Limits on Support Recovery of Sparse Signals via Multiple-Access Communication Techniques

In this paper, we consider the problem of exact support recovery of sparse signals via noisy linear measurements. The main focus is finding the sufficient and necessary condition on the number of measurements for support recovery to be reliable. By drawing an analogy between the problem of support recovery and the problem of channel coding over the Gaussian multiple-access channel (MAC), and exploiting mathematical tools developed for the latter problem, we obtain an information-theoretic framework for analyzing the performance limits of support recovery. Specifically, when the number of nonzero entries of the sparse signal is held fixed, the exact asymptotics on the number of measurements sufficient and necessary for support recovery is characterized. In addition, we show that the proposed methodology can deal with a variety of models of sparse signal recovery, hence demonstrating its potential as an effective analytical tool.