The Replica-Symmetric Prediction for Random Linear Estimation With Gaussian Matrices Is Exact


Journal Article

© 2019 IEEE. This paper considers the fundamental limit of random linear estimation 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.

Full Text

Duke Authors

Cited Authors

  • Reeves, G; Pfister, HD

Published Date

  • April 1, 2019

Published In

Volume / Issue

  • 65 / 4

Start / End Page

  • 2252 - 2283

International Standard Serial Number (ISSN)

  • 0018-9448

Digital Object Identifier (DOI)

  • 10.1109/TIT.2019.2891664

Citation Source

  • Scopus