The mutual information in random linear estimation
The mutual information in random linear estimation
复制标题
随机线性估计中的互信息
DOI：
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复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Florent Krzakala
中科院分区：
文献类型：
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作者：
Jean Barbier;M. Dia;N. Macris;Florent Krzakala
我们考虑根据信号的噪声线性随机高斯投影的知识来估计信号，这是与压缩感知、稀疏叠加码或码分多址相关的问题，仅举几例。利用统计物理中的启发式复制方法来研究这一问题的互信息已经有了许多工作。在这里，我们将这些考虑放在坚实而严格的基础上。首先，我们利用Guera-型内插证明了复制公式给出了精确互信息的一个上界。其次，对于许多相关的实际情况，我们利用空间耦合、状态演化分析和I-MMSE定理给出了一个逆下界。这特别地产生了用于互信息的单个字母公式和用于所有离散有界信号的随机高斯线性估计的最小均方误差。
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections, a problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has been a number of works considering the mutual information for this problem using the heuristic replica method from statistical physics. Here we put these considerations on a firm rigorous basis. First, we show, using a Guerra-type interpolation, that the replica formula yields an upper bound to the exact mutual information. Secondly, for many relevant practical cases, we present a converse lower bound via a method that uses spatial coupling, state evolution analysis and the I-MMSE theorem. This yields, in particular, a single letter formula for the mutual information and the minimal-mean-square error for random Gaussian linear estimation of all discrete bounded signals.
影响因子：
2.5
作者：
Rush, Cynthia;Greig, Adam;Venkataramanan, Ramji
通讯作者：
Venkataramanan, Ramji