Related papers: Codes Correcting Two Deletions
The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this paper, we study the harder model of worst-case deletions, with a…
In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial…
Despite their significant advantages over competing technologies, nanopore sequencers are plagued by high error rates, due to physical characteristics of the nanopore and inherent noise in the biological processes. It is thus paramount not…
In this work, we derive upper bounds on the cardinality of tandem duplication and palindromic deletion correcting codes by deriving the generalized sphere packing bound for these error types. We first prove that an upper bound for tandem…
We consider codes over fixed alphabets against worst-case symbol deletions. For any fixed $k \ge 2$, we construct a family of codes over alphabet of size $k$ with positive rate, which allow efficient recovery from a worst-case deletion…
Codes for correcting sticky insertions/deletions and limited-magnitude errors have attracted significant attention due to their applications of flash memories, racetrack memories, and DNA data storage systems. In this paper, we first…
Imperfect measurement can degrade a quantum error correction scheme. A solution that restores fault tolerance is to add redundancy to the process of syndrome extraction. In this work, we show how to optimize this process for an arbitrary…
Linear codes correcting one deletions have rate at most $1/2$. In this paper, we construct linear list decodable codes correcting edits with rate approaching $1$ and reasonable list size. Our encoder and decoder run in polynomial time.
The doubly shortened perfect codes of length 13 are classified utilizing the classification of perfect codes in [P.R.J. \"Osterg{\aa}rd and O. Pottonen, The perfect binary one-error-correcting codes of length 15: Part I - Classification,…
Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating…
We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a…
This manuscript presents a construction method for quantum codes capable of correcting multiple deletion errors. By introducing two new alogorithms, the alternating sandwich mapping and the block error locator, the proposed method reduces…
The explosion of the amount of data stored in cloud systems calls for more efficient paradigms for redundancy. While replication is widely used to ensure data availability, erasure correcting codes provide a much better trade-off between…
The problem of designing codes for deletion-correction and synchronization has received renewed interest due to applications in DNA-based data storage systems that use nanopore sequencers as readout platforms. In almost all instances,…
The problem of correcting deletions has received significant attention, partly because of the prevalence of these errors in DNA data storage. In this paper, we study the problem of correcting a consecutive burst of at most $t$ deletions in…
We consider the problem of constructing codes that can correct $\delta$ deletions occurring in an arbitrary binary string of length $n$ bits. Varshamov-Tenengolts (VT) codes can correct all possible single deletions $(\delta=1)$ with an…
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…
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…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
Document exchange and error correcting codes are two fundamental problems regarding communications. In the first problem, Alice and Bob each holds a string, and the goal is for Alice to send a short sketch to Bob, so that Bob can recover…