Related papers: Coded trace reconstruction
We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…
Peer-to-peer distributed storage systems provide reliable access to data through redundancy spread over nodes across the Internet. A key goal is to minimize the amount of bandwidth used to maintain that redundancy. Storing a file using an…
Recently, DNA storage has surfaced as a promising alternative for data storage, presenting notable benefits in terms of storage capacity, cost-effectiveness in maintenance, and the capability for parallel replication. Mathematically, the…
Synchronization errors, such as insertions and deletions, present a fundamental challenge in DNA-based data storage systems, arising from both synthesis and sequencing noise. These channels are often modeled as…
Distributed storage systems often introduce redundancy to increase reliability. When coding is used, the repair problem arises: if a node storing encoded information fails, in order to maintain the same level of reliability we need to…
In the \emph{trace reconstruction problem}, an unknown source string $x \in \{0,1\}^n$ is sent through a probabilistic \emph{deletion channel} which independently deletes each bit with probability $\delta$ and concatenates the surviving…
This chapter deals with the topic of designing reliable and efficient codes for the storage and retrieval of large quantities of data over storage devices that are prone to failure. For long, the traditional objective has been one of…
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 achievable rates of nanopore-based DNA storage when nanopore signals are decoded using a tractable channel model that does not rely on a basecalling algorithm. Specifically, the noisy nanopore channel (NNC) with the…
DNA-based data storage has been attracting significant attention due to its extremely high data storage density, low power consumption, and long duration compared to conventional data storage media. Despite the recent advancements in DNA…
In this work, we investigate the problem of constructing codes capable of correcting two deletions. In particular, we construct a code that requires redundancy approximately 8 log n + O(log log n) bits of redundancy, where n is the length…
This work presents a theoretical analysis of the probability of successfully retrieving data encoded with MDS codes (e.g., Reed-Solomon codes) in DNA storage systems. We study this probability under independent and identically distributed…
In the emerging field of DNA storage, data is encoded as DNA sequences and stored. The data is read out again by sequencing the stored DNA. Nanopore sequencing is a new sequencing technology that has many advantages over other methods; in…
The efficiency of a code is estimated by its redundancy $R$, while the complexity of a code is estimated by its average delay $\bar N$. In this work we construct word-based codes, for which $R \lesssim \bar N^{-5/3}$. Therefore, word-based…
DNA-based storage is an emerging technology that enables digital information to be archived in DNA molecules. This method enjoys major advantages over magnetic and optical storage solutions such as exceptional information density, enhanced…
Erasure codes are an integral part of many distributed storage systems aimed at Big Data, since they provide high fault-tolerance for low overheads. However, traditional erasure codes are inefficient on reading stored data in degraded…
Ever since deoxyribonucleic acid (DNA) was considered as a next-generation data-storage medium, lots of research efforts have been made to correct errors occurred during the synthesis, storage, and sequencing processes using error…
Owing to its several merits over other DNA sequencing technologies, nanopore sequencers hold an immense potential to revolutionize the efficiency of DNA storage systems. However, their higher error rates necessitate further research to…
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…
We consider the problem of constructing binary codes to recover from $k$-bit deletions with efficient encoding/decoding, for a fixed $k$. The single deletion case is well understood, with the Varshamov-Tenengolts-Levenshtein code from 1965…