Related papers: Extractors for Sum of Two Sources
Let $P=(x_1,\ldots,x_n)$ be a population consisting of $n\ge 2$ real numbers whose sum is zero, and let $k <n$ be a positive integer. We sample $k$ elements from $P$ without replacement and denote by $X_P$ the sum of the elements in our…
The second-order achievable asymptotics in typical random number generation problems such as resolvability, intrinsic randomness, fixed-length source coding are considered. In these problems, several researchers have derived the first-order…
This paper investigates the general distributed lossless/lossy source coding formulated by Jana and Blahut. Their multi-letter rate-distortion region, an alternative to the region derived by Yang and Qin, is characterized by entropy…
The min-entropy is a widely used metric to quantify the randomness of generated random numbers in cryptographic applications; it measures the difficulty of guessing the most likely output. An important min-entropy estimator is the…
A general method of source coding over expansion is proposed in this paper, which enables one to reduce the problem of compressing an analog (continuous-valued source) to a set of much simpler problems, compressing discrete sources.…
The min-entropy is a widely used metric to quantify the randomness of generated random numbers, which measures the difficulty of guessing the most likely output. It is difficult to accurately estimate the min-entropy of a non-independent…
This paper investigates a unification of distributed source coding, multiple description coding, and source coding with side information at decoders. The equivalence between the multiple-decoder extension of distributed source coding with…
Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems. However, the theoretical support for its efficiency in these applications has been very limited. In this paper, we…
We reexamine the classical subset sum problem: given a set $X$ of $n$ positive integers and a number $t$, decide whether there exists a subset of $X$ that sums to $t$; or more generally, compute the set $\mbox{out}$ of all numbers…
Procedures based on current methods to detect sources in X-ray images are applied to simulated XMM images. All significant instrumental effects are taken into account, and two kinds of sources are considered -- unresolved sources…
Given positive integers $a_1,..., a_n, t$, the fixed weight subset sum problem is to find a subset of the $a_i$ that sum to $t$, where the subset has a prescribed number of elements. It is this problem that underlies the security of modern…
A reduction of a source distribution is a collection of smaller sized distributions that are collectively equivalent to the source distribution with respect to the property of decomposability. That is, an arbitrary language is decomposable…
Much recent research on information retrieval has focused on how to transfer from one task (typically with abundant supervised data) to various other tasks where supervision is limited, with the implicit assumption that it is possible to…
We present the problem of two-terminal source coding with Common Sum Reconstruction (CSR). Consider two terminals, each with access to one of two correlated sources. Both terminals want to reconstruct the sum of the two sources under some…
Integer-forcing source coding has been proposed as a low-complexity method for compression of distributed correlated Gaussian sources. In this scheme, each encoder quantizes its observation using the same fine lattice and reduces the result…
A well-known conjecture in analytic number theory states that for every pair of sets $X,Y\subset\mathbb{Z}/p\mathbb{Z}$, each of size at least $\log ^C p$ (for some constant $C$) we have that the number of pairs $(x,y)\in X\times Y$ such…
Consistent sampling is a technique for specifying, in small space, a subset $S$ of a potentially large universe $U$ such that the elements in $S$ satisfy a suitably chosen sampling condition. Given a subset $\mathcal{I}\subseteq U$ it…
Consider the set of source distributions within a fixed maximum relative entropy with respect to a given nominal distribution. Lossless source coding over this relative entropy ball can be approached in more than one way. A problem…
We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources, i.e., sources that emit one of two possible quantum states with given prior probabilities. Such a…
We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…