Related papers: Near-Optimal Noisy Group Testing via Separate Deco…
In Group Synchronization, one attempts to find a collection of unknown group elements from noisy measurements of their pairwise differences. Several important problems in vision and data analysis reduce to group synchronization over various…
The rapid development of derandomization theory, which is a fundamental area in theoretical computer science, has recently led to many surprising applications outside its initial intention. We will review some recent such developments…
We study the large-coalition asymptotics of fingerprinting and group testing, and derive explicit decoders that provably achieve capacity for many of the considered models. We do this both for simple decoders (fast but suboptimal) and for…
The group testing problem is concerned with identifying a small number $k \sim n^\theta$ for $\theta \in (0,1)$ of infected individuals in a large population of size $n$. At our disposal is a testing procedure that allows us to test groups…
In query learning, the goal is to identify an unknown object while minimizing the number of "yes or no" questions (queries) posed about that object. We consider three extensions of this fundamental problem that are motivated by practical…
In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn $x=(x_1,\ldots,x_n) \in \{0,1\}^n$ from a stream of random linear equations over $\mathrm{F}_2$ that are correct with…
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…
Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of…
We consider the quantum decoding problem. It consists in recovering a codeword given a superposition of noisy versions of this codeword. By measuring the superposition, we get back to the classical decoding problem. It appears for the first…
We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease within a population of size n, based on the outcomes of pooled tests which return positive whenever there is at least…
A novel and efficient neural decoder algorithm is proposed. The proposed decoder is based on the neural Belief Propagation algorithm and the Automorphism Group. By combining neural belief propagation with permutations from the Automorphism…
We study a correlated group testing model where items are infected according to a Markov chain, which creates bursty binfection patterns. Focusing on a very sparse infections regime, we propose a non adaptive testing strategy with an…
We study group-testing algorithms for resolving broadcast conflicts on a multiple access channel (MAC) and for identifying the dead sensors in a mobile ad hoc wireless network. In group-testing algorithms, we are asked to identify all the…
We explore the problem of deriving a posteriori probabilities of being defective for the members of a population in the non-adaptive group testing framework. Both noiseless and noisy testing models are addressed. The technique, which relies…
Let $1 \le s < t$, $N \ge 1$ be integers and a complex electronic circuit of size $t$ is said to be an $s$-active, $\; s \ll t$, and can work as a system block if not more than $s$ elements of the circuit are defective. Otherwise, the…
We consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the…
Noise is an important factor that influences the reliability of information acquisition, transmission, processing, and storage. In order to suppress the inevitable noise effects, a fault-tolerant information processing approach via quantum…
This article presents an algorithm for reducing measurement uncertainty of one physical quantity when given oversampled measurements of two physical quantities with correlated noise. The algorithm assumes that the aleatoric measurement…
We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase…
We consider adaptive group testing in the linear regime, where the number of defective items scales linearly with the number of items. We analyse an algorithm based on generalized binary splitting. Provided fewer than half the items are…