery model, accounting for the uncertainty in the driving patterns of PEVs. Another source of uncertainty is related to the balancing requests, which are a function of the forecasted wind power output. A scenario-based robust approach is used to tackle both sources of uncertainty in a tractable way. The interdependency between the day-ahead market prices and the aggregator’s bidding decisions is addressed using complementarity models. A case study analyzes the capability of the PEV aggregation to provide balancing services, for different settings of the balancing contract, and both with and without the use of vehicle-to-grid. [ABSTRACT FROM PUBLISHER]

Motivated by applications of distributed storage systems to key-value stores, the multi-version coding problem has been formulated to efficiently store frequently updated data in asynchronous decentralized storage systems. Inspired by consistency requirements in distributed systems, the main goal in the multi-version coding problem is to ensure that the latest possible version of the data is decodable even if the data updates have not reached all the servers in the system. In this paper, we study the storage cost of ensuring consistency for the case where the data versions are correlated, in contrast to previous work where the data versions were treated as being independent. We provide multi-version code constructions that show that the storage cost can be significantly smaller than the previous constructions depending on the degree of correlation, despite the asynchrony and the decentralized nature. Our achievability results are based on Reed–Solomon codes and random binning. Through an information-theoretic converse, we show that our multi-version codes are asymptotically nearly optimal, within a factor of 2, in certain interesting regimes. [ABSTRACT FROM AUTHOR]

Motivated by applications in distributed storage, the storage capacity of a graph was recently defined to be the maximum amount of information that can be stored across the vertices of a graph such that the information at any vertex can be recovered from the information stored at the neighboring vertices. Computing the storage capacity is a fundamental problem in network coding and is related, or equivalent, to some well-studied problems such as index coding with side information and generalized guessing games. In this paper, we consider storage capacity as a natural information-theoretic analogue of the minimum vertex cover of a graph. Indeed, while it was known that storage capacity is upper bounded by minimum vertex cover, we show that by treating it as such we can get a 3/2 approximation for planar graphs, and a 4/3 approximation for triangle-free planar graphs. Since the storage capacity is intimately related to the index coding rate, we get a 2 approximation of index coding rate for planar graphs and 3/2 approximation for triangle-free planar graphs. Previously, only a trivial 4 approximation of the index coding rate was known for planar graphs. We also show a polynomial time approximation scheme for the index coding rate when the alphabet size is constant. We then develop a general method of “gadget covering” to upper bound the storage capacity in terms of the average of a set of vertex covers. This method is intuitive and leads to the exact characterization of storage capacity for various families of graphs. As an illustrative example, we use this approach to derive the exact storage capacity of cycles-with-chords, a family of graphs related to outerplanar graphs. Finally, we generalize the storage capacity notion to include recovery from partial node failures in distributed storage. We show tight upper and lower bounds on this partial recovery capacity that scales nicely with the fraction of failures in a vertex. [ABSTRACT FROM AUTHOR]

A code is said to be an $r$ -local locally repairable code (LRC) if each of its coordinates can be repaired by accessing at most r$ other coordinates. When some of the r$ coordinates are also erased, the r$ -local LRC cannot accomplish the local repair, which leads to the concept of (r,\delta)$ -locality. A q is said to have (r, \delta)$ -locality ( \delta \ge 2$ ) if for each coordinate i with support containing $i$ , whose length is at most $r + \delta - 1$ , and whose minimum distance is at least $\delta$ . The $(r, \delta)$ -LRC can tolerate $\delta -1$ erasures in every local code (i.e., punctured subcode), which degenerates to an $r$ -local LRC when $\delta =2$ . A $q$ -ary $(r,\delta)$ LRC is called optimal if it meets the singleton-like bound for $(r,\delta)$ -LRCs. A class of optimal $q$ -ary cyclic $r$ -local LRCs with lengths $n\mid q-1$ were constructed by Tamo, Barg, Goparaju, and Calderbank based on the $q$ -ary Reed-Solomon codes. In this paper, we construct a class of optimal $q$ -ary cyclic $(r,\delta)$ -LRCs ( $\delta \ge 2$ ) with length $n\mid q-1$ , which generalizes the results of Tamo et al. Moreover, we construct a new class of optimal $q$ -ary cyclic $r$ -local LRCs with lengths $n\mid q+1$ and a new class of optimal $q$ -ary cyclic $(r,\delta)$ -LRCs ( $\delta \ge 2$ ) with lengths $n\mid q+1$ . The constructed optimal LRCs with length $n=q+1$ have the best-known length for a given finite field with size $q$ when the minimum distance is larger than 4. [ABSTRACT FROM AUTHOR]

In this paper, we consider the update bandwidth in distributed storage systems (DSSs). The update bandwidth, which measures the transmission efficiency of the update process in DSSs, is defined as the average amount of data symbols transferred in the network when the data symbols stored in a node are updated. This paper contains the following contributions. First, we establish the closed-form expression of the minimum update bandwidth attainable by irregular array codes. Second, after defining a class of irregular array codes, called Minimum Update Bandwidth (MUB) codes, which achieve the minimum update bandwidth of irregular array codes, we determine the smallest code redundancy attainable by MUB codes. Third, the code parameters, with which the minimum code redundancy of irregular array codes and the smallest code redundancy of MUB codes can be equal, are identified, which allows us to define MR-MUB codes as a class of irregular array codes that simultaneously achieve the minimum code redundancy and the minimum update bandwidth. Fourth, we introduce explicit code constructions of MR-MUB codes and MUB codes with the smallest code redundancy. Fifth, we establish a lower bound of the update complexity of MR-MUB codes, which can be used to prove that the minimum update complexity of irregular array codes may not be achieved by MR-MUB codes. Last, we construct a class of $(n = k + 2, k)$ vertical maximum-distance separable (MDS) array codes that can achieve all of the minimum code redundancy, the minimum update bandwidth and the optimal repair bandwidth of irregular array codes. [ABSTRACT FROM AUTHOR]

In this paper we extend the notion of locally repairable codes to secret sharing schemes. The main problem that we consider is to find optimal ways to distribute the shares of a secret among a set of storage-nodes (participants) such that the content of each node (share) can be recovered by using the contents of only few other nodes, and at the same time the secret can be reconstructed by only some allowable subsets of nodes. As a special case, an eavesdropper observing some set of specific nodes (such as less than certain number of nodes) does not get any information. In other words, we propose to study a locally repairable distributed storage system that is secure against a passive eavesdropper that can observe some subsets of nodes. We provide a number of results related to such systems, including upper bounds and achievability results on the number of bits that can be securely stored with these constraints. In particular, we provide conditions under which a locally repairable code can be turned into a secret sharing scheme and extend the results of secure repairable storage to cooperative repair and storage on networks. In addition, we consider perfect secret sharing schemes over general access structures under locality constraints and give an example of a perfect secret sharing scheme that can have small locality. Finally, we provide a lower bound on the size of a share compared with the size of the secret that shows how locality affects the sizes of shares in a perfect scheme. [ABSTRACT FROM PUBLISHER]

In this paper, we reinterpret the $(k+2,k)$ zigzag code in coding matrix and then propose an optimal exact repair strategy for its parity nodes, whose repair disk I/O approaches a lower bound derived in this paper. [ABSTRACT FROM PUBLISHER]

Up to now, many $(k+r,k,N)$ minimum-storage regenerating (MSR) codes with $k$ information nodes, $r$ parity nodes, and node capacity $N$ have been proposed. However, most of them are constructed over a relatively large finite field. In this paper, we propose three high-rate MSR codes over small finite fields. First, the new MSR code $\mathcal {C}_{1}$ with the optimal access property for all nodes is constructed over small finite field $\mathbb {F}_{q}$ , for example $q=3$ for even $r$ or $q\ge r+1$ for odd $r$ , which is much smaller than that of the known one given by Ye and Barg. Further, considering to reduce the node capacity, another new MSR code $\mathcal {C}_{2}$ over $\mathbb {F}_{q}$ with $q\ge r+2$ is generated based on $\mathcal {C}_{1}$ , which can effectively reduce the node capacity of $\mathcal {C}_{1}$ by a factor of $r^{r-1}$. However, only the first $k$ nodes of $\mathcal {C}_{2}$ have the optimal access property. Therefore, the new MSR code $\mathcal {C}_{3}$ over $\mathbb {F}_{q}$ with $q\ge r+2$ which has the optimal access property for all nodes is proposed by modifying $\mathcal {C}_{2}$. Notably, in contrast to $\mathcal {C}_{1}$ , the node capacity of $\mathcal {C}_{3}$ is decreased by a factor of $r^{r-2}$. [ABSTRACT FROM AUTHOR]

In this paper, a new repair scheme for a modified construction of MDS codes is studied. The obtained repair scheme has optimal bandwidth for multiple failed nodes under the cooperative repair model. In addition, the repair scheme has relatively low access property, where the number of data accessed is less than two times the optimal value. [ABSTRACT FROM AUTHOR]

Blaum–Roth Codes are binary maximum distance separable (MDS) array codes over the binary quotient ring F 2 [ x ] / (M p (x)) , where M p (x) = 1 + x + ⋯ + x p − 1 , and p is a prime number. Two existing all-erasure decoding methods for Blaum–Roth codes are the syndrome-based decoding method and the interpolation-based decoding method. In this paper, we propose a modified syndrome-based decoding method and a modified interpolation-based decoding method that have lower decoding complexity than the syndrome-based decoding method and the interpolation-based decoding method, respectively. Moreover, we present a fast decoding method for Blaum–Roth codes based on the LU decomposition of the Vandermonde matrix that has a lower decoding complexity than the two modified decoding methods for most of the parameters. [ABSTRACT FROM AUTHOR]

Distributed storage systems (DSSs) in the presence of an external wiretapper are considered. A DSS is parameterized by $(n, k, d)$ , in which the data are stored across $n$ nodes (each with storage capacity $\alpha $ ), and must be recoverable by accessing the contents stored on any $k$ out of $n$ nodes. If a node fails, any $d \geq k$ out of $(n-1)$ nodes help in the repair (regeneration) of the failed node (by sending $d\beta $ units of repair data, where $\beta \leq \alpha $ ), so that the data can still be recovered from the DSS. For such a $(n, k, d)$ -DSS, security from the two types of wiretappers is investigated: 1) Type-I (node data) wiretapper, which can read the data stored on any $\ell

The locally repairable code (LRC) studied in this paper is an [n,k] linear code of which the value at each coordinate can be recovered by a linear combination of at most r other coordinates. The central problem in this paper is to determine the largest possible minimum distance for LRCs. First, an integer programming-based upper bound is derived for any LRC. Then, by solving the programming problem under certain conditions, an explicit upper bound is obtained for LRCs with parameters n1>n2 , where n1 = \lceil ({n}/{r+1}) \rceil and n2 = n1 (r+1) - n . Finally, an explicit construction for LRCs attaining this upper bound is presented over the finite field \mathbb F2^{m} , where m\geq n1r . Based on these results, the largest possible minimum distance for all LRCs with r \le \sqrt n-1 has been definitely determined, which is of great significance in practical use. [ABSTRACT FROM PUBLISHER]

In applications of distributed storage systems to distributed computing and implementation of key-value stores, the following property, usually referred to as consistency in distributed computing, is an important requirement: as the data stored changes, the latest version of the data must be accessible to a client that connects to the storage system. Motivated by technological trends where key-value stores are increasingly implemented in high-speed memory, an information theoretic formulation called multi-version coding is introduced in this paper in order to understand and minimize the memory overhead of consistent distributed storage. Multi-version coding is characterized by $\nu$ totally ordered versions of a message and a storage system with $n$ servers. At each server, values corresponding to an arbitrary subset of the $\nu$ versions are received and encoded. For any subset of $c$ servers in the storage system, the value corresponding to the latest common version or a later version, as per the total ordering, among the $c$ servers is required to be decodable. An achievable multi-version code construction via linear coding and a converse result that shows that the construction is asymptotically tight when $\nu |(c-1)$ are provided. An implication of the converse is that there is an inevitable price, in terms of storage cost, to ensure consistency in distributed storage systems. [ABSTRACT FROM AUTHOR]

Distributed storage systems suffer from significant repair traffic generated due to the frequent storage node failures. This paper shows that properly designed low-density parity-check (LDPC) codes can substantially reduce the amount of required block downloads for repair thanks to the sparse nature of their factor graph representation. In particular, with a careful construction of the factor graph, both low repair-bandwidth and high reliability can be achieved for a given code rate. First, a formula for the average repair bandwidth of LDPC codes is developed. This formula is then used to establish that the minimum repair bandwidth can be achieved by forcing a regular check node degree in the factor graph. Moreover, it is shown that given a fixed code rate, the variable node degree should also be regular to yield minimum repair bandwidth, under some reasonable minimum variable node degree constraint. It is also shown that for a given repair-bandwidth requirement, LDPC codes can yield substantially higher reliability than the currently utilized Reed–Solomon codes. Our reliability analysis is based on a formulation of the general equation for the mean-time-to-data-loss (MTTDL) associated with LDPC codes. The formulation reveals that the stopping number is closely related to the MTTDL. It is further shown that LDPC codes can be designed such that a small loss of repair-bandwidth optimality may be traded for a large improvement in erasure-correction capability and thus the MTTDL. [ABSTRACT FROM PUBLISHER]

We study the communication efficient secret sharing (CESS) problem. A classical threshold secret sharing scheme encodes a secret into $n$ shares given to n$ parties, such that any set of at least t$ , t n$ . However, Staircase codes may require dividing the secret and the shares into many symbols. We also describe how Staircase codes can be used to construct threshold changeable secret sharing with minimum storage cost, i.e., minimum share size. [ABSTRACT FROM AUTHOR]

Low-carbon transition plans for temperate and sub-polar regions typically involve some electrification of space heating. This poses challenges to electricity system operation and market design, as it increases overall demand and alters the temporal patterns of that demand. One response to the challenge is to 'smarten' electrical heating, enabling it to respond to network conditions by storing energy at times of plentiful supply, releasing it in response to customer demands and offering rapid-response ancillary services to the grid. Shared operation of domestic electrical heating, in such a scenario, may imply changes in everyday heating practices and will change the number of system stakeholders, their activities and how they relate to each other. This paper sets out some practical and theoretical issues relating to the potential for residential demand response via electric storage heating, drawing on academic and policy-related literature and on material from a current research project. It offers a brief history of residential storage heating and recent developments, paying particular attention to customer experience; considers the role of distributed storage in energy transitions and associated questions of value; outlines how agency and value in a smart system may be distributed between stakeholders; and assesses continuity and change in storage heating. While the paper focuses on storage heating, many of the issue raised apply to heat pumps, given their functional similarities with storage heaters and water heaters. The paper concludes with some conditions to be met if smart storage heating is to succeed in the twin tasks of providing effective customer service and demand response, and sets out questions for further research into demand response and heating practices. [ABSTRACT FROM AUTHOR]

We consider the $(n,k,d,\ell )$ secure exact-repair regenerating code problem, which generalizes the $(n,k,d)$ exact-repair regenerating code problem with the additional constraint that the stored file needs to be kept information-theoretically secure against an eavesdropper, who can access the data transmitted to regenerate a total of $\ell $ different failed nodes. For all known results on this problem, the achievable tradeoff regions between the normalized storage capacity and repair bandwidth have a single corner point, achieved by a scheme proposed by Shah, Rashmi, and Kumar (the SRK point). Since the achievable tradeoff regions of the exact-repair regenerating code problem without any secrecy constraints are known to have multiple corner points in general, these existing results suggest a phase-change-like behavior, i.e., enforcing a secrecy constraint ( $\ell \geq 1$ ) immediately reduces the tradeoff region to one with a single corner point. In this paper, we first show that when the secrecy parameter $\ell $ is sufficiently large, the SRK point is indeed the only corner point of the tradeoff region. However, when $\ell $ is small, we show that the tradeoff region can in fact have multiple corner points. In particular, we establish a precise characterization of the tradeoff region for the (7, 6, 6, 1) problem, which has exactly two corner points. Thus, a smooth transition, instead of a phase-change-type of transition, should be expected as the secrecy constraint is gradually strengthened. [ABSTRACT FROM PUBLISHER]

Erasure codes are being extensively deployed in distributed storage systems instead of replication to achieve fault tolerance in a storage efficient manner. While traditional erasure codes are storage efficient, they can result in a significant increase in the amount of data access and downloaded during rebuilding of failed or otherwise unavailable nodes. In this paper, we present a new framework, which we call piggybacking, for constructing distributed storage codes that are efficient in the amount of data read and downloaded during rebuilding, while meeting requirements arising out of system considerations in data centers—maximum-distance-separability (MDS), high-rate, and a small number of so-called substripes. Under this setting, to the best of our knowledge, piggyback codes achieve the minimum average amount of data access and downloaded during rebuilding among all existing explicit solutions. The piggybacking framework also offers a rich design space for constructing codes for a variety of other settings. In particular, we construct codes that require minimum amount of data access and downloaded for rebuilding among all existing solutions for: 1) binary MDS array codes with more than two parities and 2) MDS codes with the smallest locality during rebuilding. In addition, we show how piggybacking can be employed to enable efficient repair of parity nodes in codes that address the rebuilding of only systematic nodes. The basic idea behind the piggybacking framework is to take multiple instances of existing codes and add carefully designed functions of the data from one instance to the others. This framework provides 25% to 50% savings in the average amount of data access and downloaded during rebuilding depending on the choice of the code parameters. [ABSTRACT FROM AUTHOR]

Distributed data management requires data partitioning and deployment at the data storage level, and data querying requires the configuration and integration of query subresults at each site. The data partitioning strategy is closely related to the overhead of the distributed system. It is necessary to determine the appropriate data partitioning strategy and update strategy according to the application. This paper proposes a widely distributed storage and processing scheme for a distributed linear order partition (DLOP) based on time stamps. This scheme proposes two kinds of partition strategy based on the characteristics of an "equivalent division" of a linear order partition (LOP), namely, partitioning based on time interval equilibrium and partitioning based on query expectation. Each site in the distributed system is uniformly configured with an index-based data query mechanism to complete the distributed management of data. The corresponding experiments verify the practicability and efficiency of the proposed storage strategy and show that the proposed method is effective for the self-scalability of the data scale and reduces the cluster hardware configuration requirements. [ABSTRACT FROM AUTHOR]

In wireless sensor networks, sensor nodes are vulnerable due to the challenging environment and limited energy. Once a sensor node fails, the stored sensed data will be lost. In this paper, we develop a distributed algorithm for solving this problem based on the fountain codes and the minimum spanning tree. Similar to previous works, we adopt the Luby Transform (LT) codes, the first practical scheme of fountain codes, in our algorithm. However, different from the previous schemes, our algorithm deploys the minimum spanning tree instead of the random walk. Due to the fact that all nodes in the wireless sensor networks do not have the location information of other nodes, we use the Gallager-Humble-Spira (GHS) algorithm to generate a distributed minimum spanning tree. Data packets can be transmitted through the tree and easily reach every node in the network. We obtain the performance of the algorithm through simulations, which show that our algorithm consumes less number of the transmissions compared with the existing algorithms using the random walk. [ABSTRACT FROM AUTHOR]

The (n,k,d) regenerating code is a class of (n,k) erasure codes with the capability to recover a lost code fragment from other d existing code fragments. In this paper, we focus on the design of exact regenerating codes at minimum bandwidth regenerating (MBR) points. For d=n-1, a class of (n,k,d=n-1) exact-MBR codes, termed as repair-by-transfer codes, have been developed in prior work to avoid arithmetic operations in node repairing process. The first result of this paper presents a new class of repair-by-transfer codes via congruent transformations. As compared with prior works, the advantages of proposed codes include: i) the minimum of field size is significantly reduced from n \atopwithdelims ()2 to n; ii) the encoding complexity is decreased from n^4 to n^3. Our simulation results show that the proposed code achieves faster operations than the prior approach does under large n. The second result of this paper presents a new form of coding matrix for product-matrix exact-MBR codes. The proposed coding matrix includes the following advantages: i) the minimum of finite field size is reduced from n-k+d to n; ii) the fast Reed-Solomon erasure coding algorithms can be applied on the proposed exact-MBR codes to reduce the time complexities. [ABSTRACT FROM AUTHOR]

We consider the decoding of linear and array codes from errors when we are only allowed to download a part of the codeword. More specifically, suppose that we have encoded $k$ data symbols using an $(n,k)$ code with code length $n$ and dimension $k$. During storage, some of the codeword coordinates might be corrupted by errors. We aim to recover the original data by reading the corrupted codeword with a limit on the transmission bandwidth, namely, we can only download an $\alpha $ proportion of the corrupted codeword. For a given $\alpha $ , our objective is to design a code and a decoding scheme such that we can recover the original data from the largest possible number of errors. A naive scheme is to read $\alpha n$ coordinates of the codeword. This method used in conjunction with MDS codes guarantees recovery from any $\lfloor (\alpha n-k)/2\rfloor $ errors. In this paper we show that we can instead download an $\alpha $ proportion from each of the codeword’s coordinates. For a well-designed MDS code, this method can guarantee recovery from $\lfloor (n-k/\alpha)/2 \rfloor $ errors, which is $1/\alpha $ times more than the naive method, and is also the maximum number of errors that an $(n,k)$ code can correct by downloading only an $\alpha $ proportion of the codeword. We present two families of such optimal constructions and decoding schemes of which one is based on Interleaved Reed-Solomon codes and the other on Folded Reed-Solomon codes. We further show that both code constructions attain asymptotically optimal list decoding radius when downloading only a part of the corrupted codeword. We also construct an ensemble of random codes that with high probability approaches the upper bound on the number of correctable errors when the decoder downloads an $\alpha $ proportion of the corrupted codeword. [ABSTRACT FROM AUTHOR]

This paper considers the natural extension of locally recoverable codes (LRC) to the case of ${t} > 1$ erased symbols. While several approaches have been proposed for the handling of multiple erasures, in the approach considered here, the t erased symbols are recovered in succession, each time contacting at most r other symbols for assistance. Under the local-recovery constraint, this sequential approach is the most general and hence offers the maximum possible code rate. We characterize the rate of an LRC with sequential recovery for any ${r} \geq 3$ and any t, by first deriving an upper bound on the code rate and then constructing a binary code achieving this optimal rate. The upper bound derived here proves an earlier conjecture. Our approach permits us to deduce the structure of the parity-check matrix of a rate-optimal LRC with sequential recovery. The derived structure of parity-check matrix leads to a graphical description of the code used in code construction. A subclass of binary codes that are both rate and block-length optimal, are shown to correspond to certain regular graphs known as Moore graphs, that have the smallest number of vertices for a given girth. A connection with Tornado codes is also made. [ABSTRACT FROM AUTHOR]

Let $q$ be a prime power and $\mathbb {F}_{q}$ be the finite field of size $q$. In this paper we provide a Galois theoretical framework that allows to produce good polynomials for the Tamo and Barg construction of optimal locally recoverable codes (LRC). Using our approach we construct new good polynomials and therefore optimal LRCs with new parameters. The existing theory of good polynomials fits entirely in our new framework. The key advantage of our method is that we do not need to rely on arithmetic properties of the pair $(q,r)$ , where $r$ is the locality of the code. [ABSTRACT FROM AUTHOR]

To expand the usage, reliability, availability of power resources and some distribution system must be met which is conceivable by the support of present day information technologies. This paper concentrates on client support and electricity distribution, where payment of electric bills (counting energy utilization every month or year and association points of interest) should be possible with online arrangements. It is proposed a protected and reliable solution which joins the elements of the electrical system with the network systems to give better execution on informing issues, which is done given demand location. The electric readings of the client will be upgraded each month in the database which is kept up in the distributed storage. The client will be furnished with security keys to see the perusing values and perform payment of bills. To make the solution more available, the dynamic information will be kept up on different servers in various areas of the cloud, and there will be a service supplier who deals with the service request. The hardwired electric meter transmits the electrical reading, which turn accesses the particular service to make an entry for the specific association at the cloud. The usage data will be kept up at various area of the cloud, which is accessible with security, measures various clients. The customer availability is controlled with SCADA. [ABSTRACT FROM AUTHOR]