Related papers: Improved Condensers for Chor-Goldreich Sources
Random numbers play a crucial role in numerous scientific applications. Source-independent quantum random number generators (SI-QRNGs) can offer true randomness by leveraging the fundamental principles of quantum mechanics, eliminating the…
Randomness is one of the most important resources in modern information science, since encryption founds upon the trust in random numbers. Since it is impossible to prove if an existing random bit string is truly random, it is relevant that…
Goldreich suggested candidates of one-way functions and pseudorandom generators included in $\mathsf{NC}^0$. It is known that randomly generated Goldreich's generator using $(r-1)$-wise independent predicates with $n$ input variables and…
Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other…
Quantum random number generation is a technique to generate random numbers by extracting randomness from specific quantum processes. As for practical random number generators, they are required not only to have no information leakage but…
Given a sequence of $N$ independent sources $\mathbf{X}_1,\mathbf{X}_2,\dots,\mathbf{X}_N\sim\{0,1\}^n$, how many of them must be good (i.e., contain some min-entropy) in order to extract a uniformly random string? This question was first…
In this work, we establish lower-bounds against memory bounded algorithms for distinguishing between natural pairs of related distributions from samples that arrive in a streaming setting. In our first result, we show that any algorithm…
In 2005 Bourgain gave the first explicit construction of a two-source extractor family with min-entropy rate less than $1/2$. His approach combined Fourier analysis with innovative but inefficient tools from arithmetic combinatorics and…
We begin by presenting a simple lossy compressor operating at near-zero rate: The encoder merely describes the indices of the few maximal source components, while the decoder's reconstruction is a natural estimate of the source components…
We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…
Generating random bits from a source of biased coins (the biased is unknown) is a classical question that was originally studied by von Neumann. There are a number of known algorithms that have asymptotically optimal information efficiency,…
In this work we investigate the behavior of the minimal rate needed in order to guarantee a given probability that the distortion exceeds a prescribed threshold, at some fixed finite quantization block length. We show that the excess coding…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to…
The Shannon Noiseless coding theorem (the data-compression principle) asserts that for an information source with an alphabet $\mathcal X=\{0,\ldots ,\ell -1\}$ and an asymptotic equipartition property, one can reduce the number of stored…
We calculate an achievable secret key rate for quantum key distribution with a finite number of signals, by evaluating the min-entropy explicitly. The min-entropy can be expressed in terms of the guessing probability, which we calculate for…
It is known that if a 2-universal hash function $H$ is applied to elements of a {\em block source} $(X_1,...,X_T)$, where each item $X_i$ has enough min-entropy conditioned on the previous items, then the output distribution…
We consider finite blocklength lossy compression of information sources whose components are independent but non-identically distributed. Crucially, Gaussian sources with memory and quadratic distortion can be cast in this form. We show…
This paper addresses the design of linear and nonlinear stabilization procedures for high-order continuous Galerkin (CG) finite element discretizations of scalar conservation laws. We prove that the standard CG method is entropy…
In 1968, Witsenhausen introduced his famous counterexample where he showed that even in the simple linear quadratic static team decision problem, complex nonlinear decisions could outperform any given linear decision. This problem has…