Disjoint difference families and their applications

Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of difference families and the variations in priorities in constructions. We propose a definition of disjoint difference families that encompasses these variations and allows a comparison of the similarities and disparities. We then focus on two constructions of disjoint difference families arising from frequency hopping sequences and showed that they are in fact the same. We conclude with a discussion of the notion of equivalence for frequency hopping sequences and for disjoint difference families

Frequency Hopping against a Powerful Adversary

Abstract. Frequency hopping is a central method in wireless communication, offering improved resistance to adversarial interference and interception attempts, and easy non-coordinated control in dynamic environments. In this paper, we introduce a new model that supports a rigorous study of frequency hopping in adversarial settings. We then propose new frequency hopping protocols that allow a sender-receiver pair to essentially use the full communication capacity, despite a powerful adversary that can scan and jam a significant amount of the ongoing transmissions.