Related papers: Double and Triple Node-Erasure-Correcting Codes ov…
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…
Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…
An edit refers to a single insertion, deletion, or substitution. This paper aims to construct binary codes that can correct two edits. To do this, a necessary and sufficient condition for a code to be two-edit correctable is provided,…
A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs, e.g., Steiner systems, balanced incomplete block designs and t-designs. The…
We consider data transmission over a network where each edge is an erasure channel and where the inner nodes transmit a random linear combination of their incoming information. We distinguish two channel models in this setting, the row and…
The problem of exact repair of a failed node in multi-hop networked distributed storage systems is considered. Contrary to the most of the current studies which model the repair process by the direct links from surviving nodes to the new…
The repair bandwidth of a code is the minimum amount of data required to repair one or several failed nodes (erasures). For MDS codes, the repair bandwidth is bounded below by the so-called cut-set bound, and codes that meet this bound with…
Storage codes on graphs are an instance of \emph{codes with locality}, which are used in distributed storage schemes to provide local repairability. Specifically, the nodes of the graph correspond to storage servers, and the neighbourhood…
Maximum distance separable (MDS) codes are optimal error-correcting codes in the sense that they provide the maximum failure-tolerance for a given number of parity nodes. Suppose that an MDS code with $k$ information nodes and $r=n-k$…
In distributed storage systems reliability is achieved through redundancy stored at different nodes in the network. Then a data collector can reconstruct source information even though some nodes fail. To maintain reliability, an autonomous…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
Despite their exceptional error-correcting properties, Reed-Solomon (RS) codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the…
Network codes designed specifically for distributed storage systems have the potential to provide dramatically higher storage efficiency for the same availability. One main challenge in the design of such codes is the exact repair problem:…
A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the "help-by-transfer" property where…
This paper proposes an erasure correcting code and its systematic form for the distributed storage system. The proposed codes are encoded by exclusive OR and bit-level shift operation. By the shift operation, the encoded packets are…
Data storage in Distributed Storage Systems (DSSs) is a multidimensional optimization problem. Using network coding, one wants to provide reliability, scalability, security, reduced storage overhead, reduced bandwidth for repair and minimal…
MDS array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with $r$ redundancy nodes can correct any $r$ node erasures by accessing all the remaining information…
We consider the problem of a graph subjected to adversarial perturbations, such as those arising from cyber-attacks, where edges are covertly added or removed. The adversarial perturbations occur during the transmission of the graph between…
A novel coding scheme for exact repair-regenerating codes is presented in this paper. The codes proposed in this work can trade between the repair bandwidth of nodes (number of downloaded symbols from each surviving node in a repair…
A code construction and repair scheme for optimal functional regeneration of multiple node failures is presented, which is based on stitching together short MDS codes on carefully chosen sets of points lying on a linearized polynomial. The…