Related papers: Oblivious Deletion Codes
An edit refers to a single insertion, deletion, or substitution. This paper aims to construct binary codes that can correct two edits. To do this, a necessary and sufficient condition for a code to be two-edit correctable is provided,…
This paper studies the problem of constructing codes correcting deletions in arrays. Under this model, it is assumed that an $n\times n$ array can experience deletions of rows and columns. These deletion errors are referred to as…
A dynamic algorithm against an adaptive adversary is required to be correct when the adversary chooses the next update after seeing the previous outputs of the algorithm. We obtain faster dynamic algorithms against an adaptive adversary and…
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…
This work constructs codes that are efficiently decodable from a constant fraction of \emph{worst-case} insertion and deletion errors in three parameter settings: (i) Binary codes with rate approaching 1; (ii) Codes with constant rate for…
We study deletion-correcting codes for an adversarial nanopore channel in which at most $t$ deletions may occur. We propose an explicit construction of $q$-ary codes of length $n$ for this channel with $2t\log_q n+\Theta(\log\log n)$…
Construction of capacity achieving deletion correcting codes has been a baffling challenge for decades. A recent breakthrough by Brakensiek $et~al$., alongside novel applications in DNA storage, have reignited the interest in this…
We continue the study of rateless codes for transmission of information across channels whose rate of erasure is unknown. In such a code, an infinite stream of encoding symbols can be generated from the message and sent across the erasure…
Due to its higher data density, longevity, energy efficiency, and ease of generating copies, DNA is considered a promising storage technology for satisfying future needs. However, a diverse set of errors including deletions, insertions,…
We study uniquely decodable codes and list decodable codes in the high-noise regime, specifically codes that are uniquely decodable from $\frac{1-\varepsilon}{2}$ fraction of errors and list decodable from $1-\varepsilon$ fraction of…
We consider oblivious transfer protocols performed over binary symmetric channels in a malicious setting where parties will actively cheat if they can. We provide constructions purely based on coding theory that achieve an explicit positive…
In recent years, deep learning has shown performance breakthroughs in many applications, such as image detection, image segmentation, pose estimation, and speech recognition. However, this comes with a major concern: deep networks have been…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…
Reconstruction codes are generalizations of error-correcting codes that can correct errors by a given number of noisy reads. The study of such codes was initiated by Levenshtein in 2001 and developed recently due to applications in modern…
In this paper we study codes for correcting deletable errors in binary words, where each bit is either retained, substituted, erased or deleted and the total number of errors is much smaller compared to the length of the codeword. We…
We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems,…
We study codes that can detect the exact number of deletions and insertions in concatenated binary strings. We construct optimal codes for the case of detecting up to $\del$ deletions. We prove the optimality of these codes by deriving a…
This paper considers rateless network error correction codes for reliable multicast in the presence of adversarial errors. Most existing network error correction codes are designed for a given network capacity and maximum number of errors…
Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…
This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single…