Related papers: Applications of Derandomization Theory in Coding
The rapid development of derandomization theory, which is a fundamental area in theoretical computer science, has recently led to many surprising applications outside its initial intention. We will review some recent such developments…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
A variety of problems in distributed control involve a networked system of autonomous agents cooperating to carry out some complex task in a decentralized fashion, e.g., orienting a flock of drones, or aggregating data from a network of…
Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area most algorithms are randomized, and…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Derandomization is the process of taking a randomized algorithm and turning it into a deterministic algorithm, which has attracted great attention in classical computing. In quantum computing, it is challenging and intriguing to derandomize…
We present techniques for decreasing the error probability of randomized algorithms and for converting randomized algorithms to deterministic (non-uniform) algorithms. Unlike most existing techniques that involve repetition of the…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
We consider the problem of block-coded communication, where in each block, the channel law belongs to one of two disjoint sets. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to…
This paper studies the problem of mapping optimization in decentralized control problems. A global optimization algorithm is proposed based on the ideas of ``deterministic annealing" - a powerful non-convex optimization framework derived…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
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 consider the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a proper subset of the network edges. We model this problem via an adversarial noise, presenting a formal…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
We present a general control-theoretic framework for constructing and analyzing random decoupling schemes, applicable to quantum dynamical control of arbitrary finite-dimensional composite systems. The basic idea is to design the control…
One of the prominent current challenges in complexity theory is the attempt to prove lower bounds for $TC^0$, the class of constant-depth, polynomial-size circuits with majority gates. Relying on the results of Williams (2013), an appealing…
This paper studies the notion of computational entropy. Using techniques from convex optimization, we investigate the following problems: (a) Can we derandomize the computational entropy? More precisely, for the computational entropy, what…
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 study the problem of decoding classical information encoded on quantum states at the output of a quantum channel, with particular focus on increasing the communication rates towards the maximum allowed by Quantum Mechanics. After a brief…
In this paper, we investigate how constraints on the randomization in the encoding process affect the secrecy rates achievable over wiretap channels. In particular, we characterize the secrecy capacity with a rate-limited local source of…