An extension of the Ky Fan inequality

通过扩展Kraft不等式对Shannon下界进行改进与推广

Refinements and Generalizations of the Shannon Lower Bound via Extensions of the Kraft Inequality

本文通过扩展Kraft不等式，改进并推广了Shannon下界，应用于各种率失真编码场景，包括更精确的界限和个体序列下界。

A New Proof of Hopf's Inequality Using a Complex Extension of the Hilbert Metric

It is well known from the Perron-Frobenius theory that the spectral gap of a positive square matrix is positive. In this paper, we give a more quantitative characterization of the spectral gap. More specifically, using a complex extension of the Hilbert metric, we show that the so-called spectral ratio of a positive square matrix is upper bounded by its Birkhoff contraction coefficient, which in turn yields a lower bound on its spectral gap.