Strong data processing inequalities in power-constrained Gaussian channels

Flavio P. Calmon, Yury Polyanskiy, Yihong Wu
2015 2015 IEEE International Symposium on Information Theory (ISIT)  
To be considered for an 2015 IEEE Jack Keil Wolf ISIT Student Paper Award." This work presents strong data processing results for the power-constrained additive Gaussian channel. Explicit bounds on the amount of decrease of mutual information under convolution with Gaussian noise are shown. The analysis leverages the connection between information and estimation (I-MMSE) and the following estimation-theoretic result of independent interest. It is proved that any random variable for which there
more » ... le for which there exists an almost optimal (in terms of the mean-squared error) linear estimator operating on the Gaussiancorrupted measurement must necessarily be almost Gaussian (in terms of the Kolmogorov-Smirnov distance).
doi:10.1109/isit.2015.7282918 dblp:conf/isit/CalmonP015 fatcat:vld6noskanai7a5jakzsakcvvu