Abstract
This work introduces channel-supermodular entropies, a subset of quasi-concave entropies. Channel-supermodularity is a property shared by some of the most commonly used entropies in the literature, including Arimoto–Rényi conditional entropies (which include Shannon and min-entropy as special cases), k-tries entropies, and guessing entropy. Based on channel-supermodularity, new preorders for channels that strictly include degradedness and inclusion (or Shannon ordering) are defined, and these preorders are shown to provide a sufficient condition for the more-capable and capacity ordering, not only for Shannon entropy but also regarding analogous concepts for other entropy measures. The theory developed is then applied in the context of query anonymization. We introduce a greedy algorithm based on channel-supermodularity for query anonymization and prove its optimality, in terms of information leakage, for all symmetric channel-supermodular entropies.
Highlights
The idea of preorders over channels goes back a long way in the history of information theory
In [1], Shannon introduced the “inclusion” preorder to compare the capacities of discrete memoryless channels. Several authors, such as El Gamal [2], Korner and Marton [3], and many more, made further significant contributions to the study of channel preorders. Such preorders are of practical importance in information theory
The less noisy ordering appears recently in quantitative information flow (QIF) literature, especially the H∞ -less noisy ordering, in the study of Dalenius leakage by Bordenabe and Smith [22]. This last work is closely related to the classical implications of the work by Buscemi [23], which is mainly focused on the H∞ -less noisy ordering in quantum information theory
Summary
The idea of preorders over channels goes back a long way in the history of information theory. In [1], Shannon introduced the “inclusion” preorder to compare the capacities of discrete memoryless channels Several authors, such as El Gamal [2], Korner and Marton [3], and many more, made further significant contributions to the study of channel preorders. Whenever K1 ≥shs K2 , the capacity of K1 is higher than that of K2 Several such new channel ordering results are proven in this paper based on channel-supermodularity. The starting point will be the channel design problem, which is the problem of designing a channel that leaks the least amount of confidential information while respecting a set of operational constraints This kind of problem arises in many security systems, such as authentication systems [9], operating systems functions [10], scheduling protocols [11], bucketing schemes in cryptography [12], anonymity (Section 6.2), and so on. We provide optimal solutions for these two problems based on channel-supermodularity
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
