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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…
Recently, we introduced a new class of finite alphabet iterative decoders (FAIDs) for low-density parity-check (LDPC) codes. These decoders are capable of surpassing belief propagation in the error floor region on the Binary Symmetric…
Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…
In general, array codes consist of $m\times n$ arrays and in many cases, the arrays satisfy parity constraints along lines of different slopes (generally with a toroidal topology). Such codes are useful for RAID type of architectures, since…
In this paper, we introduce a new practical and general method for solving the main problem of designing the capacity approaching, optimal rate, irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC).…
Data centres that use consumer-grade disks drives and distributed peer-to-peer systems are unreliable environments to archive data without enough redundancy. Most redundancy schemes are not completely effective for providing high…
In network communication, the source often transmits messages at several different information rates within a session. How to deal with information transmission and network error correction simultaneously under different rates is introduced…
A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches…
In distributed quantum storage, physical qubits of a code will be stored across the network. When qubits in one of the nodes are lost i.e. when the node is erased, the remaining nodes need to communicate with a new node to replace the lost…
The reliability of erasure-coded distributed storage systems, as measured by the mean time to data loss (MTTDL), depends on the repair bandwidth of the code. Repair-efficient codes provide reliability values several orders of magnitude…
The construction of quantum error-correcting codes (QECCs) with good parameters is a hot topic in the area of quantum information and quantum computing. Quantum maximum distance separable (QMDS) codes are optimal because the minimum…
We consider the design of regenerating codes for distributed storage systems that enjoy the property of local, exact and uncoded repair, i.e., (a) upon failure, a node can be regenerated by simply downloading packets from the surviving…
In this work we continue the study of a new class of codes, called \emph{codes over graphs}. Here we consider storage systems where the information is stored on the edges of a complete directed graph with $n$ nodes. The failure model we…
Abundant high-rate (n, k) minimum storage regenerating (MSR) codes have been reported in the literature. However, most of them require contacting all the surviving nodes during a node repair process, resulting in a repair degree of d=n-1.…
Maximum distance separable (MDS) and almost maximum distance separable (AMDS) codes have been widely used in various fields such as communication systems, data storage, and quantum codes because of their algebraic properties and excellent…
Distributed storage systems need to store data redundantly in order to provide some fault-tolerance and guarantee system reliability. Different coding techniques have been proposed to provide the required redundancy more efficiently than…
In distributed storage, erasure codes -- like Reed-Solomon Codes -- are often employed to provide reliability. In this setting, it is desirable to be able to repair one or more failed nodes while minimizing the repair bandwidth. In this…
Practical storage systems often adopt erasure codes to tolerate device failures and sector failures, both of which are prevalent in the field. However, traditional erasure codes employ device-level redundancy to protect against sector…
In a modern distributed storage system, storage nodes are organized in racks, and the cross-rack communication dominates the system bandwidth. In We study the rack-aware storage system where all storage nodes are organized in racks and…
We consider a set up where a file of size M is stored in n distributed storage nodes, using an (n,k) minimum storage regenerating (MSR) code, i.e., a maximum distance separable (MDS) code that also allows efficient exact-repair of any…