Uncertainty principles and signal recovery
SIAM Journal on Applied Mathematics
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
SIAM Journal on Discrete Mathematics
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Stable distributions, pseudorandom generators, embeddings, and data stream computation
Journal of the ACM (JACM)
Uncertainty principles, extractors, and explicit embeddings of l2 into l1
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Deterministic constructions of compressed sensing matrices
Journal of Complexity
Extracting Randomness Using Few Independent Sources
SIAM Journal on Computing
Explicit constructions for compressed sensing of sparse signals
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
IEEE Transactions on Information Theory - Part 1
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Euclidean Sections of $\ell_1^N$ with Sublinear Randomness and Error-Correction over the Reals
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Message passing algorithms and improved LP decoding
Proceedings of the forty-first annual ACM symposium on Theory of computing
Explicit construction of a small epsilon-net for linear threshold functions
Proceedings of the forty-first annual ACM symposium on Theory of computing
Efficient and robust compressed sensing using optimized expander graphs
IEEE Transactions on Information Theory
Dense error correction via l1-minimization
IEEE Transactions on Information Theory
A locality-sensitive hash for real vectors
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Improved fault tolerance and secure computation on sparse networks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Almost-Euclidean subspaces of l1Nvia tensor products: a simple approach to randomness reduction
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Explicit Construction of a Small $\epsilon$-Net for Linear Threshold Functions
SIAM Journal on Computing
Journal of the ACM (JACM)
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We give an explicit (in particular, deterministic polynomial time) construction of subspaces X ⊆ ℝN of dimension (1 - o(1))N such that for every x ∈ X, {display equation}. If we are allowed to use N1/log log N ≤ N°(1) random bits and dim(X) ≥ (1 - η)N for any fixed constant η, the lower bound can be further improved to (log N)-°(1) √N||x||2. Our construction makes use of unbalanced bipartite graphs to impose local linear constraints on vectors in the subspace, and our analysis relies on expansion properties of the graph. This is inspired by similar constructions of error-correcting codes.