Abstract
It has recently been shown that the derivative of the input-output mutual information of Gaussian noise channels with respect to the signal-to-noise ratio is equal to the minimum mean-square error. This paper considers general additive noise channels where the noise may not be Gaussian distributed. It is found that, for every fixed input distribution, the derivative of the mutual information with respect to the signal strength is equal to the correlation of two conditional mean estimates associated with the input and the noise respectively. Special versions of the result are given in the respective cases of additive exponentially distributed noise, Cauchy noise, Laplace noise, and Rayleigh noise. The previous result on Gaussian noise channels is also recovered as a special case.
| Original language | English (US) |
|---|---|
| Article number | 1523430 |
| Journal | IEEE International Symposium on Information Theory - Proceedings |
| Volume | 2005-January |
| DOIs | |
| State | Published - 2005 |
| Event | 2005 IEEE International Symposium on Information Theory, ISIT 05 - Adelaide, Australia Duration: Sep 4 2005 → Sep 9 2005 |
Funding
This work was supported in part by the U.S. National Science Foundation under Grant NCR-0074277; and through collaborative participation in the Communications and Networks Consortium sponsored by the U.S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.
ASJC Scopus subject areas
- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics