2017/12/21 by Ferdinando Cicalese, Cicalese, Ferdinando, Luisa Gargano +3 · 1 citation
Decision Sciences · Engineering · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Information Theory (cs.IT) #Multi-Criteria Decision Making #Risk and Portfolio Optimization #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1712.07906
openalex publication_date 2017/12/21 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
It is well known that the entropy H(X) of a discrete random variable X is\nalways greater than or equal to the entropy H(f(X)) of a function f of X,\nwith equality if and only if f is one-to-one. In this paper, we give tight\nbounds on H(f(X)) when the function f is not one-to-one, and we illustrate\na few scenarios where this matters. As an intermediate step towards our main\nresult, we derive a lower bound on the entropy of a probability distribution,\nwhen only a bound on the ratio between the maximal and minimal probabilities is\nknown. The lower bound improves on previous results in the literature, and it\ncould find applications outside the present scenario.\n