相关论文: On Low Field Size Constructions of Access-Optimal …
Maximum distance separable (MDS) codes are optimal where the minimum distance cannot be improved for a given length and code size. Twisted Reed-Solomon codes over finite fields were introduced in 2017, which are generalization of…
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…
In modern data storage systems, non-binary LDPC codes for recovering from disk failures are increasingly considered strong competitors to MDS codes such as Reed-Solomon codes. Since disk failures can be modeled as erasures, we analyze…
Fractional repetition (FR) codes are a class of repair efficient erasure codes that can recover a failed storage node with both optimal repair bandwidth and complexity. In this paper, we study the minimum distance of FR codes, which is the…
Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…
Digital data transfer can be protected by means of suitable error correcting codes. Among the families of state-of-the-art codes, LDPC (Low Density Parity-Check) codes have received a great deal of attention recently, because of their…
Maximum Distance Profile (MDP) convolutional codes are an important class of channel codes due to their maximal delay-constrained error correction capabilities. The design of MDP codes has attracted significant attention from the research…
The construction of Maximum Distance Profile (MDP) convolutional codes in general requires the use of very large finite fields. In contrast convolutional codes with optimal column distances maximize the column distances for a given…
In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian…
Continuous variable quantum key distribution bears the promise of simple quantum key distribution directly compatible with commercial off the shelf equipment. However, for a long time its performance was hindered by the absence of good…
We establish a multi-user extrinsic information transfer (EXIT) chart area theorem for the interleave-division multiple-access (IDMA) scheme, a special form of superposition coding, in multiple access channels (MACs). A low-cost multi-user…
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…
An $(n,k,\ell)$-vector MDS code is a $\mathbb{F}$-linear subspace of $(\mathbb{F}^\ell)^n$ (for some field $\mathbb{F}$) of dimension $k\ell$, such that any $k$ (vector) symbols of the codeword suffice to determine the remaining $r=n-k$…
We study the existence over small fields of Maximum Distance Separable (MDS) codes with generator matrices having specified supports (i.e. having specified locations of zero entries). This problem unifies and simplifies the problems posed…
As consumers are increasingly engaged in social networking and E-commerce activities, businesses grow to rely on Big Data analytics for intelligence, and traditional IT infrastructures continue to migrate to the cloud and edge, these trends…
A linear code with parameters $[n,k,n-k]$ is said to be almost maximum distance separable (AMDS for short). An AMDS code whose dual is also AMDS is referred to as an near maximum distance separable (NMDS for short) code. NMDS codes have…
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…
We consider the problem of multiple-node repair in distributed storage systems under the cooperative model, where the repair bandwidth includes the amount of data exchanged between any two different storage nodes. Recently, explicit…
As storage systems grow in size, device failures happen more frequently than ever before. Given the commodity nature of hard drives employed, a storage system needs to tolerate a certain number of disk failures while maintaining data…
Distributed and cloud storage systems are used to reliably store large-scale data. Erasure codes have been recently proposed and used in real-world distributed and cloud storage systems such as Google File System, Microsoft Azure Storage,…