Related papers: Extractors for Sum of Two Sources

We put forth a new computational notion of entropy, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator. Specifically, the i'th output block of a generator G has accessible entropy at…

Ailon et al. (SICOMP 2011) proposed a self-improving sorter that tunes its performance to an unknown input distribution in a training phase. The input numbers $x_1,x_2,\ldots,x_n$ come from a product distribution, that is, each $x_i$ is…

This paper reports, by way of introduction, on the advances made by our group and the broader signal processing community on the concept of sample abundance; a phenomenon that naturally arises in one-bit and few-bit signal processing…

Given two discrete random variables $X$ and $Y$, with probability distributions ${\bf p} =(p_1, \ldots , p_n)$ and ${\bf q}=(q_1, \ldots , q_m)$, respectively, denote by ${\cal C}({\bf p}, {\bf q})$ the set of all couplings of ${\bf p}$ and…

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…

In this paper, the authors provide a weak decoding version of the traditional source coding theorem of Claude Shannon. The central bound that is obtained is \[ \chi>\log_{\epsilon}(2^{-n(H(X)+\epsilon)}) \] where \[…

In this paper, we investigate the redundancy of universal coding schemes on smooth parametric sources in the finite-length regime. We derive an upper bound on the probability of the event that a sequence of length $n$, chosen using…

We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…

This paper considers the problem of lossy compression for the computation of a function of two correlated sources, both of which are observed at the encoder. Due to presence of observation costs, the encoder is allowed to observe only…

In the semi-streaming model, an algorithm must process any $n$-vertex graph by making one or few passes over a stream of its edges, use $O(n \cdot \text{polylog }n)$ words of space, and at the end of the last pass, output a solution to the…

In the era of big data, integrating multi-source functional data to extract a subspace that captures the shared subspace across sources has attracted considerable attention. In practice, data collection procedures often follow…

A blind source separation method is described to extract sources from data mixtures where the underlying sources are assumed to be sparse and uncorrelated. The approach used is to detect and analyse segments of time where one source exists…

We develop two generalizations of contraction theory, namely, semi-contraction and weak-contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix…

There is an extensive set of methods to determine sparse sources from mixtures where the mixing coefficients are unknown. Each method involves plotting N sets of mixed data against each other in N-dimensional space. In the approach adopted…

The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress…

We derive a lower bound on the smallest output entropy that can be achieved via vector quantization of a $d$-dimensional source with given expected $r$th-power distortion. Specialized to the one-dimensional case, and in the limit of…

Real-world datasets often contain outliers, and the presence of outliers can make the clustering problems to be much more challenging. In this paper, we propose a simple uniform sampling framework for solving three representative…

This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution…

We present algorithms for generating small random samples without replacement. We consider two cases. We present an algorithm for sampling a pair of distinct integers, and an algorithm for sampling a triple of distinct integers. The…

We study the network coding problem of sum-networks with 3 sources and n terminals (3s/nt sum-network), for an arbitrary positive integer n, and derive a sufficient and necessary condition for the solvability of a family of so-called…