Related papers: Sequence-Subset Distance and Coding for Error Cont…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Encoding information in combinations of pre-synthesised deoxyribonucleic acid (DNA) strands (referred to as motifs) is an interesting approach to DNA storage that could potentially circumvent the prohibitive costs of…
Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes (thus of highest information rate) with minimum sum-rank distance at least $ 3 $ (thus one-error-correcting) for a fixed redundancy $ r $,…
In modern age, the increasing complexity of computation and communication technology is leading us towards the necessity of new paradigm. As a result, unconventional approach like DNA coding theory is gaining considerable attention. The…
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
V. Levenshtein first proposed the sequence reconstruction problem in 2001. This problem studies the model where the same sequence from some set is transmitted over multiple channels, and the decoder receives the different outputs. Assume…
The exponentially increasing demand for data storage has been facing more and more challenges during the past years. The energy costs that it represents are also increasing, and the availability of the storage hardware is not able to follow…
DNA codes have garnered significant interest due to their utilization in digital media storage, cryptography, and DNA computing. In this paper, we first extend the results of constructing reversible group codes \cite{Cengellenmis} and…
The shotgun sequencing process involves fragmenting a long DNA sequence (input string) into numerous shorter, unordered, and overlapping segments (referred to as \emph{reads}). The reads are sequenced, and later aligned to reconstruct the…
Sequencing a DNA strand, as part of the read process in DNA storage, produces multiple noisy copies which can be combined to produce better estimates of the original strand; this is called trace reconstruction. One can reduce the error rate…
When an individual's DNA is sequenced, sensitive medical information becomes available to the sequencing laboratory. A recently proposed way to hide an individual's genetic information is to mix in DNA samples of other individuals. We…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…
We present a computational method to evaluate the end-to-end and the contour length distribution functions of short DNA molecules described by a mesoscopic Hamiltonian. The method generates a large statistical ensemble of possible…
Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each…
This paper provides novel insights into channel and subspace codes in nonadaptive channel sensing with a single RF chain. Observing that this problem naturally maps to a noncoherent decoding problem, we show that the sensing performance of…
Heterogeneous Distributed Storage Systems (DSSs) are close to the real world applications for data storage. Each node of the considered DSS, may store different number of packets and each having different repair bandwidth with uniform…
Effective and reliable data retrieval is critical for the feasibility of DNA storage, and the development of random access efficiency plays a key role in its practicality and reliability. In this paper, we study the Random Access Problem,…
The central problem in sequence reconstruction is to find the minimum number of distinct channel outputs required to uniquely reconstruct the transmitted sequence. According to Levenshtein's work in 2001, this number is determined by the…