Related papers: The sequence reconstruction problem for permutatio…
This paper provides lower bounds on the reconstruction error for transmission of two continuous correlated random vectors sent over both sum and parallel channels using the help of two causal feedback links from the decoder to the encoders…
The original Calder\'on problem consists in recovering the potential (or the conductivity) from the knowledge of the related Neumann to Dirichlet map (or Dirichlet to Neumann map). Here, we first perturb the medium by injecting small-scaled…
Codes over permutations under the infinity norm have been recently suggested as a coding scheme for correcting limited-magnitude errors in the rank modulation scheme. Given such a code, we show that a simple relabeling operation, which…
Distribution-preserving integrated sensing and communication with secure reconstruction is investigated in this paper. In addition to the distortion constraint, we impose another constraint on the distance between the reconstructed sequence…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
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…
In the trace reconstruction problem our goal is to learn an unknown string $x\in \{0,1\}^n$ given independent traces of $x$. A trace is obtained by independently deleting each bit of $x$ with some probability $\delta$ and concatenating the…
This paper studies the problem of encoding messages into sequences which can be uniquely recovered from some noisy observations about their substrings. The observed reads comprise consecutive substrings with some given minimum overlap. This…
We consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval…
A permutation array(or code) of length $n$ and distance $d$, denoted by $(n,d)$ PA, is a set of permutations $C$ from some fixed set of $n$ elements such that the Hamming distance between distinct members $\mathbf{x},\mathbf{y}\in C$ is at…
The interval count problem, a classical question in the study of interval orders, was introduced by Ronald Graham in the 1980s. This problem asks: given an interval order $P$, what is the minimum number of distinct interval lengths required…
The problem of super-resolution in general terms is to recuperate a finitely supported measure $\mu$ given finitely many of its coefficients $\hat{\mu}(k)$ with respect to some orthonormal system. The interesting case concerns situations,…
Two new constructions are presented for coils and snakes in the hypercube. Improvements are made on the best known results for snake-in-the-box coils of dimensions 9, 10 and 11, and for some other circuit codes of dimensions between 8 and…
Sequence classification has numerous applications in various fields. Despite extensive studies in the last decades, many challenges still exist, particularly in pattern-based methods. Existing pattern-based methods measure the…
We define sequence patterns of length $n$ and level $\ell$ to be equivalence classes of sequences that have $n$ elements from the set of $\ell$ integer symbols $\{1,2,\ldots,\ell\}$ with no restriction on repetition, where the equivalence…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
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…
We address the problem of estimating time and frequency shifts of a known waveform in the presence of multiple measurement vectors (MMVs). This problem naturally arises in radar imaging and wireless communications. Specifically, a signal…
Let $\mathcal{Q}$ be a vertex subset problem on graphs. In a reconfiguration variant of $\mathcal{Q}$ we are given a graph $G$ and two feasible solutions $S_s, S_t\subseteq V(G)$ of $\mathcal{Q}$ with $|S_s|=|S_t|=k$. The problem is to…
We consider the problem of storing and retrieving information from synthetic DNA media. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on their collection of substrings…