Two Measures of Dependence

Two families of dependence measures between random variables are introduced. They are based on the R\'enyi divergence of order $\alpha$ and the relative $\alpha$-entropy, respectively, and both dependence measures reduce to Shannon's mutual information when their order $\alpha$ is one. The first measure shares many properties with the mutual information, including the data-processing inequality, and can be related to the optimal error exponents in composite hypothesis testing. The second measure does not satisfy the data-processing inequality, but appears naturally in the context of distributed task encoding.Comment: 40 pages; 1 figure; published in Entrop

On Multipath Fading Channels at High SNR

This paper studies the capacity of discrete-time multipath fading channels. It is assumed that the number of paths is finite, i.e., that the channel output is influenced by the present and by the L previous channel inputs. A noncoherent channel model is considered where neither transmitter nor receiver are cognizant of the fading's realization, but both are aware of its statistic. The focus is on capacity at high signal-to-noise ratios (SNR). In particular, the capacity pre-loglog - defined as the limiting ratio of the capacity to loglog SNR as SNR tends to infinity - is studied. It is shown that, irrespective of the number paths L, the capacity pre-loglog is 1.Comment: To be presented at the 2008 IEEE Symposium on Information Theory (ISIT), Toronto, Canada; replaced with version that appears in the proceeding