Typically, locally repairable codes (LRCs) and regenerating codes have been studied independently of each other, and it has not been clear how the parameters of one relate to those of the other. In this paper, a novel connection between locally repairable codes and exact regenerating codes is established. Via this connection, locally repairable codes are interpreted as exact regenerating codes. Further, some of these codes are shown to perform better than time-sharing codes between minimum bandwidth regenerating and minimum storage regenerating codes.
Constructions of exact regenerating codes between the MBR and MSR points exceeding the time-sharing line are studied in @cite_21 @cite_24 @cite_11 @cite_10 . Results in @cite_21 and @cite_24 are combined in @cite_13 . However, in contrast to these constructions we are not trying to find codes that perform as well as possible. Instead, our main purpose is to show that LRCs can be used as exact regenerating codes and, in many cases, they have quite good performance. However, when compared to the other constructions, LRCs when used as exact regenerating codes do not usually perform that well. The established connection also enables further analysis on LRCs in terms of storage space, repair bandwidth, .
@cite_13 @cite_21 @cite_24 @cite_10 @cite_11
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In this paper, distributed storage systems with exact repair are studied. Constructions for exact-regenerating codes between the minimum storage regenerating (MSR) and the minimum bandwidth regenerating (MBR) points are given. To the best of our knowledge, no previous construction of exact-regenerating codes between MBR and MSR points is done except in the works by and In contrast to their works, the methods used here are elementary. In this paper, it is shown that in the case that the parameters (n ) , (k ) , and (d ) are close to each other, the given construction is close to optimal when comparing with the known functional repair capacity. This is done by showing that when the distances of the parameters (n ) , (k ) , and (d ) are fixed but the actual values approach to infinity, the fraction of the performance of constructed codes with exact repair and the known capacity of codes with functional repair, approaches to one. Also, a simple variation of the constructed codes with almost the same performance is given. Also some bounds for the capacity of exact-repairing codes are given. These bounds illustrate the relationships between storage codes with different parameters. In this paper, we provide explicit constructions for a class of exact-repair regenerating codes that possess a layered structure. These regenerating codes correspond to interior points on the storage-repair-bandwidth tradeoff where the cut-set bound of network coding is known to be not achievable under exact repair. The codes presented in this paper compare very well in comparison to schemes that employ space-sharing between MSR and MBR points, and come closest of all-known explicit constructions to interior points of the tradeoff. The codes can be constructed for a wide range of parameters, are high-rate, can repair multiple nodes simultaneously and no computation at helper nodes is required to repair a failed node. We also construct optimal codes with locality in which the local codes are layered regenerating codes. Regenerating codes are a class of distributed storage codes that allow for efficient repair of failed nodes, as compared to traditional erasure codes. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that a failed node be repaired by connecting to any d nodes. The amount of data downloaded for repair is typically much smaller than the size of the source data. Previous constructions of exact-regenerating codes have been confined to the case n=d+1 . In this paper, we present optimal, explicit constructions of (a) Minimum Bandwidth Regenerating (MBR) codes for all values of [n, k, d] and (b) Minimum Storage Regenerating (MSR) codes for all [n, k, d ≥ 2k-2], using a new product-matrix framework. The product-matrix framework is also shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exact-regenerating codes that allow the number n of nodes in the network, to be chosen independent of the other parameters. The paper also contains a simpler description, in the product-matrix framework, of a previously constructed MSR code with [n=d+1, k, d ≥ 2k-1]. This paper addresses the issue of securing information stored on a distributed storage system from a passive eavesdropping attack. The security notion is perfect secrecy, i.e., the system is said to be secure only if the mutual information between the stored information and the observations at the adversary is zero. The paper summarizes state of the art on securing repair-efficient distributed storage systems. Then, storage systems that employ locally repairable codes with minimum bandwidth regenerating codes as local codes (MBR-LRCs) are investigated. A secure file size upper bound and a construction of secure MBR-LRCs are provided. These two are shown to match under special cases, establishing the secrecy capacity of these systems.