Related papers: Probabilistic bounds on the trapping redundancy of…
The Lovasz Local Lemma is a seminal result in probabilistic combinatorics. It gives a sufficient condition on a probability space and a collection of events for the existence of an outcome that simultaneously avoids all of those events.…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
"The Price of Robustness" by Bertsimas and Sim represented a breakthrough in the development of a tractable robust counterpart of Linear Programming Problems. However, the central modeling assumption that the deviation band of each…
In this paper, lower bounds on the probability of a finite union of events are considered, i.e. $P\left(\bigcup_{i=1}^N A_i\right)$, in terms of the individual event probabilities $\{P(A_i), i=1,\ldots,N\}$ and the sums of the pairwise…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
Weak superimposed codes are combinatorial structures related closely to generalized cover-free families, superimposed codes, and disjunct matrices in that they are only required to satisfy similar but less stringent conditions. This class…
We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern; and transposing their…
In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear function approximation for policy evaluation in discounted Markov decision processes. We show that a simple…
The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where…
The Lov\'{a}sz Local Lemma (LLL) is a powerful tool in probabilistic combinatorics which can be used to establish the existence of objects that satisfy certain properties. The breakthrough paper of Moser and Tardos and follow-up works…
We consider questions related to the computation of the capacity of codes that avoid forbidden difference patterns. The maximal number of $n$-bit sequences whose pairwise differences do not contain some given forbidden difference patterns…
A robust positioning pattern is a large array that allows a mobile device to locate its position by reading a possibly corrupted small window around it. In this paper, we provide constructions of binary positioning patterns, equipped with…
In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices $W_{t,n,k}$, representing $t$-element subsets versus $k$-element subsets of an $n$-element set. We provide…
As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $\epsilon$-accurate…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
A locally recoverable code (LRC code) is a code over a finite alphabet such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set. Bounds on the rate and distance of such codes have…
The Ku\v{c}era-G\'acs theorem is a landmark result in algorithmic randomness asserting that every real is computable from a Martin-L\"of random real. If the computation of the first $n$ bits of a sequence requires $n+h(n)$ bits of the…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as…