Related papers: Nearly optimal codebooks based on generalized Jaco…
The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the…
The article contains a survey of our results on weakly commensurable arithmetic and general Zariski-dense subgroups, length-commensurable and isospectral locally symmetric spaces and of related problems in the theory of semi-simple agebraic…
In this article, we study the weak and strong Lefschetz of higher dimensional quotients and dimension 1 almost complete intersections. We then apply the obtained results to the study of the Jacobian algebra of hyperplane arrangements.
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
We frame the problem of selecting an optimal audio encoding scheme as a supervised learning task. Through uniform convergence theory, we guarantee approximately optimal codec selection while controlling for selection bias. We present…
We calculate the $k$-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for $k=1$ to derive a closed-form expression for eigenvalue density. For real matrices we…
An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…
We derive simplified sphere-packing and Gilbert--Varshamov bounds for codes in the sum-rank metric, which can be computed more efficiently than previous ones. They give rise to asymptotic bounds that cover the asymptotic setting that has…
In this paper, we investigate very general approximation kernels with special properties, called an approximate identity, and prove almost everywhere and norm convergence of these general methods, which consists of a class of summability…
Distributed Arithmetic Coding (DAC) is an effective implementation of Slepian-Wolf coding, especially for short data blocks. To research its properties, the concept of DAC codeword distribution along proper and wrong decoding paths has been…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
The min-sum approximation is widely used in the decoding of polar codes. Although it is a numerical approximation, hardly any penalties are incurred in practice. We give a theoretical justification for this. We consider the common case of a…
Constructions of optimal locally repairable codes (LRCs) in the case of $(r+1) \nmid n$ and over small finite fields were stated as open problems for LRCs in [I. Tamo \emph{et al.}, "Optimal locally repairable codes and connections to…
We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness…
Several new constructions of 3-dimensional optical orthogonal codes are presented here. In each case the codes have ideal autocorrelation $\mathbf{ \lambda_a=0} $, and in all but one case a cross correlation of $ \mathbf{\lambda_c=1} $. All…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
We develop a framework for obtaining linear programming bounds for spherical codes whose inner products belong to a prescribed subinterval $[\ell,s]$ of $[-1,1)$. An intricate relationship between Levenshtein-type upper bounds on…
Covering numbers are a powerful tool used in the development of approximation algorithms, randomized dimension reduction methods, smoothed complexity analysis, and others. In this paper we prove upper bounds on the covering number of…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
In classical coding theory, it is common to construct new codes via propagation rules. There are various propagation rules to construct classical block codes. However, propagation rules have not been extensively explored for constructions…