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In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of \cite{ballentine2019codes,sasidharan2015codes} with an algebraic number theoretical approach that…
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…
In recent years, the rise of AI-assisted code-generation tools has significantly transformed software development. While code generators have mainly been used to support conventional software development, their use will be extended to…
Solutions to network optimization problems have greatly benefited from developments in nonlinear analysis, and, in particular, from developments in convex optimization. A key concept that has made convex and nonconvex analysis an important…
Most of the world's digital data is currently encoded in a sequential form, and compression methods for sequences have been studied extensively. However, there are many types of non-sequential data for which good compression techniques are…
In this paper, we establish a new bound tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a…
We generalized to higher dimensions the notions of optical orthogonal codes. We establish uper bounds on the capacity of general $ n $-dimensional OOCs, and on specific types of ideal codes (codes with zero off-peak autocorrelation). The…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
Subspace codes, and in particular cyclic subspace codes, have gained significant attention in recent years due to their applications in error correction for random network coding. In this paper, we introduce a new technique for constructing…
Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks…
Traditional asymptotic information-theoretic studies of the fundamental limits of wireless communication systems primarily rely on some ideal assumptions, such as infinite blocklength and vanishing error probability. While these assumptions…
We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…
We address the question of constructing explicitly quasi-uniform codes from groups. We determine the size of the codebook, the alphabet and the minimum distance as a function of the corresponding group, both for abelian and some nonabelian…
Consider the following information theoretic setup wherein independent codebooks of N correlated random variables are generated according to their respective marginals. The problem of determining the conditions on the rates of codebooks to…
We derived an asymptotic bound the accuracy of the estimation when we use the quantum correlation in the measuring apparatus. It is also proved that this bound can be achieved in any model in the quantum two-level system. Moreover, we show…
A kind of self-dual quasi-abelian codes of index $2$ over any finite field $F$ is introduced. By counting the number of such codes and the number of the codes of this kind whose relative minimum weights are small, such codes are proved to…
Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…
This paper presents a saddlepoint approximation of the random-coding union bound of Polyanskiy et al. for i.i.d. random coding over discrete memoryless channels. The approximation is single-letter, and can thus be computed efficiently.…
In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including…
The subblock energy-constrained codes (SECCs) and sliding window-constrained codes (SWCCs) have recently attracted attention due to various applications in communcation systems such as simultaneous energy and information transfer. In a…