相关论文: Correcting an ordered deletion-erasure

In this paper, we present an explicit construction of list-decodable codes for single-deletion and single-substitution with list size two and redundancy 3log n+4, where n is the block length of the code. Our construction has lower…

Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both…

Despite their exceptional error-correcting properties, Reed-Solomon codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the…

This paper addresses fundamental challenges in two-dimensional error correction by constructing optimal codes for \emph{criss-cross deletions}. We consider an $ n \times n $ array $\boldsymbol{X}$ over a $ q $-ary alphabet $\Sigma_q := \{0,…

We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been…

Two-dimensional error-correcting codes, where codewords are represented as $n \times n$ arrays over a $q$-ary alphabet, find important applications in areas such as QR codes, DNA-based storage, and racetrack memories. Among the possible…

The amount of digital data is rapidly growing. There is an increasing use of a wide range of computer systems, from mobile devices to large-scale data centers, and important for reliable operation of all computer systems is mitigating the…

In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…

In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, e.g., when the rank exceeds the tensor dimension, or when the loading components are highly collinear in several or all modes, or when CPD does…

In this paper, we investigate the optimum way to allocate redundancy of finite-length nested codes for modern nonvolatile memories suffering from both permanent defects and transient errors (erasures or random errors). A nested coding…

This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…

Owing to its several merits over other DNA sequencing technologies, nanopore sequencers hold an immense potential to revolutionize the efficiency of DNA storage systems. However, their higher error rates necessitate further research to…

This paper constructs a non-binary code correcting a single $b$-burst of insertions or deletions with a large cardinality. This paper also proposes a decoding algorithm of this code and evaluates a lower bound of the cardinality of this…

We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes our method exploits…

In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it communication} required to exactly rebuild a storage node after a failure arises. This repair bandwidth depends on the structure of the…

Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…

The substring edit error is the operation of replacing a substring $u$ of $x$ with another string $v$, where the lengths of $u$ and $v$ are bounded by a given constant $k$. It encompasses localized insertions, deletions, and substitutions…

We propose a new class of error correction codes for low-delay streaming communication. We consider an online setup where a source packet arrives at the encoder every $M$ channel uses, and needs to be decoded with a maximum delay of $T$…

We prove that every $1$-error-correcting code over a finite field can be embedded in a $1$-perfect code of some larger length. Embedding in this context means that the original code is a subcode of the resulting $1$-perfect code and can be…

This paper investigates the use of redundancy and self repairing against node failures in distributed storage systems, using various strategies. In replication method, access to one replication node is sufficient to reconstruct a lost node,…