Learn More
We consider the problem of randomness extraction from independent sources. We construct an extractor that can extract from a constant number of independent sources of length n, each of which have min-entropy n<sup>&#947;</sup> for an arbitrarily small constant &#947; &gt; 0. Our extractor is obtained by composing seeded extractors in simple ways. We(More)
In a two player game, a referee asks two cooperating players (who are not allowed to communicate) questions sampled from some distribution and decides whether they win or not based on some predicate of the questions and their answers. The parallel repetition of the game is the game in which the referee samples n independent pairs of questions and sends(More)
We give polynomial time computable extractors for low-weight affince sources. A distribution is affine if it samples a random points from some unknown low dimensional subspace of F n 2. A distribution is low weight affine if the corresponding linear space has a basis of low-weight vectors. Low-weight affine sources are thus a generalization of the well(More)
We give polynomial-time, deterministic randomness extractors for sources generated in small space, where we model space s sources on (0,1)<sup>n</sup> as sources generated by width 2<sup>s</sup> branching programs: For every constant &#948;&gt;0, we can extract .99 &#948; n bits that are exponentially close to uniform (in variation distance) from space s(More)
We show how to efficiently simulate the sending of a message M to a receiver who has partial information about the message, so that the expected number of bits communicated in the simulation is close to the amount of additional information that the message reveals to the receiver. This is a generalization and strengthening of the Slepian-Wolf theorem, which(More)
In this paper, we present and analyze a simple and robust spectral algorithm for the stochastic block model with k blocks, for any k fixed. Our algorithm works with graphs having constant edge density, under an optimal condition on the gap between the density inside a block and the density between the blocks. As a co-product, we settle an open question(More)
The main result of this paper is an explicit disperser for two independent sources on n bits, each of entropy k=n<sup>o(1)</sup>. Put differently, setting N=2<sup>n</sup> and K=2<sup>k</sup>, we construct explicit N x N Boolean matrices for which no K x K submatrix is monochromatic. Viewed as adjacency matrices of bipartite graphs, this gives an explicit(More)