Related papers: Solving underdetermined systems with error-correct…
Error correcting codes are a fundamental component in modern day communication systems, demanding extremely high throughput, ultra-reliability and low latency. Recent approaches using machine learning (ML) models as the decoders offer both…
In first-year programming courses it is often difficult to show students how an algorithm can be discovered. In this paper we present a program format that supports the development from specification to code in small and obvious steps; that…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random…
We abstract the essential aspects of network-error detecting and correcting codes to arrive at the definitions of matroidal error detecting networks and matroidal error correcting networks. An acyclic network (with arbitrary sink demands)…
This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
The authors proposed a general way to find particular solutions for overdetermined systems of PDEs previously, where the number of equations is greater than the number of unknown functions. In this paper, we propose an algorithm for finding…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
Neural metrics have achieved impressive correlation with human judgements in the evaluation of machine translation systems, but before we can safely optimise towards such metrics, we should be aware of (and ideally eliminate) biases toward…
A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the…
Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…
A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from the eigenstructure of the Fourier number theoretic transform.…
We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions.…
CUR matrix decomposition is a randomized algorithm that can efficiently compute the low rank approximation for a given rectangle matrix. One limitation with the existing CUR algorithms is that they require an access to the full matrix A for…
We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…
Efficient algorithms for the sparse solution of under-determined linear systems $Ax = b$ are known for matrices $A$ satisfying suitable assumptions like the restricted isometry property (RIP). Without such assumptions little is known and…
We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation system, neuroimaging, community detection, and multiway comparison applications. Here, we…
Divide-and-conquer is a central paradigm for the design of algorithms, through which some fundamental computational problems, such as sorting arrays and computing convex hulls, are solved in optimal time within $\Theta(n\log{n})$ in the…