Low Complexity Estimation Method of Rényi Entropy for Ergodic Sources †

Since the entropy is a popular randomness measure, there are many studies for the estimation of entropies for given random samples. In this paper, we propose an estimation method of the Rényi entropy of order [Formula: see text]. Since the Rényi entropy of order [Formula: see text] is a generalized entropy measure including the Shannon entropy as a special case, the proposed estimation method for Rényi entropy can detect any significant deviation of an ergodic stationary random source’s output. It is shown that the expected test value of the proposed scheme is equivalent to the Rényi entropy of order [Formula: see text]. After deriving a general representation of parameters of the proposed estimator, we discuss on the particular orders of Rényi entropy such as [Formula: see text] , [Formula: see text] , and [Formula: see text]. Because the Rényi entropy of order 2 is the most popular one, we present an iterative estimation method for the application with stringent resource restrictions.