Related papers: Multi-Erasure Locally Recoverable Codes Over Small…
Modern distributed storage systems apply redundancy coding techniques to stored data. One form of redundancy is based on regenerating codes, which can minimize the repair bandwidth, i.e., the amount of data transferred when repairing a…
We prove a new lower bound on the field size of locally repairable codes (LRCs). Additionally, we construct maximally recoverable (MR) codes which are cyclic. While a known construction for MR codes has the same parameters, it produces…
Recently, locally repairable codes (LRCs) with local erasure correction constraints that are unequal and disjoint have been proposed. In this work, we study the same topic and provide some improved and additional results.
We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic…
We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the…
In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated to…
Flash memory devices are winning the competition for storage density against magnetic recording devices. This outcome results from advances in physics that allow storage of more than one bit per cell, coupled with advances in signal…
A Locally Recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. We study Locally Recoverable Algebraic Geometry codes arising from…
This paper presents new FEC codes for the erasure channel, LDPC-Band, that have been designed so as to optimize a hybrid iterative-Maximum Likelihood (ML) decoding. Indeed, these codes feature simultaneously a sparse parity check matrix,…
A locally recoverable code (LRC code) is a code over a finite alphabet such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set. In this paper we derive new finite-length and…
A locally recoverable code is an error-correcting code such that any erasure in a coordinate of a codeword can be recovered from a set of other few coordinates. In this article we introduce a model of local recoverable codes that also…
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 study monomial-Cartesian codes (MCCs) which can be regarded as $(r,\delta)$-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to $(r,\delta)$-optimal…
In this paper we study the decoding capabilities of convolutional codes over the erasure channel. Of special interest will be maximum distance profile (MDP) convolutional codes. These are codes which have a maximum possible column distance…
Locally recoverable codes (LRCs) with locality parameter $r$ can recover any erased code symbol by accessing $r$ other code symbols. This local recovery property is of great interest in large-scale distributed classical data storage systems…
MDS codes are erasure-correcting codes that can correct the maximum number of erasures for a given number of redundancy or parity symbols. If an MDS code has $r$ parities and no more than $r$ erasures occur, then by transmitting all the…
Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating…
Erasure coding techniques are getting integrated in networked distributed storage systems as a way to provide fault-tolerance at the cost of less storage overhead than traditional replication. Redundancy is maintained over time through…
This paper aims to go beyond resilience into the study of security and local-repairability for distributed storage systems (DSS). Security and local-repairability are both important as features of an efficient storage system, and this paper…
A code is called a locally repairable code (LRC) if any code symbol is a function of a small fraction of other code symbols. When a locally repairable code is employed in a distributed storage systems, an erased symbol can be recovered by…