Related papers: Applications of Derandomization Theory in Coding
Most coding theorems in quantum Shannon theory can be proven using the decoupling technique: to send data through a channel, one guarantees that the environment gets no information about it; Uhlmann's theorem then ensures that the receiver…
Traditional wireless network design relies on optimization algorithms derived from domain-specific mathematical models, which are often inefficient and unsuitable for dynamic, real-time applications due to high complexity. Deep learning has…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
In the last few years the so--called "linear deterministic" model of relay channels has gained popularity as a means of studying the flow of information over wireless communication networks, and this approach generalizes the model of…
The use of a learnable codebook provides an efficient way for semantic communications to map vector-based high-dimensional semantic features onto discrete symbol representations required in digital communication systems. In this paper, the…
Rerandomization is a modern experimental design technique that repeatedly randomizes treatment assignments until covariates are deemed balanced between treatment groups. This enhances the precision and coherence of causal effect estimators,…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
This paper studies fixed-rate randomized vector quantization under the constraint that the quantizer's output has a given fixed probability distribution. A general representation of randomized quantizers that includes the common models in…
Randomized protocols are procedures that incorporate probabilistic choices during their execution and they play a central role in quantum algorithms, spanning Hamiltonian simulation, noise mitigation, and measurement tasks. In practical…
This paper considers the problem of decentralized analysis and control synthesis to verify and ensure properties like stability and dissipativity of a large-scale networked system comprised of linear subsystems interconnected in an…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…
We address the problem of optimizing the throughput of network coded traffic in mobile networks operating in challenging environments where connectivity is intermittent and locally available memory space is limited. Random linear network…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
The scheduling problem is a key class of optimization problems and has various kinds of applications both in practical and theoretical scenarios. In the scheduling problem, probabilistic analysis is a basic tool for investigating…
This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…