Related papers: Asymptotically Optimal Codes Correcting Fixed-Leng…
An indel refers to a single insertion or deletion, while an edit refers to a single insertion, deletion or substitution. In this paper, we investigate codes that combat either a single indel or a single edit and provide linear-time…
The problem of storing large amounts of information safely for a long period of time has become essential. One of the most promising new data storage mediums are the polymer-based data storage systems, like the DNA-storage system. These…
In this paper we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where a data set is represented by an unordered set of $M$ sequences, each of length $L$. Errors…
It has been widely observed that there exists a fundamental trade-off between the minimum (Hamming) distance properties and the iterative decoding convergence behavior of turbo-like codes. While capacity achieving code ensembles typically…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…
This paper introduces a new solution to DNA storage that integrates all three steps of retrieval, namely clustering, reconstruction, and error correction. DNA-correcting codes are presented as a unique solution to the problem of ensuring…
DNA synthesis is considered as one of the most expensive components in current DNA storage systems. In this paper, focusing on a common synthesis machine, which generates multiple DNA strands in parallel following a fixed supersequence,we…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
Consider two or more strings $\mathbf{x}^1,\mathbf{x}^2,\ldots,$ that are concatenated to form $\mathbf{x}=\langle \mathbf{x}^1,\mathbf{x}^2,\ldots \rangle$. Suppose that up to $\delta$ deletions occur in each of the concatenated strings.…
A family of high rate quantum error correcting codes adapted to the amplitude damping channel is presented. These codes are nonadditive and exploit self-complementarity structure to correct all first-order errors. Their rates can be higher…
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…
We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known…
The storage of large-scale quantum information at finite temperature requires an autonomous and reliable quantum hard drive, also known as a self-correcting quantum memory. It is a long-standing open problem to find a self-correcting…
We study error-correcting codes for permutations under the infinity norm, motivated by a novel storage scheme for flash memories call rank modulation. In this scheme, a set of $n$ flash cells are combined to create a single virtual…
Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n, k, d] code having all-symbol (r, \delta})-locality, denoted as (r, {\delta})a, is considered optimal if it also meets the minimum…
Rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines. Modeling rank modulation involves construction of packings of the space of permutations equipped with…
This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…
Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation)…
DNA, with remarkable properties of high density, durability, and replicability, is one of the most appealing storage media. Emerging DNA storage technologies use composite DNA letters, where information is represented by probability…