相关论文: Cauchy MDS Array Codes With Efficient Decoding Met…
We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…
Recently, error correcting codes in the erasure channel have drawn great attention for various applications such as distributed storage systems and wireless sensor networks, but many of their decoding algorithms are not practical because…
Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing…
We present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $n \times n$ distance matrix as input, where $n$ is the number of individuals,…
We propose a coded computing strategy and examine communication costs of coded computing algorithms to make distributed Fast Fourier Transform (FFT) resilient to errors during the computation. We apply maximum distance separable (MDS) codes…
The size reduction of transistors in the latest flash memory generation has resulted in programming and data erasure issues within these designs. Consequently, ensuring reliable data storage has become a significant challenge for these…
A Maximum Distance Separable code over an alphabet $F$ is defined via an encoding function $C:F^k \rightarrow F^n$ that allows to retrieve a message $m \in F^k$ from the codeword $C(m)$ even after erasing any $n-k$ of its symbols. The…
This work presents a theoretical analysis of the probability of successfully retrieving data encoded with MDS codes (e.g., Reed-Solomon codes) in DNA storage systems. We study this probability under independent and identically distributed…
Coded computing is an effective technique to mitigate "stragglers" in large-scale and distributed matrix multiplication. In particular, univariate polynomial codes have been shown to be effective in straggler mitigation by making the…
Coded distributed matrix multiplication (CDMM) schemes, such as MatDot codes, seek efficient ways to distribute matrix multiplication task(s) to a set of $N$ distributed servers so that the answers returned from any $R$ servers are…
Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed storage system uses a linear code to encode a large file across…
We present the construction of a family of erasure correcting codes for distributed storage that achieve low repair bandwidth and complexity at the expense of a lower fault tolerance. The construction is based on two classes of codes, where…
For high-rate maximum distance separable (MDS) codes, most of them are designed to optimally repair a single failed node by connecting all the surviving nodes. However, in practical systems, sometimes not all the surviving nodes are…
In distributed computing systems, it is well recognized that worker nodes that are slow (called stragglers) tend to dominate the overall job execution time. Coded computation utilizes concepts from erasure coding to mitigate the effect of…
Due to its low storage cost and fast query speed, hashing has been widely used in large-scale image retrieval tasks. Hash bucket search returns data points within a given Hamming radius to each query, which can enable search at a constant…
Symbol-pair codes are block codes with symbol-pair metrics designed to protect against pair-errors that may occur in high-density data storage systems. MDS symbol-pair codes are optimal in the sense that it can attain the highest pair-error…
Decoding and repair schemes are proposed for shift-exclusive-or (shift-XOR) product-matrix (PM) regenerating codes, which outperform the existing schemes in terms of both communication and computation costs. In particular, for the shift-XOR…
In a distributed storage environment, where the data is placed in nodes connected through a network, it is likely that one of these nodes fails. It is known that the use of erasure coding improves the fault tolerance and minimizes the…
In a distributed storage system based on erasure coding, an important problem is the \emph{repair problem}: If a node storing a coded piece fails, in order to maintain the same level of reliability, we need to create a new encoded piece and…