**Papers Published**

- Reeves, G; Pfister, HD,
*The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact*, IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August (August, 2016), pp. 665-669, ISBN 9781509018062

(last updated on 2017/12/14)**Abstract:**

© 2016 IEEE. This paper considers the fundamental limit of compressed sensing for i.i.d. signal distributions and i.i.d. Gaussian measurement matrices. Its main contribution is a rigorous characterization of the asymptotic mutual information (MI) and minimum mean-square error (MMSE) in this setting. Under mild technical conditions, our results show that the limiting MI and MMSE are equal to the values predicted by the replica method from statistical physics. This resolves a well-known problem that has remained open for over a decade.