Related papers: Efficiently Extracting Randomness from Imperfect S…
We study the problem of extracting random bits from weak sources that are sampled by algorithms with limited memory. This model of small-space sources was introduced by Kamp, Rao, Vadhan and Zuckerman (STOC'06), and falls into a line of…
The problem of exactly generating a general random process (target process) by using another general random process (coin process) is studied. The performance of the interval algorithm, introduced by Han and Hoshi, is analyzed from the…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
Randomness extraction is an essential post-processing step in practical quantum cryptography systems. When statistical fluctuations are taken into consideration, the requirement of large input data size could heavily penalise the speed and…
Suppose we have a memory storing $0$s and $1$s and we want to estimate the frequency of $1$s by sampling. We want to do this I/O-efficiently, exploiting that each read gives a block of $B$ bits at unit cost; not just one bit. If the input…
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…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
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…
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…
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 paper, we analyze several critical issues in semi-device independent quantum information processing protocol. In practical experimental realization randomness generation in that scenario is possible only if the efficiency of the…
With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources…
It is a well-known fact in classical information theory that no deterministic procedure can extract close-to-ideal randomness from an arbitrary entropy source. On the other hand, if additional knowledge about the source is available --…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
A device-independent randomness expansion protocol aims to take an initial random seed and generate a longer one without relying on details of how the devices operate for security. A large amount of work to date has focussed on a particular…
Non-deterministic random bits are needed in many scientific fields. Unfortunately today's computers are very limited in ability to produce them. We present here a method for extraction of non-deterministic random bits from random physics…
We study the problem of generating a random variate $X$ from a finite discrete probability distribution $P$ using an entropy source of independent fair coin flips. A classic result from Knuth and Yao shows that the optimal expected number…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
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…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…