Related papers: Sequence-Subset Distance and Coding for Error Cont…
The nucleotide sequence representation of DNA can be inadequate for resolving protein-DNA binding sites and regulatory substrates, such as those involved in gene expression and horizontal gene transfer. Considering that sequence-like…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
One of the basic tasks in bioinformatics is localizing a short subsequence $S$, read while sequencing, in a long reference sequence $R$, like the human geneome. A natural rapid approach would be finding a hash value for $S$ and compare it…
In this paper motivated from subspace coding we introduce subspace-metric codes and subset-metric codes. These are coordinate-position independent pseudometrics and suitable for the folded codes. The half-Singleton upper bounds for linear…
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…
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…
We study the combination of two recent coding approaches, in the context of DNA based data storage. Composite DNA alphabets leverage properties of the DNA synthesis and sequencing process. A composite symbol does not represent a single…
We consider data transmission across discrete memoryless channels (DMCs) using variable-length codes with feedback. We consider the family of such codes whose rates are $\rho_N$ below the channel capacity $C$, where $\rho_N$ is a positive…
Nanopore sequencing, superior to other sequencing technologies for DNA storage in multiple aspects, has recently attracted considerable attention. Its high error rates, however, demand thorough research on practical and efficient coding…
The biochemical processes underlying DNA data storage, including synthesis, amplification, and sequencing, are inherently noisy. Consequently, base-level insertion, deletion, and substitution (IDS) errors, as well as sequence-level…
We introduce the notion of weakly mutually uncorrelated (WMU) sequences, motivated by applications in DNA-based data storage systems and for synchronization of communication devices. WMU sequences are characterized by the property that no…
Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of…
Reference-guided DNA sequencing and alignment is an important process in computational molecular biology. The amount of DNA data grows very fast, and many new genomes are waiting to be sequenced while millions of private genomes need to be…
Given a database of bit strings $A_1,\ldots,A_m\in \{0,1\}^n$, a fundamental data structure task is to estimate the distances between a given query $B\in \{0,1\}^n$ with all the strings in the database. In addition, one might further want…
Technologies for sequencing (reading) and synthesizing (writing) DNA have progressed on a Moore's law-like trajectory over the last three decades. This has motivated the idea of using DNA for data storage. Theoretically, DNA-based storage…
In this paper, fundamental limits in sequencing of a set of closely related DNA molecules are addressed. This problem is called pooled-DNA sequencing which encompasses many interesting problems such as haplotype phasing, metageomics, and…
This work is motivated by the problem of error correction in bit-shift channels with the so-called $ (d,k) $ input constraints (where successive $ 1 $'s are required to be separated by at least $ d $ and at most $ k $ zeros, $ 0 \leq d < k…
DNA is a promising medium for digital information storage for its exceptional density and durability. While prior studies advanced coding theory, workflow design, and simulation tools, challenges such as synthesis costs, sequencing errors,…
A mathematical algorithm to describe DNA or RNA sequences of $N$ nucleotides by a string of $2N$ integers numbers is presented in the framework of the so called crystal basis model of the genetic code. The description allows to define a not…