Conditional Rényi Entropy and the Relationships between Rényi Capacities

A Preferred Definition of Conditional Rényi Entropy

The Rényi entropy is a generalization of Shannon entropy to a one-parameter family of entropies. Tsallis entropy too is a generalization of Shannon entropy. The measure for Tsallis entropy is non-logarithmic. After the introduction of Shannon entropy , the conditional Shannon entropy was derived and its properties became known. Also, for Tsallis entropy, the conditional entropy was introduced a...

On the Conditional Rényi Entropy

Stefan Berens Conditional Rényi entropy

The introduction of the Rényi entropy allowed a generalization of the Shannon entropy and unified its notion with that of other entropies. However, so far there is no generally accepted conditional version of the Rényi entropy corresponding to the one of the Shannon entropy. Different definitions proposed so far in the literature lacked central and natural properties one way or another. In this...

Smooth Entropy and Rényi Entropy

The notion of smooth entropy allows a unifying, generalized formulation of privacy ampli-cation and entropy smoothing. Smooth entropy is a measure for the number of almost uniform random bits that can be extracted from a random source by probabilistic algorithms. It is known that the R enyi entropy of order at least 2 of a random variable is a lower bound for its smooth entropy. On the other ha...

Maximum Rényi Entropy Rate

Two maximization problems of Rényi entropy rate are investigated: the maximization over all stochastic processes whose marginals satisfy a linear constraint, and the Burg-like maximization over all stochastic processes whose autocovariance function begins with some given values. The solutions are related to the solutions to the analogous maximization problems of Shannon entropy rate.