The Replica-Symmetric Prediction for Random Linear Estimation With Gaussian Matrices Is Exact
The Replica-Symmetric Prediction for Random Linear Estimation With Gaussian Matrices Is Exact
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DOI：
10.1109/tit.2019.2891664
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发表时间：
2019-04-01
影响因子：
2.5
通讯作者：
Pfister, Henry D.
中科院分区：
文献类型：
--
作者：
Reeves, Galen;Pfister, Henry D.
本文考虑了I.I.D的随机线性估计的基本限制。信号分布和I.I.D.高斯测量矩阵。它的主要贡献是在这种情况下对渐近互信息（MI）和最小均方误差（MMSE）的严格表征。在轻度的技术条件下，我们的结果表明，限制MI和MMSE等于统计物理学的复制方法预测的值。这解决了一个众所周知的问题，该问题已经开放了十多年。
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.