Related papers: On the Spread of Random Interleaver

We study almost sure separating and interpolating properties of random sequences in the polydisc and the unit ball. In the unit ball, we obtain the 0-1 Komolgorov law for a sequence to be interpolating almost surely for all the…

We provide a lower bound on the expected discovery time of one-way neighbor discovery in multi antenna system. We assume that the scheme allows to use different directional transmission probabilities, which result in different probability…

The effects of the odd-even constraint - as an interleaver design criterion - on the performance of rate-1/2 binary turbo codes are revisited. According to the current understanding, its adoption is favored because it makes the information…

We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…

A simple symmetric random walk is considered on a spider that is a collection of half lines (we call them legs) joined at the origin. We establish a strong approximation of this random walk by the so-called Brownian spider. Transition…

We derive two related novel bounds on single-variable marginal probability distributions in factor graphs with discrete variables. The first method propagates bounds over a subtree of the factor graph rooted in the variable, and the second…

We study the probability of two Brownian particles to meet before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance of the two particles using the Weierstrass…

The asymptotic normality of the maximum likelihood estimator (MLE) under regularity conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds on the distributional distance between the distribution of…

The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…

We provide new upper and lower bounds on the minimum possible ratio of the spectral and Frobenius norms of a (partially) symmetric tensor. In the particular case of general tensors our result recovers a known upper bound. For symmetric…

In this paper we study bounds for the total variation distance between two second degree polynomials in normal random variables provided that they essentially depend on at least three variables.

Let $s$ be a finite sequence over a field of length $n$. It is well-known that if $s$ satisfies a linear recurrence of order $d$ with non-zero constant term, then the reverse of $s$ also satisfies a recurrence of order $d$ (with…

We consider a regular $n$-ary tree of height $h$, for which every vertex except the root is labelled with an independent and identically distributed continuous random variable. Taking motivation from a question in evolutionary biology, we…

We derive a sphere-packing error exponent for coded transmission over discrete memoryless channels with a fixed decoding metric. By studying the error probability of the code over an auxiliary channel, we find a lower bound to the…

An intercalate in a Latin square is a $2\times2$ Latin subsquare. Let $N$ be the number of intercalates in a uniformly random $n\times n$ Latin square. We prove that asymptotically almost surely…

We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average cut size of a random two-forest. The main tool is an identity…

We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a…

We introduce and study the r-Lah distribution whose definition involves r-Stirling numbers of both kinds. We compute its expectation and variance, show its log-concavity and prove limit theorems for this distribution. We use these results…

Let G=(V,E) be an undirected loopless graph with possible parallel edges and s and t be two vertices of G. Assume that vertex s is labelled at the initial time step and that every labelled vertex copies its labelling to neighbouring…

We prove a new inequality bounding the probability that the random walk on a group has small total displacement in terms of the spectral and isoperimetric profiles of the group. This inequality implies that if the random walk on the group…