New proof of Shannon's entropy power inequality

Event Detail

Event type: Colloquium
Date/Time: 11/30/2009-14:00   
Location: Kidd 364

Speaker info

Speaker: Mark Kelbert, Swansea University

Abstract:
This talk addresses the issue of the proof of the entropy power inequality, an important tool in the analysis of Gaussian channels of information transmission, proposed by Shannon. This inequality has many relations with different problems in geometry, linear algebra, analysis, etc. We analyze continuity properties of the mutual entropy of the input and output signals in an additive memoryless channel and show how this can be used for a correct proof of the entropy-power inequality. To introduce the entropy power inequality, consider two independent random variables $X_1$ and $X_2$ taking values in $\R^d$, with probability density functions $f_{X_1}(x)$ and $f_{X_2}(x)$, respectively, where $x\in\R^d$. Let $h(X_i)$, $i=1,2$ stand for the differential entropies $$h(X_i)=-\int_{\R^d}f_{X_i}(x)\ln\;f_{X_i}(x){\rm d}x:= -\E\ln\;f_{X_i}(X_i),$$ and assume that $-\infty