Abstract
Shannon’s source entropy formula is not appropriate to measure the uncertainty of non-stationary processes. In this paper, we propose a new entropy measure for non-stationary processes, which is greater than or equal to Shannon’s source entropy. The maximum entropy of the non-stationary process has been considered, and it can be used as a design guideline in cryptography.
Highlights
Information science considers an information process, uses the probability measure for random states and Shannon’s entropy as the uncertainty function of these states [1,2,3]
For a non-stationary process, if its parametric is a Entropy 2014, 16 stationary random variable, this kind of non-stationary process can be considered as a piecewise stationary process, and many papers use the following source entropy formula, proposed by Shannon, to measure the uncertainty [5,6,7,8,9]: H pi H i Pi pi ( j ) log pi ( j )
The rest of this paper is organized as follows: Section 2 shows that Shannon’s source entropy formula is not appropriate to measure the uncertainty of non-stationary processes
Summary
Information science considers an information process, uses the probability measure for random states and Shannon’s entropy as the uncertainty function of these states [1,2,3]. The entropy of non-stationary process is still not fully understood, except for some specific types of non-stationary process [4] that use the following entropy formula to measure the uncertainty:. This kind of non-stationary process requires a known probability function, and the probability function is deterministically varied. For a non-stationary process, if its parametric is a Entropy 2014, 16 stationary random variable, this kind of non-stationary process can be considered as a piecewise stationary process, and many papers use the following source entropy formula, proposed by Shannon, to measure the uncertainty [5,6,7,8,9]:.
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