相关论文: Common Randomness Generation from Sources with Cou…
The generation of random numbers via quantum processes is an efficient and reliable method to obtain true indeterministic random numbers that are of vital importance to cryptographic communication and large-scale computer modeling. However,…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
Secure random numbers are a fundamental element of many applications in science, statistics, cryptography and more in general in security protocols. We present a method that enables the generation of high-speed unpredictable random numbers…
A random phenomenon may have two sources of random variation: an unstable identity and a set of external variation-generating factors. When only a single source is active, two mutually exclusive extreme scenarios may ensue that result in…
The entanglement-assisted classical capacity of a quantum channel is known to provide the formal quantum generalization of Shannon's classical channel capacity theorem, in the sense that it admits a single-letter characterization in terms…
We show that estimating the complexity (mean and distribution) of the instances of a fixed size Constraint Satisfaction Problem (CSP) can be very hard. We deal with the main two aspects of the problem: defining a measure of complexity and…
Understanding the way in which random entities interact is of key interest in numerous scientific fields. This can range from a full characterization of the joint distribution to single scalar summary statistics. In this work we identify a…
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…
We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed…
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when…
We study the problem of generating a shared secret key between two terminals in a joint source-channel setup -- the sender communicates to the receiver over a discrete memoryless wiretap channel and additionally the terminals have access to…
The Shannon capacity of graphs, introduced by Shannon in 1956 to model zero-error communication, asks for determining the rate of growth of independent sets in strong powers of graphs. Much is still unknown about this parameter, for…
For any discrete probability distributions with bounded entropy, we can generate exactly a random variate using only a finite expected number of perfect coin flips. A perfect coin flip is the outcome of an unbiased Bernoulli random…
Shannon's entropy and other entropy-based concepts are derived from the new, more general concept of relative divergence of one "grading' function on a linearly ordered set from another such function. The definition of relative divergence…
Researchers have proposed formal definitions of quantitative information flow based on information theoretic notions such as the Shannon entropy, the min entropy, the guessing entropy, and channel capacity. This paper investigates the…
The aim of this work is to provide bounds connecting two probability measures of the same event using R\'enyi $\alpha$-Divergences and Sibson's $\alpha$-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence…
Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent…
Suppose Alice wishes to send messages to Bob through a communication channel C_1, but her transmissions also reach an eavesdropper Eve through another channel C_2. The goal is to design a coding scheme that makes it possible for Alice to…
One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$…
Consider the setting of sparse graphs on N vertices, where the vertices have distinct "names", which are strings of length O(log N) from a fixed finite alphabet. For many natural probability models, the entropy grows as cN log N for some…