Related papers: Improved Condensers for Chor-Goldreich Sources
We provide a unified method for constructing explicit distributions which are difficult for restricted models of computation to generate. Our constructions are based on a new notion of robust extractors, which are extractors that remain…
Compressed Counting (CC), based on maximally skewed stable random projections, was recently proposed for estimating the p-th frequency moments of data streams. The case p->1 is extremely useful for estimating Shannon entropy of data…
Shannon entropy is the shortest average codeword length a lossless compressor can achieve by encoding i.i.d. symbols. However, there are cases in which the objective is to minimize the \textit{exponential} average codeword length, i.e. when…
Pulsars exhibit signals with precise inter-arrival times that are on the order of milliseconds to seconds, depending on the individual pulsar. There are subtle variations in the timing of pulsar signals. We show that these variations can…
Randomized (dithered) quantization is a method capable of achieving white reconstruction error independent of the source. Dithered quantizers have traditionally been considered within their natural setting of uniform quantization. In this…
Several conjectures concern the lower bound for the differential entropy $H(X_t)$ of an $n$-dimensional random vector $X_t$ introduced by Costa. Cheng and Geng conjectured that $H(X_t)$ is completely monotone, that is, $C_1(m,n):…
A random variable $X$ is an $(n,k)$-zero-fixing source if for some subset $V\subseteq[n]$, $X$ is the uniform distribution on the strings $\{0,1\}^n$ that are zero on every coordinate outside of $V$. An $\epsilon$-extractor for…
Poulin, Tillich, and Ollivier discovered an important separation between the classical and quantum theories of convolutional coding, by proving that a quantum convolutional encoder cannot be both non-catastrophic and recursive.…
We describe a methodology and standard of proof for experimental claims of quantum random number generation (QRNG), analogous to well-established methods from precision measurement. For appropriately constructed physical implementations,…
We consider the problem of identifying the causal direction between two discrete random variables using observational data. Unlike previous work, we keep the most general functional model but make an assumption on the unobserved exogenous…
A general multi-terminal source code and a general multi-terminal channel code are presented. Constrained-random-number generators with sparse matrices, which are building blocks for the code construction, are used in the construction of…
How to generate provably true randomness with minimal assumptions? This question is important not only for the efficiency and the security of information processing, but also for understanding how extremely unpredictable events are possible…
Brakerski et. al [BCM+18] introduced the model of cryptographic testing of a single untrusted quantum device and gave a protocol for certifiable randomness generation. We use the leakage resilience properties of the Learning With Errors…
This article studies the fundamental problem of using i.i.d. coin tosses from an entropy source to efficiently generate random variables $X_i \sim P_i$ $(i \ge 1)$, where $(P_1, P_2, \dots)$ is a random sequence of rational discrete…
In this paper, we propose a source coding scheme that represents data from unknown distributions through frequency and support information. Existing encoding schemes often compress data by sacrificing computational efficiency or by assuming…
We consider the problem of extracting entropy by sparse transformations, namely functions with a small number of overall input-output dependencies. In contrast to previous works, we seek extractors for essentially all the entropy without…
We propose a new model of a weakly random source that admits randomness extraction. Our model of additive sources includes such natural sources as uniform distributions on arithmetic progressions (APs), generalized arithmetic progressions…
It is shown that an i.i.d. binary source sequence $X_1, \ldots, X_n$ can be losslessly compressed at any rate above entropy such that the individual decoding of any $X_i$ reveals \emph{no} information about the other bits $\{X_j : j \neq…
The Contrastive Divergence (CD) algorithm has achieved notable success in training energy-based models including Restricted Boltzmann Machines and played a key role in the emergence of deep learning. The idea of this algorithm is to…
As a fundamental phenomenon in nature, randomness has a wide range of applications in the fields of science and engineering. Among different types of random number generators (RNG), quantum random number generator (QRNG) is a kind of…