Related papers: Construction of two SD Codes
Cloud storage systems generally add redundancy in storing content files such that $K$ files are replicated or erasure coded and stored on $N > K$ nodes. In addition to providing reliability against failures, the redundant copies can be used…
DNA storage systems face significant challenges, including insertion, deletion, and substitution (IDS) errors. Therefore, designing effective synchronization codes, i.e., codes capable of correcting IDS errors, is essential for DNA storage…
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 $r=n-k$…
We describe a replacement for RAID 6, based on a new linear, systematic code, which detects and corrects any combination of $E$ errors (unknown location) and $Z$ erasures (known location) provided that $Z+2E \leq 4$. We investigate some…
This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the…
Maximum distance separable (MDS) codes have the optimal trade-off between storage efficiency and fault tolerance, which are widely used in distributed storage systems. As typical non-MDS codes, simple regenerating codes (SRCs) can achieve…
Cooperative regenerating codes are designed for repairing multiple node failures in distributed storage systems. In contrast to the original repair model of regenerating codes, which are for the repair of single node failure, data exchange…
In this paper we study array-based codes over graphs for correcting multiple node failures. These codes have applications to neural networks, associative memories, and distributed storage systems. We assume that the information is stored on…
Motivated by the application of Reed-Solomon codes to recently emerging decentralized storage systems such as Storj and Filebase/Sia, we study the problem of designing compact repair groups for recovering multiple failures in a…
In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it repair bandwidth} required to exactly regenerate a storage node after a failure arises. This repair bandwidth depends on the structure of the…
In this paper, we propose locally repairable codes (LRCs) with optimal minimum distance for distributed storage systems (DSS). A two-layer encoding structure is employed to ensure data reconstruction and the designated repair locality. The…
Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a…
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…
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…
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…
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…
A $(k+r,k,l)$ binary array code of length $k+r$, dimension $k$, and sub-packetization $l$ is composed of $l\times(k+r)$ matrices over $\mathbb{F}_2$, with every column of the matrix stored on a separate node in the distributed storage…
This paper studies the design of codes for distributed storage systems (DSS) that enable local repair in the event of node failure. This paper presents locally repairable codes based on low degree multivariate polynomials. Its code…
Erasure coding is widely used for massive storage in data centers to achieve high fault tolerance and low storage redundancy. Since the cross-rack communication cost is often high, it is critical to design erasure codes that minimize the…
This dissertation considers new constructions and decoding approaches for error-correcting codes based on non-conventional polynomials, with the objective of providing new coding solutions to the applications mentioned above. With skew…