Related papers: An Explicit, Coupled-Layer Construction of a High-…
This paper presents an explicit construction for an $((n,k,d=n-1), (\alpha,\beta))$ regenerating code over a field $\mathbb{F}_Q$ operating at the Minimum Storage Regeneration (MSR) point. The MSR code can be constructed to have rate $k/n$…
This paper presents a novel construction of $(n,k,d=n-1)$ access-optimal regenerating codes for an arbitrary sub-packetization level $\alpha$ for exact repair of any systematic node. We refer to these codes as general sub-packetized because…
We present a high-rate $(n,k,d=n-1)$-MSR code with a sub-packetization level that is polynomial in the dimension $k$ of the code. While polynomial sub-packetization level was achieved earlier for vector MDS codes that repair systematic…
This paper presents an explicit construction of a class of optimal-access, minimum storage regenerating (MSR) codes, for small values of the number $d$ of helper nodes. The construction is valid for any parameter set $(n,k,d)$ with $d \in…
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, and compare…
Wang et al. (IEEE Transactions on Information Theory, vol. 62, no. 8, 2016) proposed an explicit construction of an $(n=k+2,k)$ Minimum Storage Regenerating (MSR) code with $2$ parity nodes and subpacketization $2^{k/3}$. The number of…
An $(n,k,d)$ cooperative regenerating code provides the optimal-bandwidth repair for any $t~(t\!>\!1)$ node failures in a cooperative way. In particular, an MSCR (minimum storage cooperative regenerating) code retains the same storage…
This paper uses the reconstruction-computation-quantization (RCQ) paradigm to decode low-density parity-check (LDPC) codes. RCQ facilitates dynamic non-uniform quantization to achieve good frame error rate (FER) performance with very low…
The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size, and hence may be hard to implement in practice. By using notions from the theory of extension fields, we…
In large data centers, storage nodes are organized in racks, and the cross-rack transmission dominates the bandwidth cost. For the repair of single node failures, codes achieving the tradeoff between the storage redundancy and cross-rack…
Regenerating codes for distributed storage have attracted much research interest in the past decade. Such codes trade the bandwidth needed to repair a failed node with the overall amount of data stored in the network. Minimum storage…
The sub-packetization $\ell$ and the field size $q$ are of paramount importance in the MSR array code constructions. For optimal-access MSR codes, Balaji et al. proved that $\ell\geq s^{\left\lceil n/s \right\rceil}$, where $s = d-k+1$.…
An erasure code is said to be a code with sequential recovery with parameters $r$ and $t$, if for any $s \leq t$ erased code symbols, there is an $s$-step recovery process in which at each step we recover exactly one erased code symbol by…
Flash memory is a non-volatile computer memory comprising blocks of cells, wherein each cell can take on q different values or levels. While increasing the cell level is easy, reducing the level of a cell can be accomplished only by erasing…
Regenerating code is a class of code very suitable for distributed storage systems, which can maintain optimal bandwidth and storage space. Two types of important regenerating code have been constructed: the minimum storage regeneration…
A code $\mathcal{C}(n, k, d)$ defined over $\texttt{GF}(q^{n})$ is conventionally designed to encode a $k$-symbol user data into a codeword of length $n$, resulting in a fixed-rate coding. This paper proposes a coding procedure to derive a…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these…
We consider the rack-aware storage system where $n=\bar{n}u$ nodes are organized in $\bar{n}$ racks each containing $u$ nodes, and any $k=\bar{k}u+u_0~(0\leq u_0<u)$ nodes can retrieve the original data file. More importantly, the…
An early paper by Rashmi et. al. presented the construction of an $(n,k,d=n-1)$ MBR regenerating code featuring the inherent double replication of all code symbols and repair-by-transfer (RBT), both of which are important in practice. We…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…