How much coordination is needed for robust broadcasting over arbitrarily varying bidirectional broadcast channels

The paradigm shift from an exclusive to a shared use of frequencies comes along with the necessity of new concepts since interference will be ubiquitous. Resulting channels may vary in an arbitrary and unknown manner from channel use to channel use. This is the arbitrarily varying channel (AVC). Here, coordination resources such as common randomness or correlated sources have been shown to be important for reliable communication; especially for symmetrizable AVCs where deterministic approaches with pre-specified encoder and decoder fail. Here, we study the arbitrarily varying bidirectional broadcast channel (AVBBC), which is motivated by the broadcast phase of bidirectional relaying. Here, a relay establishes a bidirectional communication between two nodes while sharing resources with other coexisting networks. The question is asked how much coordination is needed for reliable communication. The capacity region of the AVBBC is established and it is shown that for a transmission of block length n no more than O(log n) outputs of the correlated source suffices to achieve the same as with the much stronger resource of common randomness. Such weak coordination resources of correlated sources can easily be realized by broadcasting a signal (e.g. via satellite) observed by all users only as correlated versions.