We prove the Courtade-Kumar conjecture, for certain classes of n-dimensional Boolean functions, ∀n ≥ 2 and for all values of the error probability of the binary symmetric channel, ∀0 ≤ p ≤ 1 2 . Let X = [X1 . . . Xn] be a vector of independent and identically distributed Bernoulli( 1 2 ) random variables, which are the input to a memoryless binary symmetric channel, with the error probability i...

We prove the Courtade-Kumar conjecture, which states that the mutual information between any Boolean function of an n-dimensional vector of independent and identically distributed inputs to a memoryless binary symmetric channel and the corresponding vector of outputs is upper-bounded by 1 − H(p), where H(p) represents the binary entropy function. That is, let X = [X1 . . . Xn] be a vector of in...

We consider a binary symmetric channel where the input, modeled as an innnite sequence of bits, is distorted by a Bernoulli noise. In 8], a consistent estimator of the distortion, i.e., of the probability that a single bit is changed, is described under the basic assumption that the complexity of the input is nite. Here, we deal with two shortcomings: 1. Simons' estimator requires some informat...

Abstract We develop a method for generating pseudorandom binary sequences using the Bernoulli map on cubic algebraic integers. The distinguishing characteristic of our generator is that it generates chaotic true orbits of the Bernoulli map by exact computation. In particular, we clarify a way to properly prepare a set of initial points (i.e., seeds), which is needed when generating multiple pse...

At time 0, start a time-continuous binary branching process, where particles give birth to a single particle independently (at a possibly time-dependent rate) and die independently (at a possibly time-dependent and age-dependent rate). A particular case is the classical birth–death process. Stop this process at time T > 0. It is known that the tree spanned by the N tips alive at time T of the t...

We consider a type of long-range percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word appears within an iid Bernoulli sequence at locations that satisfy certain constraints. We settle the issue in some cases, and provide partial results in ot...

Mixture modelling of class-conditional densities is a standard pattern recognition technique. Although most research on mixture models has concentrated on mixtures for continuous data, emerging pattern recognition applications demand extending research e/orts to other data types. This paper focuses on the application of mixtures of multivariate Bernoulli distributions to binary data. More concr...

a single server queue with bernoulli vacation has been considered. in addition the admission to queue is based on a bernoulli process and the server gives two type of services. for this model the probability generating function for the number of customers in the queue at different server's state are obtained using supplementary variable technique. some performance measures are calculated. ...

We consider a binary-symmetric channel where the input, modeled as an infinite sequence of bits, is distorted by a Bernoulli noise. In [8], a consistent estimator of the distortion, i.e., of the probability that a single bit is changed, is described under the basic assumption that the complexity of the input is finite. Here, we deal with two shortcomings: 1) Simons’ estimator requires some info...

We study iterations of the Bernoulli measure under nearest-neighbour asynchronous binary cellular automata (CA) with a single transition. For these CA, we show that a coarse-level description of the orbit of the Bernoulli measure can be obtained, that is, one can explicitly compute measures of short cylinder sets after arbitrary number of iterations of the CA. In particular, we give expressions...