相关论文: Multiple Criss-Cross Insertion and Deletion Correc…
We propose two systematic constructions of deletion-correcting codes for protecting quantum information. The first one works with qudits of any dimension, but only one deletion is corrected and the constructed codes are asymptotically bad.…
An indel refers to a single insertion or deletion, while an edit refers to a single insertion, deletion or substitution. In this paper, we investigate codes that combat either a single indel or a single edit and provide linear-time…
A new family of codes, called clustering-correcting codes, is presented in this paper. This family of codes is motivated by the special structure of data that is stored in DNA-based storage systems. The data stored in these systems has the…
In distributed storage systems that use coding, the issue of minimizing the communication required to rebuild a storage node after a failure arises. We consider the problem of repairing an erased node in a distributed storage system that…
The coded trace reconstruction problem asks to construct a code $C\subset \{0,1\}^n$ such that any $x\in C$ is recoverable from independent outputs ("traces") of $x$ from a binary deletion channel (BDC). We present binary codes of rate…
In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to…
In order to provide high data reliability, distributed storage systems disperse data with redundancy to multiple storage nodes. Regenerating codes is a new class of erasure codes to introduce redundancy for the purpose of improving the data…
By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local…
This thesis makes several significant contributions to the theory of both Regenerating (RG) and Locally Recoverable (LR) codes. The two principal contributions are characterizing the optimal rate of an LR code designed to recover from $t$…
Consider a binary maximum distance separable (MDS) array code composed of an $m\times (k+r)$ array of bits with $k$ information columns and $r$ parity columns, such that any $k$ out of $k+r$ columns suffice to reconstruct the $k$…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
We investigate in this work the problem of Erasure Combinatorial Batch Codes, in which $n$ files are stored on $m$ servers so that every set of $n-r$ servers allows a client to retrieve at most $k$ distinct files by downloading at most $t$…
The analysis of the decoding failure rate of the bit-flipping algorithm has received increasing attention. For a binary linear code we consider the minimum number of rows in a parity-check matrix such that the bit-flipping algorithm is able…
Let C be a linear code with length n and minimum distance d. The stopping redundancy of C is defined as the minimum number of rows in a parity-check matrix for C such that the smallest stopping sets in the corresponding Tanner graph have…
We introduce synchronization strings as a novel way of efficiently dealing with synchronization errors, i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to deal with than commonly considered…
We introduce fast-decodable indexing schemes for edit distance which can be used to speed up edit distance computations to near-linear time if one of the strings is indexed by an indexing string $I$. In particular, for every length $n$ and…
This paper introduces a new solution to DNA storage that integrates all three steps of retrieval, namely clustering, reconstruction, and error correction. DNA-correcting codes are presented as a unique solution to the problem of ensuring…
We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which…
We present many new results related to reliable (interactive) communication over insertion-deletion channels. Synchronization errors, such as insertions and deletions, strictly generalize the usual symbol corruption errors and are much…
The coding matrix design plays a fundamental role in the prediction performance of the error correcting output codes (ECOC)-based multi-class task. {In many-class classification problems, e.g., fine-grained categorization, it is difficult…