Related papers: Sequence Reconstruction over the Deletion Channel
Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…
In the standard trace reconstruction problem, the goal is to \emph{exactly} reconstruct an unknown source string $\mathsf{x} \in \{0,1\}^n$ from independent "traces", which are copies of $\mathsf{x}$ that have been corrupted by a…
This paper considers a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit is added after it with probability i, or it is…
The ''trace reconstruction'' problem asks, given an unknown binary string $x$ and a channel that repeatedly returns ''traces'' of $x$ with each bit randomly deleted with some probability $p$, how many traces are needed to recover $x$? There…
\emph{Population recovery} is the problem of learning an unknown distribution over an unknown set of $n$-bit strings, given access to independent draws from the distribution that have been independently corrupted according to some noise…
Suppose a binary string x = x_1...x_n is being broadcast repeatedly over a faulty communication channel. Each time, the channel delivers a fixed number m of the digits (m<n) with the lost digits chosen uniformly at random, and the order of…
A permutation code is a nonlinear code whose codewords are permutation of a set of symbols. We consider the use of permutation code in the deletion channel, and consider the symbol-invariant error model, meaning that the values of the…
In this paper, we present a novel communication channel, called the absorption channel, inspired by information transmission in neurons. Our motivation comes from in-vivo nano-machines, emerging medical applications, and brain-machine…
The Damerau-Levenshtein distance between two sequences is the minimum number of operations (deletions, insertions, substitutions, and adjacent transpositions) required to convert one sequence into another. Notwithstanding a long history of…
The rapid development of DNA storage has brought the deletion and insertion channel, once again, to the front line of research. When the number of deletions is equal to the number of insertions, the Fixed Length Levenshtein (FLL) metric is…
The rapid development of DNA storage has brought the deletion and insertion channel to the front line of research. When the number of deletions is equal to the number of insertions, the Fixed Length Levenshtein (FLL) metric is the right…
We consider binary input deletion/substitution channels, which model certain types of synchronization errors encountered in practice. Specifically, we focus on the regime of small deletion and substitution probabilities, and by extending an…
Consider a length-$n$ sequence $\bm{x}$ over a $q$-ary alphabet. The \emph{fixed-length Levenshtein ball} $\mathcal{L}_t(\bm{x})$ of radius $t$ encompasses all length-$n$ $q$-ary sequences that can be derived from $\bm{x}$ by performing $t$…
We study the problem of retrieving data from a channel that breaks the input sequence into a set of unordered fragments of random lengths, which we refer to as the chop-and-shuffle channel. The length of each fragment follows a geometric…
In the usual trace reconstruction problem, the goal is to exactly reconstruct an unknown string of length $n$ after it passes through a deletion channel many times independently, producing a set of traces (i.e., random subsequences of the…
The construction of deletion codes for the Levenshtein metric is reduced to the construction of codes over the integers for the Manhattan metric by run length coding. The latter codes are constructed by expurgation of translates of…
In coding theory, handling errors that occur when symbols are inserted or deleted from a transmitted message is a long-standing challenge. Optimising redundancy for insertion and deletion channels remains a key open problem with significant…
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
In this paper, we investigate the reconstruction of permutations on {1, 2, ..., n} from betweenness constraints involving the minimum and the maximum element located between t and t+1, for all t=1, 2, ..., n-1. We propose two variants of…