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In distributed storage systems, an r-Locally Repairable Code (r-LRC) ensures that a failed symbol can be recovered by accessing at most r other symbols. Prakash et al. in (Proceedings of IEEE International Symposium on Information Theory, pp. 2776–2780, 2012) further introduced the concept of (r , δ) -LRC, where δ ≥ 2 , which can deal with the symbol failure in the presence of extra δ - 2 symbol failures still by accessing at most r other symbols. In particular, an r-LRC is just an (r, 2)-LRC. Luo and Ling in (Des Codes Cryptogr 90:1271–1287, 2022) obtained some alphabet-optimal r-LRCs concerning the Cadambe–Mazumdar bound from optimal linear codes constructed by special projective spaces. In this paper, we generalize the results of Luo and Ling in (Des Codes Cryptogr 90:1271–1287, 2022). Firstly, we generalize the result of constructing optimal linear codes to larger code length. In particular, we present the conditions for the constructed linear codes to qualify as Griesmer codes or distance-optimal codes. Secondly, we explore the locality of the constructed codes. The novelty of our work lies in establishing the locality as (r , δ) -locality and (r , δ) -locality with availability, in contrast to the previous literature that only considered r-locality. In addition, through the analysis combining the code parameters and the Cadambe–Mazumdar-like bound for (r , δ) -LRCs, we obtained some alphabet-optimal (r , δ) -LRCs and alphabet-optimal (r , δ) -LRCs with availability. [ABSTRACT FROM AUTHOR]

Locally repairable codes (LRCs), which can recover any symbol of a codeword by reading only a small number of other symbols, have been widely used in real-world distributed storage systems, such as Microsoft Azure Storage and Ceph Storage Cluster. Since binary linear LRCs can significantly reduce coding and decoding complexity, constructions of binary LRCs are of particular interest. The aim of this paper is to construct dimensional optimal binary LRCs with disjoint local repair groups. We introduce a method to connect intersection subspaces with binary LRCs and construct dimensional optimal binary linear LRCs with locality 2b (b ≽ 3) and minimum distance d ≽ 6 by employing intersection subspaces deduced from the direct sum. This method will sufficiently increase the number of possible repair groups of dimensional optimal LRCs, thus efficiently expanding the range of the construction parameters while keeping the largest code rates compared with all known binary linear LRCs with minimum distance d ≽ 6 and locality 2b. [ABSTRACT FROM AUTHOR]

Fractional Repetition (FR) codes break the data into smaller fragments and distribute these fragments across multiple storage nodes. This paper focuses on extension-based construction methods for obtaining new FR codes from existing FR codes. Additionally, it formulates a particular case of extension codes as an exact cover problem, enabling an algorithmic construction of FR codes. [ABSTRACT FROM AUTHOR]

A locally repairable code (LRC) is a code that can recover any symbol of a codeword by reading at most r other symbols, denoted by r -LRC. In this paper, we study binary and ternary linear LRCs with disjoint repair groups and minimum distance d = 6. Using the intersection subspaces technique, we explicitly construct dimensional optimal LRCs. First, based on the intersection subspaces constructed by t -spread, a construction of binary LRCs is designed. Particularly, a class of binary linear LRCs with r = 11 is optimal in terms of achieving a sphere-packing type upper bound. Next, by using the Kronecker product of two matrices, two classes of dimensional optimal ternary LRCs with small locality (r = 3, 5) are presented. Compared to previous results, our construction is more flexible regarding code parameters. Finally, we also discuss the parameters of a code obtained by applying a shortening operation to our LRCs. We show that these shortened LRCs are also k -optimal. [ABSTRACT FROM AUTHOR]

In most storage systems, the storage nodes store data on a local filesystem. Thus, unless they have a dedicated caching layer, they benefit from the usual filesystem cache in the host's free memory. However, in erasure-coded storage systems, caching is effective only if all the systematic fragments corresponding to an object are in the cache. In this work, we propose a new caching policy adapting traditional methods to erasure-coded storage systems. The main idea of our solution is to cache a full object rather than fragments object. A simulation-based evaluation showed that our full replica solution is able to improve the cache hit ratio and reduce the cache waste ratio compared to the traditional caching method. Moreover, experimental evaluation has been conducted. It indicates that our implementation not only validates the previous results but also shows that cache hits on full replicas have a better request response time. [ABSTRACT FROM AUTHOR]

In recent years, the rapidly increasing amounts of data created and processed through the internet resulted in distributed storage systems employing erasure coding based schemes. Aiming to balance the tradeoff between data recovery for correlated failures and efficient encoding and decoding, distributed storage systems employing maximally recoverable codes came up. Unifying a number of topologies considered both in theory and practice, Gopalan et al. [15] initiated the study of maximally recoverable codes for grid-like topologies. In this paper, we focus on the maximally recoverable codes that instantiate grid-like topologies T m × n (1 , b , 0) . To characterize the property of codes for these topologies, we introduce the notion of pseudo-parity check matrix. Then, using the Combinatorial Nullstellensatz, we establish the new upper bound on the field size needed for achieving the maximal recoverability in topologies T m × n (1 , b , 0) . By relating the problem to generalized Sidon sets in F q , we obtain a polynomial lower bound on the field size for maximally recoverable codes that instantiate topologies T m × n (1 , 2 , 0) . Moreover, using hypergraph independent set approach, we further improve our general upper bound for topologies T 4 × n (1 , 2 , 0) and T 3 × n (1 , 3 , 0) . [ABSTRACT FROM AUTHOR]

In the Distributed Storage Systems (DSSs), the encoded fraction of information is stored in a distributed fashion on different chunk servers. Recently a new paradigm of Fractional Repetition (FR) codes has been introduced, in which, encoded data information is stored on distributed servers using an encoding involving a Maximum Distance Separable (MDS) code and a Repetition code. In this work, we have considered FR codes with asymmetric parameters known as Generalized Fractional Repetition (GFR) codes. We have shown that any GFR code is equivalent to a hypergraph. Using the correspondence, the properties and the bounds of a hypergraph are directly mapped to the associated GFR code. In general, using the correspondence, the necessary and sufficient conditions for the existence of a GFR code is obtained. It is also shown that any GFR code associated with a linear hypergraph is universally good, and any locally repairable GFR code is associated with a class of non-linear hypergraph. [ABSTRACT FROM AUTHOR]

Locally repairable codes (LRCs) with (r, t)-locality have received considerable attention in recent years, since they are able to solve common problems in distributed storage systems such as repairing multiple node failures and managing hot data. Constructing LRCs with excellent parameters becomes an interesting research subject in distributed storage systems and coding theory. In this paper, we present two constructions of LRCs with information (r, t)-locality based on linear algebra and partial geometry, respectively. Both constructions generate LRCs with new parameters which are optimal with respect to the bound proposed by Rawat et al. (IEEE Trans Inf Theory 62(8):4481–4493, 2016). [ABSTRACT FROM AUTHOR]

Locally repairable codes (LRCs) were proposed to reduce the repair degree in distributed storage systems. 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. In this paper, we propose four types of (n, k, r, t)q LRCs from combinatorial designs. We introduce several constructions of LRCs with strict availability and some constructions of distance-optimal LRCs with information-symbol locality. Most of our constructions in this paper are over F 2 , i.e., they are suitable for implementation. [ABSTRACT FROM AUTHOR]

Distributed storage systems, built on peer-to-peer networks, can provide large-scale data storage and high data reliability by redundancy. Data backup is the process to store data into a set of redundant storage nodes. Rapid completion of such a process is very critical to maintain system performance. In traditional data backup in distributed systems based on erasure codes, star-structured scheme is used, in which each redundant block is just sent to each target storage node from the source node directly, so the storage throughput and delay are limited by the bottleneck bandwidth, due to bandwidth heterogeneity. The recent "in-network" redundancy generation scheme uses locally repairable property of self-repairing codes to speed up data backup. However, such kind of code does not own maximum distance separable property, thus does not achieve optimal storage efficiency. We still lack a fast backup scheme in distributed systems based on general erasure coding. To this end, we proposed that instead of only focusing on bandwidths between the source node and target nodes, the bandwidths between target storage nodes should be fully taken into account. In our scheme, each redundant data block is divided into some parts according to different proportions and each part of the block is sent to the target storage node via other different storage nodes. The benefit is that spare bandwidths between target storage nodes are used to reduce backup time. We further show how this process can be modeled and derive a formula about the final backup time. We can achieve minimum backup time by solution for classical quadratic programming problem. We conduct both numerical analysis and experimental study. Our experiments shows, the delay reduces 59 %, compared with common star-structured scheme. Meanwhile, the throughput is increased significantly in backup process. [ABSTRACT FROM AUTHOR]

In this paper we study the problem of storing reliably an archive of versioned data. Specifically, we focus on systems where the differences (deltas) between subsequent versions rather than the whole objects are stored-a typical model for storing versioned data. For reliability, we propose erasure encoding techniques that exploit the sparsity of information in the deltas while storing them reliably in a distributed back-end storage system, resulting in improved I/O read performance to retrieve the whole versioned archive. Along with the basic techniques, we propose a few optimization heuristics, and evaluate the techniques' efficacy analytically and with numerical simulations. [ABSTRACT FROM AUTHOR]

Three transmission schemes over a new type of multiple-access channel (MAC) model with inter-source communication links are proposed and investigated in this paper. This new channel model is well motivated by, e.g., wireless distributed storage networks, where communication to repair a lost node takes place from helper nodes to a repairing node over a wireless channel. Since in many wireless networks nodes can come and go in an arbitrary manner, there must be an inherent capability of inter-node communication between every pair of nodes. Assuming that communication is possible between every pair of helper nodes, the newly proposed schemes are based on various smart time-sharing and relaying strategies. In other words, certain helper nodes will be regarded as relays, thereby converting the conventional uncooperative multiple-access channel to a multiple-access relay channel (MARC). The diversity-multiplexing gain tradeoff (DMT) of the system together with efficient sphere-decodability and low structural complexity in terms of the number of antennas required at each end is used as the main design objectives. While the optimal DMT for the new channel model is fully open, it is shown that the proposed schemes outperform the DMT of the simple time-sharing protocol and, in some cases, even the optimal uncooperative MAC DMT. While using a wireless distributed storage network as a motivating example throughout the paper, the MAC transmission techniques proposed here are completely general and as such applicable to any MAC communication with inter-source communication links. [ABSTRACT FROM AUTHOR]

Data grids are middleware systems that offer secure shared storage of massive scientific datasets over wide area networks. The main challenge in their design is to provide reliable storage, search, and transfer of numerous or large files over geographically dispersed heterogeneous platforms. The Storage Resource Broker (SRB) is an example of a system that provides these services and that has been deployed in multiple high-performance scientific projects during the past few years. In this paper, we take a detailed look at several of its functional features and examine its scalability using synthetic and trace-based workloads. Unlike traditional file systems, SRB uses a commodity database to manage both system- and user-defined metadata. We quantitatively evaluate this decision and draw insightful conclusions about its implications to the system architecture and performance characteristics. We find that the bulk transfer facilities of SRB demonstrate good scalability properties, and we identify the bottleneck resources across different data search and transfer tasks. We examine the sensitivity to several configuration parameters and provide details about how different internal operations contribute to the overall performance. [ABSTRACT FROM AUTHOR]