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An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a…

Information Theory · Computer Science 2017-02-14 Andrew Knyazev , Akshay Gadde , Hassan Mansour , Dong Tian

Consider a source that produces independent copies of a triplet of jointly distributed random variables, $\{X_{i},Y_{i},Z_{i}\}_{i=1}^{\infty}$. The process $\{X_{i}\}$ is observed at the encoder, and is supposed to be reproduced at two…

Information Theory · Computer Science 2008-12-18 Alina Maor , Neri Merhav

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…

Data Structures and Algorithms · Computer Science 2025-12-03 Arnav Burudgunte , Paul Valiant , Hongao Wang

We revisit the problem of broadcasting on $d$-ary trees: starting from a Bernoulli$(1/2)$ random variable $X_0$ at a root vertex, each vertex forwards its value across binary symmetric channels $\mathrm{BSC}_\delta$ to $d$ descendants. The…

Information Theory · Computer Science 2020-05-19 Yuzhou Gu , Hajir Roozbehani , Yury Polyanskiy

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 $,…

Information Theory · Computer Science 2021-01-13 Umberto Martínez-Peñas

Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion…

Information Theory · Computer Science 2020-06-01 Sundara Rajan Srinivasavaradhan , Michelle Du , Suhas Diggavi , Christina Fragouli

The $k$-mismatch problem consists in computing the Hamming distance between a pattern $P$ of length $m$ and every length-$m$ substring of a text $T$ of length $n$, if this distance is no more than $k$. In many real-world applications, any…

Embedding graphs in a geographical or latent space, i.e.\ inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We…

Computational Geometry · Computer Science 2022-05-18 Varsha Dani , Josep Díaz , Thomas P. Hayes , Cristopher Moore

In distance query reconstruction, we wish to reconstruct the edge set of a hidden graph by asking as few distance queries as possible to an oracle. Given two vertices $u$ and $v$, the oracle returns the shortest path distance between $u$…

Data Structures and Algorithms · Computer Science 2024-10-17 Paul Bastide , Carla Groenland

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…

Information Theory · Computer Science 2025-04-21 Ville Junnila , Tero Laihonen , Tuomo Lehtilä

We derive exact reconstruction methods for cracks consisting of unions of Lipschitz hypersurfaces in the context of Calder\'on's inverse conductivity problem. Our first method obtains upper bounds for the unknown cracks, bounds that can be…

Analysis of PDEs · Mathematics 2024-05-24 Henrik Garde , Michael Vogelius

Cayley graph techniques are introduced for the problem of constructing networks having the maximum possible number of nodes, among networks that satisfy prescribed bounds on the parameters maximum node degree and broadcast diameter. The…

Combinatorics · Mathematics 2009-09-25 Michael J. Dinneen , Vance Faber , Michael R. Fellows

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…

Data Structures and Algorithms · Computer Science 2014-12-15 Irena Rusu

For the emerging Internet of Things (IoT), one of the most critical problems is the real-time reconstruction of signals from a set of aged measurements. During the reconstruction, distortion occurs between the observed signal and the…

Information Theory · Computer Science 2019-01-25 Meng Wang , Wei Chen , Anthony Ephremides

Sampling is classically performed by recording the amplitude of an input signal at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the…

Signal Processing · Electrical Eng. & Systems 2020-04-22 Karen Adam , Adam Scholefield , Martin Vetterli

The broadcast phase (downlink transmission) of the two-way relay network is studied in the source coding and joint source-channel coding settings. The rates needed for reliable communication are characterised for a number of special cases…

Information Theory · Computer Science 2010-11-23 Roy Timo , Alex Grant , Gerhard Kramer

We introduce a new distance-based phylogeny reconstruction technique which provably achieves, at sufficiently short branch lengths, a polylogarithmic sequence-length requirement -- improving significantly over previous polynomial bounds for…

Probability · Mathematics 2011-09-30 Sebastien Roch

In this paper, we consider a broadcasting process in which information is propagated from a given root node on a noisy tree network, and answer the question that whether the symbols at the nth level of the tree contain non-vanishing…

Probability · Mathematics 2019-02-20 Wenjian Liu , Ning Ning

We study the problem of reconstructing an unknown point in $\mathbb{R}^d$ from approximate linear queries. This setting arises naturally in applications ranging from low-dimensional remote sensing and signal recovery to high-dimensional…

Machine Learning · Computer Science 2026-05-20 Yuval Filmus , Shay Moran , Elizaveta Nesterova

We consider the `one-shot frame synchronization problem' where a decoder wants to locate a sync pattern at the output of a channel on the basis of sequential observations. We assume that the sync pattern of length N starts being emitted at…

Information Theory · Computer Science 2007-08-23 Venkat Chandar , Aslan Tchamkerten , Gregory Wornell