Consider a Bernoulli-Gaussian complex n-vector whose components are X<inf>i</inf>B<inf>i</inf>, with B<inf>i</inf> ∼Bernoulli-q and X<inf>i</inf> ∼ CN(0; σ<sup>2</sup>), iid across i and mutually independent. This random q-sparse vector is multiplied by a random matrix U, and a randomly chosen subset of the components of average size np, p ∈ [0; 1], of the resulting vector is then observed in additive Gaussian noise. We extend the scope of conventional noisy compressive sampling models where U is typically the identity or a matrix with iid components, to allow U that satisfies a certain freeness condition, which encompasses Haar matrices and other unitarily invariant matrices. We use the replica method and the decoupling principle of Guo and Verdú, as well as a number of information theoretic bounds, to study the input-output mutual information and the support recovery error rate as n → ∞.
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- Publication year
2011
- Venue
IEEE International Symposium on Information Theory. Proceedings
- Publication date
2011-07-01
- Fields of study
Mathematics, Computer Science
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