Related papers: Codes for Correcting $t$ Limited-Magnitude Sticky …
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
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…
An insdel refers to a deletion or an insertion, and an edit refers to an insdel or a substitution. In this paper, we consider the segmented single-insdel (resp. single-edit) channel, where the channel's input bit stream is partitioned into…
Nanopore sequencing, superior to other sequencing technologies for DNA storage in multiple aspects, has recently attracted considerable attention. Its high error rates, however, demand thorough research on practical and efficient coding…
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…
$\epsilon$-Minimum Storage Regenerating ($\epsilon$-MSR) codes form a special class of Maximum Distance Separable (MDS) codes, providing mechanisms for exact regeneration of a single code block in their codewords by downloading slighly…
The rank modulation scheme has been proposed for efficient writing and storing data in non-volatile memory storage. Error-correction in the rank modulation scheme is done by considering permutation codes. In this paper we consider codes in…
DNA synthesis is considered as one of the most expensive components in current DNA storage systems. In this paper, focusing on a common synthesis machine, which generates multiple DNA strands in parallel following a fixed supersequence,we…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
The repair problem in distributed storage addresses recovery of the data encoded using an erasure code, for instance, a Reed-Solomon (RS) code. We consider the problem of repairing a single node or multiple nodes in RS-coded storage systems…
Data redundancy techniques have been tested in several different applications to provide fault tolerance and performance gains. The use of these techniques is mostly seen at the hardware, device driver, or file system level. In practice,…
This paper studies the cardinality of codes correcting insertions and deletions. We give improved upper and lower bounds on code size. Our upper bound is obtained by utilizing the asymmetric property of list decoding for insertions and…
We give an explicit construction of length-$n$ binary codes capable of correcting the deletion of two bits that have size $2^n/n^{4+o(1)}$. This matches up to lower order terms the existential result, based on an inefficient greedy choice…
This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit…
For a systematic erasure code, update complexity (UC) is defined as the maximum number of parity blocks needed to be changed when some information blocks are updated. Locally repairable codes (LRCs) have been recently proposed and used in…
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…
We consider the problem of designing [n; k] linear codes for distributed storage systems (DSS) that satisfy the (r, t)-Local Repair Property, where any t'(<=t) simultaneously failed nodes can be locally repaired, each with locality r. The…
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…
We construct Gray codes over permutations for the rank-modulation scheme, which are also capable of correcting errors under the infinity-metric. These errors model limited-magnitude or spike errors, for which only single-error-detecting…
We investigate threshold-based multi-trial decoding of concatenated codes with an inner Maximum-Likelihood decoder and an outer error/erasure (L+1)/L-extended Bounded Distance decoder, i.e. a decoder which corrects e errors and t erasures…