Entropy Bounds for Discrete Random Variables via Maximal Coupling

Monotonicity of Entropy and Fisher Information: A Quick Proof via Maximal Correlation

A simple proof is given for the monotonicity of entropy and Fisher information associated to sums of i.i.d. random variables. The proof relies on a characterization of maximal correlation for partial sums due to Dembo, Kagan and Shepp.

Maximal Repetition and Zero Entropy Rate

Maximal repetition of a string is the maximal length of a repeated substring. This paper investigates maximal repetition of strings drawn from stochastic processes. Strengthening previous results, two new bounds for the almost sure growth rate of maximal repetition are identified: an upper bound in terms of conditional Rényi entropy of order $γ>1$ given a sufficiently long past and a lower bound in terms of unconditional Shannon entropy ($γ=1$). Both the upper and the lower bound can be proved using an inequality for the distribution of recurrence time. We also supply an alternative proof of t…

Nonsymmetric entropy I: basic concepts and results

A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally from maximal nonsymmetric entropy principle.

使用 Mrs. Gerber 引理针对最小熵的掩码实现的最大泄漏

Maximal Leakage of Masked Implementations Using Mrs. Gerber's Lemma for Min-Entropy

本文针对任意阶掩码实现，利用最大泄漏和条件最小熵，通过主化不等式推广了有限阿贝尔群中的 Mrs. Gerber 引理，为侧信道攻击成功概率提供上界。

On entropy for mixtures of discrete and continuous variables

Let $X$ be a discrete random variable with support $S$ and $f : S \to S^\prime$ be a bijection. Then it is well-known that the entropy of $X$ is the same as the entropy of $f(X)$. This entropy preservation property has been well-utilized to establish non-trivial properties of discrete stochastic processes, e.g. queuing process \cite{prg03}. Entropy as well as entropy preservation is well-defined only in the context of purely discrete or continuous random variables. However for a mixture of discrete and continuous random variables, which arise in many interesting situations, the notions of entr…