The Replica-Symmetric Prediction for Random Linear Estimation With Gaussian Matrices Is Exact
Publication
, Journal Article
Reeves, G; Pfister, HD
Published in: IEEE Transactions on Information Theory
April 1, 2019
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.
Duke Scholars
Published In
IEEE Transactions on Information Theory
DOI
ISSN
0018-9448
Publication Date
April 1, 2019
Volume
65
Issue
4
Start / End Page
2252 / 2283
Related Subject Headings
- Networking & Telecommunications
- 4613 Theory of computation
- 4006 Communications engineering
- 1005 Communications Technologies
- 0906 Electrical and Electronic Engineering
- 0801 Artificial Intelligence and Image Processing
Citation
APA
Chicago
ICMJE
MLA
NLM
Reeves, G., & Pfister, H. D. (2019). The Replica-Symmetric Prediction for Random Linear Estimation With Gaussian Matrices Is Exact. IEEE Transactions on Information Theory, 65(4), 2252–2283. https://doi.org/10.1109/TIT.2019.2891664
Reeves, G., and H. D. Pfister. “The Replica-Symmetric Prediction for Random Linear Estimation With Gaussian Matrices Is Exact.” IEEE Transactions on Information Theory 65, no. 4 (April 1, 2019): 2252–83. https://doi.org/10.1109/TIT.2019.2891664.
Reeves G, Pfister HD. The Replica-Symmetric Prediction for Random Linear Estimation With Gaussian Matrices Is Exact. IEEE Transactions on Information Theory. 2019 Apr 1;65(4):2252–83.
Reeves, G., and H. D. Pfister. “The Replica-Symmetric Prediction for Random Linear Estimation With Gaussian Matrices Is Exact.” IEEE Transactions on Information Theory, vol. 65, no. 4, Apr. 2019, pp. 2252–83. Scopus, doi:10.1109/TIT.2019.2891664.
Reeves G, Pfister HD. The Replica-Symmetric Prediction for Random Linear Estimation With Gaussian Matrices Is Exact. IEEE Transactions on Information Theory. 2019 Apr 1;65(4):2252–2283.
Published In
IEEE Transactions on Information Theory
DOI
ISSN
0018-9448
Publication Date
April 1, 2019
Volume
65
Issue
4
Start / End Page
2252 / 2283
Related Subject Headings
- Networking & Telecommunications
- 4613 Theory of computation
- 4006 Communications engineering
- 1005 Communications Technologies
- 0906 Electrical and Electronic Engineering
- 0801 Artificial Intelligence and Image Processing