Broadcast anti-jamming systems

In a traditional anti-jamming system a transmitter who wants to send a signal to a single sender spreads the signal power over a wide frequency spectrum with the aim of stopping a jammer from blocking the transmission. In this paper we consider the case that there are multiple receivers and the sender wants to broadcast a message to all receivers such that colluding groups of receivers cannot jam the reception of any other receiver. We propose efficient coding methods that achieve this goal and link this problem to well-known problems in combinatorics. We also link a generalisation of this problem to the key distribution pattern problem studied in combinatorial cryptography.