Related papers: On Unique Decoding from Insertions and Deletions
Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion…
We study the amount of reliable information that can be stored in a DNA-based storage system with noisy sequencing, where each codeword is composed of short DNA molecules. We analyze a concatenated coding scheme, where the outer code is…
In this paper, we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where data is represented by an unordered set of $M$ sequences, each of length $L$. Errors…
We consider hard-decision iterative decoders for product codes over the erasure channel, which employ repeated rounds of decoding rows and columns alternatingly. We derive the exact asymptotic probability of decoding failure as a function…
Motivated by applications of biometric identification and content identification systems, we consider the problem of random coding for channels, where each codeword undergoes lossy compression (vector quantization), and where the decoder…
Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…
Labeling of DNA molecules is a fundamental technique for DNA visualization and analysis. This process was mathematically modeled in [1], where the received sequence indicates the positions of the used labels. In this work, we develop error…
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…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
Consider two remote nodes (encoder and decoder), each with a binary sequence. The encoder's sequence $X$ differs from the decoder's sequence $Y$ by a small number of edits (deletions and insertions). The goal is to construct a message $M$,…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
We consider error-correcting coding for deoxyribonucleic acid (DNA)-based storage using nanopore sequencing. We model the DNA storage channel as a sampling noise channel where the input data is chunked into $M$ short DNA strands, which are…
Constrained sequence codes have been widely used in modern communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel, hence enabling efficient and reliable…
Error correction codes are an integral part of communication applications, boosting the reliability of transmission. The optimal decoding of transmitted codewords is the maximum likelihood rule, which is NP-hard due to the curse of…
Burst errors involving simultaneous insertions, deletions, and substitutions occur in practical scenarios, including DNA data storage and document synchronization, motivating developments of channel codes that can correct such errors. In…
In this paper, we assume an error such that a single insertion occurs and then a single deletion occurs. Under such an error model, this paper provides a decoding algorithm for non-binary quantum codes constructed by Matsumoto and Hagiwara.
Despite their growing capabilities, language models still frequently reproduce content from their training data, generate repetitive text, and favor common grammatical patterns and vocabulary. A possible cause is the decoding strategy: the…
As the global need for large-scale data storage is rising exponentially, existing storage technologies are approaching their theoretical and functional limits in terms of density and energy consumption, making DNA based storage a potential…
The performance of ``typical set (pairs) decoding'' for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding, error happens when the information transmission is corrupted by an untypical noise or…
Channels with synchronization errors, such as deletion and insertion errors, are crucial in DNA storage, data reconstruction, and other applications. These errors introduce memory to the channel, complicating its capacity analysis. This…