  A noisy underdetermined system of linear equations is considered in which a
sparse vector (a vector with a few nonzero elements) is subject to measurement.
The measurement matrix elements are drawn from a Gaussian distribution. We
study the information-theoretic constraints on exact support recovery of a
sparse vector from the measurement vector and matrix. We compute a tight,
sufficient condition that is applied to ergodic wide-sense stationary sparse
vectors. We compare our results with the existing bounds and recovery
conditions. Finally, we extend our results to approximately sparse signals.
