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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>γ</sup> for an arbitrarily small constant γ > 0. Our extractor is obtained by composing seeded extractors in simple ways. We… (More)

A construction of Bourgain [Bou05] gave the first 2-source extractor to break the min-entropy rate 1/2 barrier. In this note, we write an exposition of his result, giving a high level way to view his extractor construction. We also include a proof of a generalization of Vazirani's XOR lemma that seems interesting in its own right, and an argument (due to… (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 describe new ways to simulate 2-party communication protocols to get protocols with potentially smaller communication. We show that every communication protocol that communicates C bits and reveals I bits of information about the inputs to the participating parties can be simulated by a new protocol involving at most ~O(√CI) bits of communication.… (More)

We show that it is possible to encode any communication protocol between two parties so that the protocol succeeds even if a (1/4-ε) fraction of all symbols transmitted by the parties are corrupted adversarially, at a cost of increasing the communication in the protocol by a constant factor (the constant depends on epsilon). This encoding uses a… (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 δ>0, we can extract .99 δ 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)

- Peter Chin, Anup Rao, Van H. Vu
- ArXiv
- 2015

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)