Related papers: On MDS Convertible Codes in the Merge Regime
Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes where each local code is a bandwidth-optimal regenerating MDS code.…
Partial-MDS (PMDS) codes are a family of locally repairable codes, mainly used for distributed storage. They are defined to be able to correct any pattern of $s$ additional erasures, after a given number of erasures per locality group have…
Array codes have been widely used in communication and storage systems. To reduce computational complexity, one important property of the array codes is that only XOR operation is used in the encoding and decoding process. In this work, we…
As compared to a large spectrum of performance optimizations, relatively little effort has been dedicated to optimize other aspects of embedded applications such as memory space requirements, power, real-time predictability, and…
In this paper, we propose two new constructions of exact-repair minimum storage regenerating (exact-MSR) codes. For both constructions, the encoded symbols are obtained by treating the message vector over GF(q) as a linearized polynomial…
In modern practical data centers, storage nodes are usually organized into equally sized groups, which is called racks. The cost of cross-rack communication is much more expensive compared with the intra-rack communication cost. The codes…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
In a distributed storage network, reliability and bandwidth optimization can be provided by regenerating codes. Recently table based regenerating codes viz. DRESS (Distributed Replication-based Exact Simple Storage) codes has been proposed…
In an $(n,k,d)$ rack-aware storage model, the system consists of $n$ nodes uniformly distributed across $\bar{n}$ successive racks, such that each rack contains $u$ nodes of equal capacity and the reconstructive degree satisfies…
An $(m,n,a,b)$-tensor code consists of $m\times n$ matrices whose columns satisfy `$a$' parity checks and rows satisfy `$b$' parity checks (i.e., a tensor code is the tensor product of a column code and row code). Tensor codes are useful in…
We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the…
Array codes have been widely employed in storage systems, such as Redundant Arrays of Inexpensive Disks (RAID). The row-diagonal parity (RDP) codes and EVENODD codes are two popular double-parity array codes. As the capacity of hard disks…
We investigate the problem of maintaining an encoded distributed storage system when some nodes contain adversarial errors. Using the error-correction capabilities that are built into the existing redundancy of the system, we propose a…
Maximum distance separable (MDS) are constructed to required specifications. The codes are explicitly given over finite fields with efficient encoding and decoding algorithms. Series of such codes over finite fields with ratio of distance…
Erasure codes are an integral part of many distributed storage systems aimed at Big Data, since they provide high fault-tolerance for low overheads. However, traditional erasure codes are inefficient on reading stored data in degraded…
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…
We consider the problem of constructing linear Maximum Distance Separable (MDS) error-correcting codes with generator matrices that are sparsest and balanced. In this context, sparsest means that every row has the least possible number of…
Consider the following fundamental question of distributed storage networks: Given any arbitrary $(n,k,d)$ values, whether there exists an intelligent helper selection scheme (assuming unlimited memory and computing power) that can strictly…
One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$ such that the subspace distance satisfies $\operatorname{d_S}(U,V) =…
Piggybacking codes are a special class of MDS array codes that can achieve small repair bandwidth with small sub-packetization by first creating some instances of an $(n,k)$ MDS code, such as a Reed-Solomon (RS) code, and then designing the…