Related papers: Detecting Deletions and Insertions in Concatenated…
Insertion-deletion codes (insdel codes for short) are used for correcting synchronization errors in communications, and in other many interesting fields such as DNA storage, date analysis, race-track memory error correction and language…
This work continues the study of linear error correcting codes against adversarial insertion deletion errors (insdel errors). Previously, the work of Cheng, Guruswami, Haeupler, and Li \cite{CGHL21} showed the existence of asymptotically…
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…
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 improve the upper bound of Levenshtein for the cardinality of a code of length 4 capable of correcting single deletions over an alphabet of even size. We also illustrate that the new upper bound is sharp. Furthermore we will construct an…
We study the application of polar codes in deletion channels by analyzing the cascade of a binary erasure channel (BEC) and a deletion channel. We show how polar codes can be used effectively on a BEC with a single deletion, and propose a…
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 present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
We study segmented burst-deletion channels motivated by the observation that synchronization errors commonly occur in a bursty manner in real-world settings. In this channel model, transmitted sequences are implicitly divided into…
Motivated by applications in DNA-based storage and communication systems, we study deletion and insertion errors simultaneously in a burst. In particular, we study a type of error named $t$-deletion-$s$-insertion-burst ($(t,s)$-burst for…
This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study the unique recovery of $n \times n$ arrays affected by $t$-criss-cross deletions defined as any combination…
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…
List decoding of insertions and deletions in the Levenshtein metric is considered. The Levenshtein distance between two sequences is the minimum number of insertions and deletions needed to turn one of the sequences into the other. In this…
We consider the problem of constructing binary codes for correcting deletions that are localized within certain parts of the codeword that are unknown a priori. The model that we study is when $\delta \leq w$ deletions are localized in a…
This paper studies on the cardinality of perfect multi deletion binary codes. The lower bound for any perfect deletion code with the fixed code length and the number of deletions, and the asymptotic achievable of Levenshtein's upper bound…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
We consider the problem of block-coded communication, where in each block, the channel law belongs to one of two disjoint sets. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has 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…
The design of low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. Our approach employs EXIT chart analysis and differential evolution to design such ensembles for the binary…
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…